Growth-dependent tree mortality: ecological

Diss. ETH No. 15145

Growth-dependent tree mortality: ecological processes and modeling approaches based on tree-ring data

A dissertation submitted to the Swiss Federal Institute of Technology Zurich for the degree of Doctor of Sciences

presented by Christof J. Bigler Dipl. Natw. ETH born March 26, 1972 citizen of Worb (BE)

accepted on the recommendation of Prof. Dr. H. Bugmann, examiner Prof. Dr. F. H. Schweingruber, co-examiner Prof. Dr. B. S. Pedersen, co-examiner

2003

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Table of contents

Preface …………………………………………………………………………...…… iii Summary ………………………………………………………………………...……

1

Zusammenfassung ……………………………………………………………..…….

4

General introduction …………………………………………………………..…….

7

Chapter I

Growth-dependent tree mortality models based on tree rings …..…….

Chapter II

Predicting the time of tree death using dendrochronological data ……. 45

Chapter III

Assessing the performance of theoretical and empirical tree mortality models using tree-ring series …………………………..

69

Drought as an inciting mortality factor in Scots pine stands of the Valais, Switzerland ………………………………………….…

91

Chapter IV

19

Synthesis ………………………………………………………………………….…. 121 Acknowledgments …………………………………………………………………... 129 Curriculum vitæ ……………………………………………………………...……... 131

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Preface As far as I can remember, my first experiments with trees date from my childhood. The seedling experiments at this time were – in the statistical sense – highly uncontrolled and dealt mainly with beech (Fagus silvatica L.), oak (Quercus sp.), and Norway spruce (Picea abies (L.) Karst.). Much later on, I improved my scientific skills considerably, and my interests focused largely on tree growth. During my diploma thesis, I investigated regeneration processes of Mountain pine (Pinus montana Mill.) in the Swiss National Park, followed by studies on forest succession. But it was only with the beginning of my Ph.D. when I realized that a more detailed knowledge of tree mortality provides an improved understanding of tree growth and regeneration processes. Many issues on forest dynamics suddenly appeared in a different light when regarded from the perspective of a dying tree. There is a question that kept me busy during the last three years: Is there eternal life for trees? I must admit that answering this question with reasonable certainty is over my head, in spite of my detailed studies on tree mortality. Although one could discuss this issue at the purely esoteric level, I would prefer a more scientific answer. According to my experiences over the last few years and considering the various mortality factors, I would finally dare to say that trees have an infinitesimally small probability to live eternally. However, due to a lack of time, I couldn’t follow up this question any more. Therefore, I leave the final answer to the reader. But I truly hope that you may gain new insights into other fascinating aspects of tree mortality processes when reading the present thesis:

“Growth-dependent tree mortality: ecological processes and modeling approaches based on tree-ring data”

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Summary

1

Summary Tree mortality constitutes a major element of forest dynamics. However, the ecological processes of individual tree death are poorly understood, since they often result from a complex of multiple biotic and abiotic environmental factors that occur consecutively in time. In many growth-dependent tree mortality studies, recent growth patterns of tree rings are used as an indicator of mortality risk, which is often adopted in tree mortality models. Generally, empirical mortality models pursue a cross-sectional approach and aim at discriminating between dead and living trees at a particular time. Under a longitudinal approach, models are optimized to predict the time of individual tree death. The objectives of the present thesis are (i) to derive tree-ring based growth patterns that indicate impending tree death, (ii) to optimize and validate models for predicting the time of tree death based on these time-dependent growth patterns, and (iii) to relate growth patterns prior to death to biotic and abiotic stress factors. As a first step in this thesis, a cross-sectional approach was used to model tree mortality (chapter I). Different tree-ring based, recent growth patterns (growth level and growth trend variables) over varying time windows were derived that allowed to discriminate between dead and living Norway spruce (Picea abies (L.) Karst.) trees. For mature stands in the Swiss Alps, logistic regression models were developed including different combinations of growth variables as predictors. The consideration of growth trends significantly improved the performance of the mortality models compared with models that were based on “classical” growth level variables only. A low growth level in combination with a negative growth trend drastically increased the relative mortality risk of a tree. The effect of competition explained more than 50% of the recent growth variability of currently living trees, while only 25% of the variability of growth prior to death could be attributed to competition. The verification of the mortality model showed that nearly 80% of the dead and living Norway spruce trees at one site were correctly classified as being dead or alive. The predictive power of the logistic model was validated successfully at two climatically and geologically different sites, where 71% and 81% of the dead and living trees were correctly classified, which supports the generality of the mortality model for Norway spruce in subalpine forests of the Alps. Based upon these results, the approach was expanded to a longitudinal consideration. Chapter II deals with predicting the timing of individual tree death based on timedependent growth patterns of tree rings. Entire time series of the binary response (dead or alive) and growth patterns (growth levels, growth trends, relative growth rate) as predictors were used to fit logistic regression models. Twelve different combinations of growth patterns from dead and living Norway spruce trees from one area in the subalpine zone of Switzerland were used to calibrate mortality models. The autocorrelation of the response variable was taken into account by correcting the biased variances with an infinitesimal

2

Summary

jackknife variance estimator. Validation methods based on a multiple performance criterion (two criteria for classification accuracy and three criteria for prediction errors) were developed to test the mortality models. The six models with the highest overall performance correctly classified 71 – 78% of all dead trees and 73 – 75% of all living trees. For these six models, 44 – 56% of all dead trees were predicted to die within 0 – 15 years prior to the actual year of death. A maximum of 1.7% of all dead trees and 5% of all living trees were predicted to die more than 60 years prior to the actual year of death or prior to the last measured year, respectively. Models including the relative growth rate and a growth trend as predictors were most reliable with respect to inference and prediction. The reliability of the mortality models was successfully tested by applying them to two independent P. abies data sets from different areas. These promising results were used to compare the performance of a range of previously derived, empirical mortality functions (EMFs) with theoretical mortality functions (TMFs) that are commonly implemented in gap models (chapter III). Gap models, a subset of forest succession models that simulate establishment, growth, and mortality of trees are used to investigate successional dynamics of forests under current and changed climate. The mortality models were applied to tree-ring data of dead and living Norway spruce trees from three different study sites in Switzerland. Three of the four EMFs performed substantially better at all three sites, while three of the four TMFs performed worse than the remaining mortality models. The presence of persistent suppression periods in the growth curves of some trees was not adequately reflected by the models, which led particularly for the TMFs to large prediction errors. We conclude that the TMFs – unless the parameters are optimized for individual species – are not appropriate models to predict the time of tree death, in spite of their widespread use. A substantial change in the simulated forest succession is to be expected if the currently implemented TMFs in gap models are replaced by species-specific EMFs. As the final step of this thesis, some of the methods that were developed in chapters I and II were applied to reveal the ecological causes that have led to the high mortality rates of Scots pine (Pinus silvestris L.) in the Valais (chapter IV). Scots pine decline has been observed during the 20th century over a large area in the Valais, a central alpine dry valley in Switzerland, and in other dry valleys of the European Alps. At first, the impact of competition on growth rates of dead and living Scots pine trees was quantified. At two investigated sites, competition had a highly significant effect on recent growth rates of living trees. Growth rates of dying trees were less affected by neighboring trees, and additional environmental factors must be taken into account to explain low growth prior to death. Changed management activities over the last 50 years must have resulted in increasing stand densities, which affect the shade-intolerant Scots pine more than other, currently invading tree species. The focus of the study was on the verification of drought as an inciting factor of Scots pine decline. Standardized tree-ring series from eleven study sites were moderately associated with drought indices. Single, extreme drought years had generally a short-term, reversible effect on tree growth, while multi-year drought initiated prolonged growth decreases that increased a tree’s risk to die at long-term. Trees normally reacted

Summary

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with a lagged mortality response that occurred several years or decades after a drought period, probably as a result of increasing competition in combination with drought-insect interactions as final lethal factors.

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Zusammenfassung

Zusammenfassung Baummortalität ist ein wichtiges Element der Walddynamik. Die ökologischen Prozesse des Absterbens von Einzelbäumen werden jedoch nur ungenügend verstanden, da diese häufig aus dem Zusammenwirken multipler biotischer und abiotischer Umweltfaktoren resultieren, welche zeitlich aufeinander folgen. In vielen wachstumsabhängigen Baummortalitätsstudien werden aktuelle Wachstumsmuster von Jahrringen als Indikator für das Mortalitätsrisiko benutzt, was häufig in entsprechende Modelle übernommen wird. Im allgemeinen beabsichtigen empirische Mortalitätsmodelle, für einen bestimmten Zeitpunkt zwischen toten und lebenden Bäumen zu unterscheiden. In einem anderen Ansatz wird versucht, Modelle für die Voraussage des individuen-spezifischen Absterbezeitpunktes zu optimieren. Die Ziele der vorliegendenen Dissertation sind (i) jahrring-basierte Wachstumsmuster herzuleiten, welche auf den bevorstehenden Baumtod hinweisen, (ii) Modelle, welche auf diesen zeitabhängigen Wachstumsmustern basieren, für die Voraussage des Absterbezeitpunktes zu optimieren und zu validieren, und (iii) Wachstumsmuster vor dem Tod mit biotischen und abiotischen Stressfaktoren in Verbindung zu bringen. In der vorliegenden Dissertation wurde in einem ersten Schritt die Baummortalität für einen bestimmten Zeitpunkt modelliert (Kapitel I). Über variierende Zeitfenster wurden verschiedene jahrring-basierte, aktuelle Wachstumsmuster (Wachstumslevel- und Wachstumstrend-Variablen) hergeleitet, welche erlaubten, zwischen toten und lebenden Fichten (Picea abies (L.) Karst.) zu unterscheiden. Für reife Waldbestände in den Schweizer Alpen wurden logistische Regressionsmodelle entwickelt, welche verschiedene Kombinationen von Wachstumsvariablen als Prädiktoren enthielten. Die Berücksichtigung von Wachstumstrends erhöhte die Leistung der Mortalitätsmodelle signifikant, verglichen mit Modellen, welche nur auf “klassischen” Wachstumslevel-Variablen basierten. Ein tiefer Wachstumslevel in Kombination mit einem negativen Wachstumstrend erhöhte das relative Mortalitätsrisiko eines Baumes drastisch. Der Effekt der Konkurrenz erklärte mehr als 50% der aktuellen Wachstumsvariabilität von momentan lebenden Bäumen, während nur 25% der Wachstumsvariabilität vor dem Tod auf Konkurrenz zurückgeführt werden konnte. In der Verifikation des Mortalitätsmodelles wurden fast 80% der toten und lebenden Fichten an einem Standort korrekt als tot oder lebend klassifiziert. Die Voraussagekraft des logistischen Modelles wurde erfolgreich an zwei klimatisch und geologisch unterschiedlichen Standorten validiert, wo 71% respektive 81% der toten und lebenden Bäume korrekt klassifiziert wurden, was die Allgemeingültigkeit des Mortalitätsmodelles für Fichten in subalpinen Wäldern der Alpen unterstützt. Basierend auf diesen Resultaten wurde der Ansatz ausgeweitet, um Baummortalität über einen Zeitraum zu modellieren. Kapitel II beschäftigt sich mit der zeitlichen Absterbevoraussage von Einzelbäumen, basierend auf zeitabhängigen Wachstumsmustern von Jahrringen. Vollständige Zeitreihen der binären Zielgrösse (tot oder lebend) und

Zusammenfassung

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Wachstumsmuster der Ausgangsgrössen (Wachstumslevel, Wachstumstrends, relative Wachstumsrate) wurden benutzt, um logistische Regressionsmodelle anzupassen. Zwölf verschiedene Kombinationen von Wachstumsmustern von toten und lebenden Fichten aus einem Gebiet in der subalpinen Zone der Schweiz wurden benutzt, um die Mortalitätsmodelle zu kalibrieren. Die Autokorrelation der Zielgrösse wurde berücksichtigt, indem die verzerrten Varianzen durch einen infinitesimalen Jackknife-Varianz-Schätzer korrigiert wurden. Es wurden Validierungsmethoden basierend auf einem multiplen Leistungskriterium (zwei Kriterien für Klassifikationsgenauigkeit und drei Kriterien für Voraussagefehler) entwickelt, um die Mortalitätsmodelle zu testen. Die sechs Modelle mit der höchsten Gesamtleistung klassifizierten 71 – 78% aller toten Bäume und 73 – 75% aller lebenden Bäume korrrekt. Bei diesen sechs Modellen wurden 44 – 56% aller toten Bäume innerhalb von 0 – 15 Jahren vor dem tatsächlichen Todesjahr als tot vorausgesagt. Für lediglich maximal 1.7% aller toten Bäume sowie 5% aller lebenden Bäume war die Absterbevoraussage mehr als 60 Jahre vor dem effektiven Todesjahr respektive vor dem letzten gemessenen Jahr. Modelle mit der relativen Wachstumsrate und dem Wachstumstrend als Ausgangsgrössen waren am zuverlässigsten bezüglich Inferenz und Voraussage. Die Zuverlässigkeit der Mortalitätsmodelle wurde anhand von zwei unabhängigen P. abies Datensätzen aus unterschiedlichen Gebieten erfolgreich getestet. Diese vielversprechenden Resultate wurden benutzt, um die Leistung einer Reihe empirischer Mortalitätsfunktionen (EMFs) mit theoretischen Mortalitätsfunktionen (TMFs) zu vergleichen, welche üblicherweise in Gapmodellen (engl. gap = Lücke) implementiert sind (Kapitel III). Gapmodelle sind Waldsukzessionsmodelle, welche Etablierung, Wachstum und Mortalität von Bäumen simulieren. Sie werden benutzt, um die Sukzessionsdynamik von Wäldern unter dem aktuellen und einem veränderten Klima zu untersuchen. Die Mortalitätsmodelle wurden auf Jahrringdaten von toten und lebenden Bäumen aus drei verschiedenen Studiengebieten in der Schweiz angewendet. Drei der vier EMFs zeigten in allen Studiengebieten eine deutlich bessere Leistung, während drei von vier TMFs schlechtere Voraussagen als die verbleibenden Mortalitätsmodelle lieferten. Langanhaltende Unterdrückungsperioden in den Wachstumskurven einiger Bäume wurden durch die Modelle nicht angemessen widerspiegelt, was besonders bei den TMFs zu grossen Voraussagefehlern führte. Wir schliessen daraus, dass die häufig angewendeten TMFs – sofern die Parameter nicht für einzelne Arten optimiert werden – für zeitliche Absterbevoraussagen nicht geeignet sind. Falls die in den Gapmodellen implementierten TMFs durch artspezifische EMFs ersetzt werden, wird eine beträchtliche Änderung der simulierten Waldsukzession erwartet. Als letzter Schritt dieser Dissertation wurden einige der in Kapitel I und II entwickelten Methoden angewendet, um die ökologischen Gründe aufzudecken, welche zu den hohen Mortalitätsraten der Waldföhre (Pinus silvestris L.) im Wallis führten (Kapitel IV). Das Absterben der Waldföhre wird seit dem 20. Jahrhundert in einem grossen Gebiet des Wallis beobachtet, einem zentralalpinen Trockental in der Schweiz, sowie in anderen Trockentälern der Europäischen Alpen. Es wurde zuerst der Einfluss der Konkurrenz auf Wachstumsraten von toten und lebenden Waldföhren quantifiziert. An zwei untersuchten

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Zusammenfassung

Standorten hatte Konkurrenz einen hochsignifikanten Effekt auf die aktuellen Wachstumsraten von lebenden Bäumen. Die Wachstumsraten von absterbenden Bäumen wurden weniger stark durch Nachbarbäume beeinflusst; zusätzliche Umweltfaktoren müssen berücksichtigt werden, um das geringe Wachstum vor dem Tod zu erklären. Mit grosser Wahrscheinlichkeit haben geänderte Managementmassnahmen über die letzten 50 Jahre zu erhöhten Bestandesdichten geführt, welche die schattenintolerante Waldföhre mehr beeinflussen als andere, seit kurzem invadierende Baumarten. Der Fokus der Studie lag bei der Verifikation von Trockenheit als Faktor für das Absterben der Waldföhre. Standardisierte Jahrringreihen waren mittelgradig mit Trockenheitsindizes assoziiert. Einzelne, extreme Trockenjahre hatten im allgemeinen einen kurzfristigen, reversiblen Effekt auf das Baumwachstum, während mehrjährige Trockenperioden anhaltende Wachstumseinbrüche initiierten, welche das Absterberisiko der Bäume langfristig erhöhten. Die Bäume reagierten normalerweise mit einer verzögerten Mortalitätsreaktion, welche mehrere Jahre oder Jahrzehnte nach einer Trockenperiode erfolgte, wahrscheinlich als Resultat von erhöhter Konkurrenz in Kombination mit Trockenheits-Insekten-Interaktionen als finale, letale Faktoren.

General introduction

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General introduction Overview Forests are subject to a multitude of natural environmental influences, and they are increasingly affected by human-induced impacts, in particular land-use change and climate change (Watson et al. 2000, Houghton et al. 2001). On the global scale, forests play a major role in the biogeochemical cycle, which comprises carbon, nutrient, and water cycles (Waring and Running 1998), and they influence geophysical processes, such as the reflection of radiation. On the regional scale, forests provide water, food, timber, nonwood products, and they are an important landscape element and protect humans from natural hazards in mountainous regions. Understanding the individual elements of forest dynamics is a necessary prerequisite for spatio-temporal predictions of forest structure and composition on a global and regional scale.

Fig. 1. Dead Norway spruce tree in the karst area of Bödmerenwald, central Switzerland (picture: Christof Bigler).

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Besides regeneration and tree growth, tree mortality constitutes a major element of forest dynamics. The process of tree death can be considered at different levels and from different viewpoints. At the individual tree level, it reflects the inability of a tree to cope with adverse environmental conditions. Due to small-scale differences of site conditions and a variable genetic make-up, varying longevities of individual trees result within one species (Robichaud and Methven 1993, Larson 2001). At the species level, tree mortality is reflected in the varying average longevities of tree species that pursue different survival strategies (Coley et al. 1985, Loehle 1988, Lorimer et al. 2001). At the community level, mortality plays a major role in the succession process, since tree mortality creates gaps in the forest, which leads to the release of suppressed, smaller individuals and the establishment of new trees (Szwagrzyk and Szewczyk 2001). Therefore, gap formation has been a core subject of forest succession research (Clinton et al. 1993, Lertzman 1995, Beckage et al. 2000), and it has also been incorporated as a central element in many forest succession models (Shugart 1984, Bugmann 2001). In spite of the evident relevance of tree mortality for forest ecology and particularly for succession research, the ecological processes of individual tree death are not well understood (Franklin et al. 1987), which in turn is reflected in the poor parameterization of mortality algorithms in forest succession models (Hawkes 2000, Keane et al. 2001). However, given the implications of the potential effects of climatic change on forest dynamics, the topic of tree mortality has gained interest at the interface between process-oriented forest ecology research and ecological modeling. In the present thesis, I combine investigations on ecological processes with predictive modeling approaches to analyze mortality processes, which will result in applications that provide an improved foundation for understanding tree mortality. Tree mortality factor s From the ecological point of view, tree mortality can be described in terms of two different kinds of factors that contribute to tree death. Growth-dependent mortality factors affect tree vigor, sometimes for decades prior to death, while growth-independent factors directly lead to tree death, often without being detectable in the growth pattern of a tree. Growth-dependent and growth-independent mortality can be caused either by abiotic factors (e.g., fire, lightning strikes, flooding, avalanches, air pollution, wind storms, ice storms, volcanic eruptions, climatic extremes, or climatic change), or by biotic factors (e.g., senescence, competition, herbivory, or pathogens) (Franklin et al. 1987). On the one hand, episodic, growth-independent mortality factors often have devastating effects, killing most or all of the trees in a stand within some hours; examples are fires or wind storms (Harcombe 1987). On the other hand, the so-called ‘background mortality’ has a continuous character, which includes mainly growth-dependent factors such as competition, leading to annual mortality rates of up to a few percent.


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Over the past decades, it has been increasingly realized that tree mortality typically results from a complex of multiple biotic and abiotic factors that occur consecutively or simultaneously in time rather than from a single mortality factor (Innes 1993, Pedersen 1998a). This superimposition of various mortality triggering factors and the time lag between the occurrence of the different mortality factors and the mortality response itself complicates the investigation of cause-effect relationships. Decline d isease theor y The decline disease theory, as developed by Sinclair (1967), Houston (1981, 1984), and Manion (1981), provides a general conceptual model for understanding complex decline diseases. According to this theory, predisposing, inciting, and contributing mortality factors are lowering a tree’s vigor along time (Fig. 2). In this context, vigor refers to the extent to which a tree has been affected by environmental stress, and/or the tree’s potential for continued survival (Pedersen 1992).

Fig. 2. Schematic model of the decline disease theory (adapted from Pedersen 1998a). The upper gray curve represents a surviving tree, the lower gray curve represents a dying tree. Predisposing factors have – in the example shown – a stronger negative impact on the vigor of the dying tree. The inciting factor leads to a decrease in vigor of both trees, but due to the higher vigor, only the living tree recovers – without being affected by contributing factors. The dying tree is subsequently affected by contributing factors. Gradients from black to gray indicate persistent respectively decreasing effects of mortality factors.

Predisposing factors reduce a tree’s vigor over the long term; examples are constantly low soil moisture and nutrient availability on shallow soils (Sinclair 1967), a decrease of soil moisture and nutrients due to increasing competition (Kozlowski et al. 1991, Elliott and Swank 1994, Smith and Hinckley 1995), a lowered soil water table (Tainter et al. 1983,

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Bégin and Payette 1988), a shift in the climatic conditions (Innes 1998), or harmful air pollutants (Sutherland and Martin 1990, Innes 1992). Some trees react in a more sensitive manner to predisposing factors (as shown in Fig. 2), and the degree of this reaction is likely to be dependent on the genetic status of a tree (Kozlowski et al. 1991, Innes 1998). These long-term effective factors normally continue to act also when other stress factors, such as inciting or contributing factors occur. Inciting stress factors, such as drought (Condit et al. 1995, Orwig and Abrams 1997, Villalba and Veblen 1998, Ogle et al. 2000), insect defoliation (Veblen et al. 1991, Swetnam and Lynch 1993), frost (Liu and Muller 1993, Innes 1998), very high emissions of air pollutants (Kozlowski et al. 1991), or mechanical injury (Schweingruber 1996) may lead to a strongly decreased tree vigor. Trees that suffered persistent loss of vigor due to predisposing factors are particularly sensitive to inciting stress factors, and the latter generally occur several times during a tree’s life. Contributing factors, such as secondary insects (Mattson and Haack 1987, LeBlanc 1998), fungal diseases (Cherubini et al. 2002), or viruses that infest a stressed tree may further reduce its vigor to the point where the tree dies. Additional inciting factors are also suggested to act as contributing factors, which can lead to relatively rapid tree death. Therefore, the length of this final period prior to death may depend on the type, the persistence, and the intensity of the contributing factor. Tree ring s and growth patterns pr ior to death Tree rings have been used successfully as a proxy measure of tree vigor, as shown in many tree mortality studies (e.g., Buchman et al. 1983, Hamilton 1986, Pedersen 1998b). Radial growth increments (i.e., tree-ring widths) are the integrated response of a tree to a broad range of intrinsic factors (genetic structure and ageing), abiotic factors (mainly light, temperature, humidity, nutrient and soil moisture availability, but also wind, mechanical injury, air and soil pollution), and biotic factors (insect defoliation, browsing, fungi, competition, forest management) (Fritts 1976, Schweingruber 1996). Tree rings are also a sensitive indicator of tree vigor because diameter growth has a low priority in the allocation scheme of a tree (Waring and Pitman 1985). Lastly, one advantage over other measures of vigor, such as crown characteristics, growth efficiency, tree starch reserves, or cambial electrical resistance, is the possibility to reconstruct dendrochronological time series extending over hundreds of years. In many growth-dependent tree mortality studies, the growth patterns prior to death have been used as an indicator of mortality risk (Kozlowski et al. 1991). Generally, a period of low radial growth increments, which may be due to the effects of predisposing and inciting factors, was related to an increased mortality probability. Often, these growth patterns over a few years prior to death could be explained fairly well by a single biotic or abiotic stress factor, or by combinations of stress factors. However, these mortality studies might give us an overly optimistic impression of the predictability of the relationship between


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growth rates and mortality over the entire life span of a tree. It is well known that many trees can survive several short- or long-term periods of low growth during their life, which can be related e.g. to drought periods, or to the impact of competing neighbor trees (Canham 1985, Szwagrzyk and Szewczyk 2001). Thus, the question arises why some trees survive periods of low growth, while others die. A possible explanation might be that dying trees have previously been weakened to a larger extent by predisposing and inciting factors, and were ultimately killed by a contributing factor that did not affect the surviving trees (cf. Fig. 2). Predictive mode ling of tree death Due to the lack of a detailed mechanistic understanding of tree mortality processes, growth-dependent, individual-based tree mortality is commonly modeled using empirical, statistical models, which do not explicitly incorporate any physiological processes. The objective of these empirical models is to quantify the relationship between the response, i.e., tree status (dead or alive), and tree-specific explanatory variables (e.g., tree size, growth increments, or crown defoliation) using mathematical functions. Predictions are made in the form of a mortality probability (e.g., logistic regression) that is converted to a binary response (dead or alive) or based on a classification rule (e.g., classification and regression trees, or discriminant analysis) that assigns a tree to the group of dead or living trees. Most empirical tree mortality models aim at discriminating between dead and living trees at one given point in time based on the recent growth pattern. This approach represents a cross-sectional study, since predictions are made for each subject (i.e., each tree) at one point in time only. In contrast, longitudinal tree mortality studies consider the entire time series of tree status and the associated growth patterns, allowing simultaneously for the autocorrelation of the response (Diggle et al. 1994, Hand and Crowder 1996, Lindsey 1999). In longitudinal studies, the risk of tree death can be predicted along time when a threshold is applied to the annual mortality probabilities of each tree. Species-specific, empirical mortality functions have recently been developed as a useful tool to improve forest succession models, which include the mortality process as a part of the model (Hawkes 2000, Keane et al. 2001). However, many mortality formulations in these models still rely on simple algorithms that are based on theoretical assumptions only. In several case studies, the implementation of empirical mortality functions has been shown to result in a considerable change of the modeled succession (Pacala et al. 1996, Bugmann 2001, Wyckoff and Clark 2002). Still, many empirical and virtually all theoretical mortality functions that were intended to predict the time of tree death have not been tested rigorously, e.g., against independent, empirical data (Loehle and LeBlanc 1996), although appropriate validation procedures would be crucial to assess the performance of mortality functions (Hawkes 2000).

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App licati ons and significance To better understand tree mortality processes, we need to detect the environmental stress factors that affect tree growth and vigor at a particular site. Growth patterns prior to death can be related to mortality factors, and allow us to define and develop mortality models. The resulting tree mortality models in turn provide an improved understanding of tree mortality processes, which should be highly significant for several applied research questions: (i)

The differences in growth patterns between dying and surviving trees, as revealed by the significance of the explanatory growth variables in mortality models, can be related to various biotic and abiotic stress factors that influence a tree prior to death. When these stress factors are considered e.g. in the context of the decline disease theory, it may become possible to identify cause-effect relationships.

(ii)

The capability of predicting the timing of individual tree death is useful in forest ecology and management. For example, tree vigor and the resulting forest dynamics can be assessed more realistically based on reliable mortality predictions.

(iii)

The reliability of projections from forest succession models can be increased when species-specific, empirically derived mortality functions are employed that have been validated with empirical data. As a consequence, conclusions on the impacts of a changing climate on forest structure and composition may differ from earlier assessments.

(iv)

Time series of mortality probabilities for individual trees can be used to reconstruct population-based mortality risks. This method allows to assess the impact of past stress factors, such as drought periods, on the risk of tree mortality.

Main objectives & research questions The main objectives of this thesis are threefold: 1.

to derive tree-ring based growth patterns that indicate impending tree death,

2.

to optimize and validate models for predicting the time of tree death based on growth patterns, and

3.

to relate growth patterns prior to death to stress factors (e.g., competition, drought, or pathogens).


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Chapters I to IV of this thesis deal with the following main questions: (i)

What combinations of growth patterns should be considered to optimize the discrimination between dead and living trees (chapter I)?

(ii)

Which statistical methods can be used to predict the timing of tree death based on time-dependent growth patterns (chapter II)?

(iii)

How can the mortality models resulting from questions (i) and (ii) be validated (chapters I and II)?

(iv)

How well do theoretical mortality functions that have been used to predict the time of tree death compare to the performance of empirical mortality functions (chapter III)?

(v)

What are the biotic and abiotic factors that likely affect tree mortality in the stands that were investigated as case studies (chapters I and IV)?

Growth-dependent tree mortality models (chapter I) In growth-dependent, individual-based tree mortality models that adopt a cross-sectional approach, a range of explanatory variables has been used in earlier studies to discriminate between dead and living trees. These variables can be classified as size-related variables, growth-related variables, crown-related variables, ratios of crown- and growth-related variables, and other variables, such as age, competition, or social position. Growth patterns derived from tree rings proved to be useful for addressing mortality issues, since the entire development of a tree can be traced back. In earlier studies, periods of low growth rates were often found to be associated with increased mortality risk. However, slow but stationary growth does not necessarily imply a high risk of tree mortality. Rather, longterm reduced tree growth may be interpreted as an adaptation to decreasing resources, such as light, water, or nutrients. Therefore, besides growth levels (i.e., growth rates), growth trends (i.e., changes of growth rates; see LeBlanc et al. 1992) are evaluated in this chapter as a growth pattern to provide insights into growth-mortality relationships. In the present study, growth-dependent tree mortality models are developed for Norway spruce (Picea abies (L.) Karst.) for one subalpine site in the Swiss Alps using logistic regression analysis. Then, the models are validated against two independent data sets from subalpine forests that differ both climatically and geologically. Finally, the impact of competition as a long-term predisposing mortality factor is quantified with respect to recent growth of living trees and growth prior to death of dead trees, respectively.

14


Predicting the time of tree death (chapter II) The prediction of tree death along time requires a longitudinal approach. Here, growth patterns over entire tree-ring series are considered for calibrating the models, which is a distinct difference to the cross-sectional approach that relies on growth patterns at one time point, as exemplified in chapter I. Notably, the autocorrelation of the longitudinal data does not affect the estimates of the coefficients of the logistic mortality models; however, the associated variances may be biased (McCullagh and Nelder 1989, Collett 1991). In chapter II, mortality models for Norway spruce are developed using logistic regression, based on combinations of three types of growth patterns (growth levels, growth trends, and relative growth rate). The bias of the variances is corrected by applying the infinitesimal jackknife variance estimator (Lumley and Heagerty 1999), a robust variance estimator. The resulting probability curves of survival in combination with a threshold are used to determine the time of individual tree death. Model performance is verified using multiple performance criteria, including two classification accuracy criteria and three prediction error criteria. Validation is performed by applying the mortality models that were fitted using one data set to two independent data sets.

Assessing the performance of theoretical and empirical tree mortality models (chapter III) The impacts of various anthropogenic influences on long-term forest dynamics, including changing climatic conditions, have often been assessed using gap models, a subset of forest succession models that simulate establishment, growth, and mortality of trees (Shugart 1984, Bugmann 2001). Two considerable shortcomings of gap models are the poor parameterization of the mortality algorithms, which are largely based on theoretical assumptions, and the lack of adequate testing of these formulations (Loehle and LeBlanc 1996, Hawkes 2000, Keane et al. 2001). The analyses in Chapter III, which can be viewed as an application of the methods developed in chapter II, deal with the comparison of theoretical and empirical tree mortality functions that aim to predict the time of tree death. Specifically, the performance of a range of (1) stochastic, theoretical mortality functions that have commonly been used in forest gap models, and (2) deterministic, empirical mortality functions (see chapter II) is compared. Classification accuracies and prediction errors are assessed after applying the mortality functions to measured tree-ring data of dead and living Norway spruce trees from three sites in subalpine forests of Switzerland.


15

Drought as an inciting mortality factor (chapter IV) Since the beginning of the 20th century, high mortality rates of Scots pine (Pinus silvestris L.) have been observed in the Rhône Valley (Valais, Switzerland), a dry valley in the Central Alps. Earlier investigations to reveal the causes of these exceptionally high mortality rates mainly focused on fluorine emissions of aluminum smelters in the valley. However, more recent studies suggest drought to be a major factor in the complex of mortality triggering causes (Rigling and Cherubini 1999, Rigling et al. 2002). In chapter IV, the decline disease theory is applied to provide the framework for relating tree death of Scots pine to various environmental factors.

Fig. 3. Group of dead Scots pine trees in the Gliswald Gamsen, Valais, Switzerland (picture: Christof Bigler).

In this integrated study, the focus is on drought as a potential inciting factor for Scots pine decline in the Valais. For 11 sites, the relationship between two different drought indices and standardized tree-ring indices is assessed. The method to predict the time of tree death that was developed in chapter II is used to estimate the temporal distribution of tree mortality risk, which in turn is related to single and multiple drought years. For three sites, the

16


impact of drought on the mean growth of living trees and on tree growth prior to death is reconstructed. At two sites, the effect of competition on recent growth of living trees and on tree growth prior to death is assessed as a predisposing mortality factor. Finally, the impact of pathogens as contributing tree mortality factor is discussed based on observations of insect occurrences at these three sites.

References Beckage, B., J. S. Clark, B. D. Clinton, and B. L. Haines. 2000. A long-term study of tree seedling recruitment in southern Appalachian forests: the effects of canopy gaps and shrub understories. Canadian Journal of Forest Research 30:1617-1631. Bégin, Y., and S. Payette. 1988. Dendroecological evidence of lake-level changes during the last three centuries in subarctic Québec. Quaternary Research 30:210-220. Buchman, R. G., S. P. Pederson, and N. R. Walters. 1983. A tree survival model with applications to species of the Great Lakes region. Canadian Journal of Forest Research 13:601-608. Bugmann, H. 2001. A review of forest gap models. Climatic Change 51:259-305. Canham, C. D. 1985. Suppression and release during canopy recruitment in Acer saccharum. Bulletin of the Torrey Botanical Club 112:134-145. Cherubini, P., G. Fontana, D. Rigling, M. Dobbertin, P. Brang, and J. L. Innes. 2002. Tree-life history prior to death: two fungal root pathogens affect tree-ring growth differently. Journal of Ecology 90:839850. Clinton, B. D., L. R. Boring, and W. T. Swank. 1993. Canopy gap characteristics and drought influences in oak forests of the Coweeta basin. Ecology 74:1551-1558. Coley, P. D., J. P. Bryant, and F. S. Chapin III. 1985. Resource availability and plant antiherbivore defense. Science (Washington, D. C.) 230:895-899. Collett, D. 1991. Modelling binary data. Chapman & Hall, London. Condit, R., S. P. Hubbell, and R. B. Foster. 1995. Mortality rates of 205 neotropical tree and shrub species and the impact of a severe drought. Ecological Monographs 65:419-439. Diggle, P. J., K.-Y. Liang, and S. L. Zeger. 1994. Analysis of longitudinal data. Oxford University Press, New York. Elliott, K. J., and W. T. Swank. 1994. Impacts of drought on tree mortality and growth in a mixed hardwood forest. Journal of Vegetation Science 5:229-236. Franklin, J. F., H. H. Shugart, and M. E. Harmon. 1987. Tree death as an ecological process. BioScience 37:550-556. Fritts, H. C. 1976. Tree rings and climate. Academic Press, London. Hamilton, D. A. 1986. A logistic model of mortality in thinned and unthinned mixed conifer stands of northern Idaho. Forest Science 32:989-1000. Hand, D., and M. Crowder. 1996. Practical longitudinal data analysis. Chapman & Hall, London etc. Harcombe, P. A. 1987. Tree life tables. BioScience 37:557-568. Hawkes, C. 2000. Woody plant mortality algorithms: description, problems and progress. Ecological Modelling 126:225-248. Houghton, J. T., Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, and D. Xiaosu, editors. 2001. Climate change 2001: the scientific basis. Cambridge University Press, Cambridge, UK.


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Houston, D. R. 1981. Stress triggered tree diseases - the diebacks and declines. USDA. For. Serv. NE-INF41-81, Washington, DC. Houston, D. R. 1984. Stress related to diseases. Arboricultural Journal 8:137-149. Innes, J. L. 1992. Forest decline. Progress in Physical Geography 16:1-64. Innes, J. L. 1993. Forest health: its assessment and status, Wallingford, Oxon, UK. Innes, J. L. 1998. The impact of climatic extremes on forests: an introduction. Pages 1-18 in M. Beniston and J. L. Innes, editors. The impacts of climate variability on forests. Springer, Berlin etc. Keane, R. E., M. Austin, C. Field, A. Huth, M. J. Lexer, D. Peters, A. Solomon, and P. Wyckoff. 2001. Tree mortality in gap models: application to climate change. Climatic Change 51:509-540. Kozlowski, T. T., P. J. Kramer, and S. G. Pallardy. 1991. The physiological ecology of woody plants. Academic Press, San Diego. Larson, D. W. 2001. The paradox of great longevity in a short-lived tree species. Experimental Gerontology 36:651-673. LeBlanc, D. C. 1998. Interactive effects of acidic deposition, drought, and insect attack on oak populations in the midwestern United States. Canadian Journal of Forest Research 28:1184-1197. LeBlanc, D. C., N. S. Nicholas, and S. M. Zedaker. 1992. Prevalence of individual-tree growth decline in red spruce populations of the southern Appalachian Mountains. Canadian Journal of Forest Research 22:905-914. Lertzman, K. P. 1995. Forest dynamics, differential mortality and variable recruitment probabilities. Journal of Vegetation Science 6:191-204. Lindsey, J. K. 1999. Models for repeated measurements. Oxford University Press, Oxford. Liu, Y., and R. N. Muller. 1993. Effect of drought and frost on radial growth of overstory and understory stems in a deciduous forest. American Midland Naturalist 129:19-25. Loehle, C. 1988. Tree life history strategies: the role of defenses. Canadian Journal of Forest Research 18:209-222. Loehle, C., and D. LeBlanc. 1996. Model-based assessments of climate change effects on forests: a critical review. Ecological Modelling 90:1-31. Lorimer, C. G., S. E. Dahir, and E. V. Nordheim. 2001. Tree mortality rates and longevity in mature and old-growth hemlock-hardwood forests. Journal of Ecology 89:960-971. Lumley, T., and P. Heagerty. 1999. Weighted empirical adaptive variance estimators for correlated data regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61:459-477. Manion, P. D. 1981. Tree disease concepts. Prentice-Hall, Englewood Cliffs, New Jersey, USA. Mattson, W. J., and R. A. Haack. 1987. The role of drought in outbreaks of plant-eating insects. BioScience 37:110-118. McCullagh, P., and J. A. Nelder. 1989. Generalized linear models, 2nd edition. Chapman and Hall, London. Ogle, K., T. G. Whitham, and N. S. Cobb. 2000. Tree-ring variation in pinyon predicts likelihood of death following severe drought. Ecology 81:3237-3243. Orwig, D. A., and M. D. Abrams. 1997. Variation in radial growth responses to drought among species, site, and canopy strata. Trees 11:474-484. Pacala, S. W., C. D. Canham, J. Saponara, J. A. Silander, R. K. Kobe, and E. Ribbens. 1996. Forest models defined by field measurements: II. Estimation, error analysis and dynamics. Ecological Monographs 66:1-43.

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Pedersen, B. S. 1992. Tree mortality in Midwestern oak-hickory forests: rates and processes. Ph.D. Dissertation. Oregon State University, Corvallis, Oregon, USA. Pedersen, B. S. 1998a. Modeling tree mortality in response to short- and long-term environmental stresses. Ecological Modelling 105:347-351. Pedersen, B. S. 1998b. The role of stress in the mortality of midwestern oaks as indicated by growth prior to death. Ecology 79:79-93. Rigling, A., O. Bräker, G. Schneiter, and F. Schweingruber. 2002. Intra-annual tree-ring parameters indicating differences in drought stress of Pinus sylvestris forests within the Erico-Pinion in the Valais (Switzerland). Plant Ecology 163:105-121. Rigling, A., and P. Cherubini. 1999. Wieso sterben die Waldföhren im "Telwald" bei Visp? Eine Zusammenfassung bisheriger Studien und eine dendroökologische Untersuchung. Schweizerische Zeitschrift für Forstwesen 150:113-131. Robichaud, E., and I. R. Methven. 1993. The effect of site quality on the timing of stand breakup, tree longevity, and the maximum attainable height of black spruce. Canadian Journal of Forest Research 23:1514-1519. Schweingruber, F. H. 1996. Tree rings and environment: dendroecology. Verlag Paul Haupt, Bern. Shugart, H. H. 1984. A theory of forest dynamics. The ecological implications of forest succession models. Springer, New York. Sinclair, W. A. 1967. Decline of hardwoods: possible causes. Pages 17-32 in International Shade Tree Conference. Smith, W. K., and T. M. Hinckley, editors. 1995. Resource physiology of conifers: acquisition, allocation, and utilization. Academic Press, San Diego, California. Sutherland, E. K., and B. Martin. 1990. Growth response of Pseudotsuga menziesii to air pollution from copper smelting. Canadian Journal of Forest Research 20:1020-1030. Swetnam, T. W., and A. M. Lynch. 1993. Multicentury, regional-scale patterns of western spruce budworm outbreaks. Ecological Monographs 63:399-424. Szwagrzyk, J., and J. Szewczyk. 2001. Tree mortality and effects of releases from competition in an oldgrowth Fagus-Abies-Picea stand. Journal of Vegetation Science 12:621-626. Tainter, F. H., T. M. Williams, and J. B. Cody. 1983. Drought as a cause of oak decline and death on the South Carolina coast. Plant Disease 67:195-197. Veblen, T. T., K. S. Hadley, M. S. Reid, and A. J. Rebertus. 1991. Methods of detecting past spruce beetle outbreaks in Rocky Mountain subalpine forests. Canadian Journal of Forest Research 21:242-254. Villalba, R., and T. T. Veblen. 1998. Influences of large-scale climatic variability on episodic tree mortality in northern Patagonia. Ecology 79:2624-2640. Waring, R. H., and G. B. Pitman. 1985. Modifying lodgepole pine stands to change susceptibility to mountain pine beetle attack. Ecology 66:889-897. Waring, R. H., and S. W. Running. 1998. Forest ecosystems: analysis at multiple scales. Academic Press, San Diego, CA. Watson, R. T., I. R. Noble, B. Bolin, N. H. Ravindranath, D. J. Verardo, and D. J. Dokken, editors. 2000. Land use, land-use change, and forestry. Cambridge University Press, Cambridge. Wyckoff, P. H., and J. S. Clark. 2002. The relationship between growth and mortality for seven co-occuring tree species in the southern Appalachian Mountains. Journal of Ecology 90:604-615.

Chapter I

19

Chapter I Growth-dependent tree mortality models based on tree rings

Published as: Bigler, C., and H. Bugmann. 2003. Growth-dependent tree mortality models based on tree rings. Canadian Journal of Forest Research 33(2): 210-221. Mountain Forest Ecology, Department of Forest Sciences, Swiss Federal Institute of Technology (ETH), ETH-Zentrum, CH-8092 Zurich, Switzerland

Abstract – Mortality is a crucial element of population dynamics. However, tree mortality is not well understood, particularly at the individual level. The objectives of this study were to (i) determine growth patterns (growth levels and growth trends) over different time windows that can be used to discriminate between dead and living Norway spruce (Picea abies (L.) Karst.) trees, (ii) optimize the selection of growth variables in logistic mortality models, and (iii) assess the impact of competition on recent growth in linear regression models. The logistic mortality model we developed for mature stands classified an average of nearly 80% of the 119 trees from one site correctly as being dead or alive. While more than 50% of the variability of recent growth of living trees can be attributed to the influence of competition, this percentage was only 25% for standing dead trees. The predictive power of the logistic mortality model was validated successfully at two additional sites, where 29 of 41 (71%) and 34 of 42 (81%) trees were classified correctly, respectively. This supports the generality of the mortality model for Norway spruce in subalpine forests of the Alps. We conclude that growth trends in addition to the commonly used growth level significantly improves the prediction of growth-dependent tree mortality of Norway spruce. Key words Tree mortality; dendroecology; competition; growth patterns; growth trends; growth levels; Picea abies (Norway spruce); models; logistic regression; odds ratio

20

Growth-dependent tree mortality models

Introduction Tree mortality is a crucial element of population dynamics, and it is important for the maintenance of biological and structural diversity in forested ecosystems (Franklin et al. 1987, McComb and Lindenmayer 1999). A complex of biotic and abiotic factors, acting as mortality agents, lead to tree death over the short to long term (Manion 1981, Waring 1987). Often, these agents are effective only after a substantial time lag, which separates the mortality response from its underlying causes (Pedersen 1999). Also, very different mortality agents may be dominant during different developmental stages of trees (Franklin et al. 1987, Kozlowski et al. 1991). Usually, growth-independent mortality due to fire, windthrow, and severe epidemics is distinguished from growth-dependent mortality causes like senescence, competition, climate effects, and weak pathogens (Jenkins and Pallardy 1995, Pedersen 1998b). In this study, we do not attempt to reveal the entire range of causes leading to individual tree mortality, but we attempt to (i) predict the likelihood of tree death based on growthrelated variables, and (ii) determine the effect of competition on current growth as the influence of neighboring trees on mortality risk. Improved predictions of tree mortality allow us to understand and more accurately project forest development. This in turn may be extended to estimate the economic and habitat values of forests (Price 1989, Hunter 1999), or to assess the impact of environmental stresses and disturbances on forests using succession models (e.g., Kienast 1991, Bugmann 1997). However, mortality predictions in dynamic succession models such as gap models (Bugmann 2001, Shugart 1984) rely mainly on theoretical considerations and are not based on empirical data (Keane et al. 2001, Hawkes 2000). Recently, Wyckoff and Clark (2002) have demonstrated that the implementation of empirically derived mortality functions resulted in a considerable change of the predictions of a succession model. A variety of empirical approaches have been used for describing and modeling tree mortality at different scales. A common approach is followed in stand-based studies focusing on the relationship between stand density and mortality rates of different tree size or age classes (e.g., Glover and Hool 1979, West 1981, Buford and Hafley 1985, Hamilton 1986, 1990). A distinctly different approach is used in individual-based models, which tend to include characteristics such as tree growth rates, size, and competitive status (e.g., Dursky 1997, Zhang et al. 1997, Dobbertin and Biging 1998, Wyckoff and Clark 2000). In individual-based models, tree death is predicted based on a range of variables that can be classified roughly as (i) size-related variables (e.g., diameter at breast height or tree height; Buchman et al. 1983, Buford and Hafley 1985), (ii) growth-related variables (e.g., ring-widths or basal area increments; Buchman et al. 1983, Kobe 1996, Wyckoff and Clark 2000), (iii) crown-related variables (e.g., leaf area index or crown defoliation; Crow and Hicks 1990, Monserud and Sterba 1999, Dobbertin and Brang 2001), (iv) ratios of crown-related and growth-related variables (e.g., growth efficiency; Coyea and Margolis

Chapter I

21

1994), and (v) other variables such as age, competition, or social position (Keister 1972, Burgman et al. 1994). Tree ring data (ring widths or basal area increments) have proven to be useful for addressing mortality issues, since tree rings are integrators of biotic and abiotic influences that reflect the entire growth history of a tree (Fritts 1976, Waring and Pitman 1985, Kozlowski et al. 1991, Schweingruber 1996). Furthermore, tree rings have been shown to be an index of mortality risk (Wyckoff and Clark 2000). Long-term low growth rates are a commonly accepted trait of dying trees, as reflected in the low growth hypothesis (Manion 1981, Kozlowski et al. 1991, Pedersen 1998b). Competition is one of the major biotic factors that can have a long-term negative impact on growth rate (Peet and Christensen 1987, Biging and Dobbertin 1992, de Luis et al. 1998), and it integrates the effects of other factors such as relative water and nutrient availability. Long-term reduced stem growth may be interpreted as a tree’s response to decreasing resources, since under most circumstances stem growth has a lower priority in resource allocation compared to, for example, allocation to defenses (Waring and Pitman 1985). Changing resource supply can lead to growth trade-offs (Bloom et al. 1985, Loehle 1988), forcing a tree to invest in growth rather than in defense, or vice versa (Coley et al. 1985, Herms and Mattson 1992). Trees can be expected to follow either a survival strategy or a growth strategy (also see Loehle 1988), depending on their genetic background (Monserud and Sterba 1999), competitive position, and site conditions. Notably, slow but stationary growth does not necessarily imply a high risk of tree mortality. Higher growth at the expense of investment in defenses may ultimately increase a tree’s probability of dying. In mortality models that are based on diameter growth, the period under consideration is typically 1 – 5 years prior to death (e.g., Buchman et al. 1983, Hamilton 1986). However, recent theoretical and empirical findings have shown that the consideration of longer-term growth rates may be of high importance for many mortality issues (LeBlanc and Foster 1992, Foster and LeBlanc 1993, Jenkins and Pallardy 1995, Filion et al. 1998, LeBlanc 1998, Pedersen 1998b, He and Alfaro 2000, Ogle et al. 2000). Most previous studies have focused on average growth, and little effort has been devoted to investigating the relationship between changes of growth rates and tree mortality, i.e., the relevance of sustained increases or decreases of growth across time (Kaufmann 1996). Trees can adapt to the prevailing environmental conditions, and low growth alone may be an insufficient predictor of tree mortality. Increasing or decreasing growth rates, however, imply an improvement or, more importantly, a deterioration of the conditions as perceived by a tree. We surmise that a combination of growth level and growth trend variables could improve predictions of tree mortality. Such a combination can be interpreted as the interaction of tree adaptation, tree vitality, and changing environmental conditions. In the present article, we provide insight into growth-mortality relationships and the effect of competition on current growth. Data came from a study of Norway spruce (Picea abies (L.) Karst.) mortality at three sites in the European Alps. We generate different stem-

22


growth related variables, covering a variety of time windows, as predictors of mortality of P. abies. An ecologically motivated, systematic selection of combinations of these variables is used to derive logistic regression models. We evaluate the ecological significance of this approach and validate the resulting mortality model with respect to its predictive accuracy. Finally, we quantify the impact of competition on recent growth of living and dead trees.

Material & methods Tree species and stud y site s Our analysis focuses on Norway spruce (Picea abies), a very widespread, dominant tree species of the subalpine zone in the European Alps. Picea abies is a frost-resistant, shallow-rooting species with a broad ecological spectrum (Ellenberg 1996). Three study sites in subalpine forests were selected, located in climatically and geologically different regions of Switzerland (Davos, Bödmeren, and Scatlé) (Table 1). Only mature near-natural or primeval forests with P. abies as the dominant tree species were considered. All three sites are characterized by a similar mortality rate, which can likely be attributed to competition. For Bödmeren and Scatlé, insect outbreaks had resulted in small groups of dead trees, scattered throughout the forest. Details on competition within the samples of the three study sites are given in Table 2. Table 1. Site information of the study sites. Sites

Davos Dischma

Flüela

Bödmeren

Scatlé

Coordinates (N, E)

46°47’, 09°53’

46°49’, 09°52’

46°59’, 08°51’

46°47’, 09°03’

Altitude (m a.s.l.)

1600 – 2000

1700 – 2000

1500 – 1600

1500 – 1700

Exposition

SW

SW

W

ENE

Slope (%)

60

75

35

60

Geology

Silicate

Silicate

Limestone

Silicate

(gneiss)

(gneiss)

(karst)

(verrucano)

Annual rainfall (mm)

1075

1075

ª 2500

1440

Mean annual temperature (°C)

2.4

2.4

ª3–4

2.2

Distance to Dischma valley (km)

0

3

80

60

Note: Davos (Dischma and Flüela): Landolt et al. (1986), Krause (1986), Ellenberg (1996), Bebi (1999), climate station Schatzalp (1868 m a.s.l.); Bödmeren: Bettschart (1994), Hantke (1995), and Kälin and Scagnet (1997), rainfall and temperature estimated for 1400 – 1650 m a.s.l.; Scatlé: Hartl (1967), Hillgarter (1971), methods for climate data see Badeck et al. (2001).

Chapter I

23

The largest sample of trees was collected in two parallel valleys near Davos, the Dischma and Flüela valleys, located in eastern Switzerland (Table 1). These near-natural forests are dominated by P. abies, with small proportions of European larch (Larix decidua Mill.) and Swiss stone pine (Pinus cembra L.). The Davos area is characterized by a continental to suboceanic climate (Landolt et al. 1986). Because of the very similar conditions in these two valleys, the data from Dischma and Flüela were pooled to form the Davos data set. The two forests in Bödmeren and Scatlé resemble primeval forests, since they are unlikely to have experienced any management during the past few centuries. At the Bödmeren site in central Switzerland, mainly P. abies can be found, at some places together with small amounts of mountain pine (Pinus montana Mill.) or birch (Betula spp.) (Bettschart 1994). The suboceanic climate with high rainfall amounts (Table 1) weathered the limestone, leading to a typical karst landscape (Hantke 1995). However, owing to the high daily temperature amplitudes and the low water capacity of the soil, the site is clearly continental in character (Kälin and Scagnet 1997). The second primeval forest is located in Scatlé in eastern Switzerland, growing on the remains of a former landslide. It is composed almost exclusively of P. abies (Hartl 1967, Hillgarter 1971). Table 2. Competition indices (CIs) and their medians for the three study sites. Median CI n

CI1 = Â I(j)

Davos (n = 119)

Bödmeren (n = 41)

Scatlé (n = 42)

4.0

2.0

4.0

142.0

67.5

116.8

57.7

21.1

48.9

5.4

1.5

4.5

2.3

0.4

2.0

j=1 n

CI2 = Â DBH j j=1

† n

CI3 = Â j=1

† n

†

DBH j DIST ij 2

DBH j CI4 = Â 2 j=1 DBH i 2

n

CI5 = Â

†

†

j=1

2

DBH j DBHi DIST ij

Note: I(j) = indicator variable for competitor tree j (I(j) = 1 for tree j, I(j) = 0 for other trees); n, number of competitor trees; DBHi, DBH of subject tree i; DBHj, DBH of competitor tree j; DISTij, distance between subject tree i and competitor tree j. References: CI1, Stöckli (1996); CI2 and CI3, Lorimer (1983); CI4 and CI5, Daniels (1976).

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Field sam pling and laboratory analyses In summer 2000, pairs of standing dead and living P. abies trees were sampled that were similar with respect to diameter at breast height (DBH), competition, and microsite conditions. Only trees with a DBH greater than 10 cm were considered. Trees were not included if they had been noticeably affected by strong pathogens, avalanches, wind, fire or human influences. Dead and living trees of most of the pairs were found some meters away from each other; the maximum distance was 40 m. The following selection criteria for the pairs were applied: (i) their DBH must not differ by more than 30% (this difference was less than 15% for most pairs), (ii) both trees must be surrounded by a similar number of trees of comparable DBH, and (iii) both trees must grow on similar microsites (rockiness, trough, slope, aspect). This sampling strategy corresponds to a matched-pairs case-control study, which is widely used in epidemiology (Breslow and Day 1989, Woodward 1999). In Davos, 60 pairs of living and dead trees were examined, 23 pairs in Bödmeren, and 22 pairs in Scatlé, resulting in a total sample size of 210 trees. The Davos data set was used to fit and validate the models; the Bödmeren and Scatlé data sets were used exclusively to validate the models. From each tree, two cores at breast height (1.3 m) were taken with an increment borer. The DBH of each cored tree was measured, as well as the distance to and the DBH of neighboring trees larger than 10 cm DBH within a radius of 5 m. The latter data were used for calculating tree competition indices (see below). A frequency distribution of DBH for the three sites is shown in Fig. 1.

Fig. 1. Frequency distribution of diameter at breast height (DBH) of sampled dead and living trees at the sites Davos (n = 119), Bödmeren (n = 41), and Scatlé (n = 42).

Chapter I

25

The sampling strategy used in this study was feasible only because of the relatively good preservation of the dead trees. Some reliably crossdated standing dead trees had been dead for 30 to 40 years but were not greatly decayed. However, about 10% of the trees selected initially could not be cored at all because of advanced wood decay. Growth increments were measured with a Lintab 3 measuring system (F. Rinn S.A., Heidelberg, Germany) and the TSAP tree ring program (Rinn 1996). The last tree rings of dead trees were often close to the measurement limit, given by the minimal number of xylem cell rows. Four trees were excluded during the measuring process because of low wood quality of the cores (one tree from the Davos site, one tree from the Bödmeren site, and two trees from the Scatlé site). At the Bödmeren site, four dead trees with abrupt growth reductions were not considered in the analysis, since they were sampled 20 m away from a group of trees that had been killed by bark beetles some years ago. In the field, we could not find any distinct signs of bark beetles on the stems of the cored trees, but the laboratory analysis suggested that strong pathogen pressure was the main mortality factor for these trees. In order to obtain a consistent dendrochronological data base without any missing rings, single cores of dead and living trees were crossdated using the averaged time series of 6 – 12 well-growing, living trees as a reference at each site (Fritts 1976). The two time series of tree-ring widths from each tree were averaged. Death year determination was useful for interpreting the data and comparing competition-growth relationships between dead and living trees. The most recent tree ring of most of the cores was bounded by parts of the bark or by a smooth layer of cambial tissue, thus indicating that no tree rings had eroded. A frequency distribution of the year of tree death is shown in Fig. 2.

Fig. 2. Frequency distribution of year of death. Only reliably dated trees that died between 1967 and 1999 are shown (Davos data set, n = 33).

26


Ring widths were converted to basal area increments (BAI, cm2/year), assuming a circular outline of stem cross-sections (cf. Visser 1995). BAI is commonly assumed to be a more meaningful indicator of tree growth than ring width, since BAI can remain high despite an apparent decline in ring width (West 1980). Der ivation of g rowth- relate d vari ables A range of growth variables was derived from BAI, aimed at optimizing the predictive power of the mortality model. The resulting growth variables were classified as (i) growth level variables and (ii) growth trend variables. We define a growth level variable as the average of growth increments over a certain period of time. Growth level variables can be characterized as the ‘classical’ way to describe growth patterns of dead and living trees (e.g., Jenkins and Pallardy 1995, Pedersen 1998a). In tree mortality studies, growth level variables are commonly referred to as ‘recent growth’ (e.g., Wyckoff and Clark 2000). To derive a first set of growth level variables, we calculated the averages of BAI (cm2/year) over the tree’s last 3, 5, or 7 years (BAI3, BAI5, BAI7), with 1999 being the last year for the living trees. For the second set of growth level variables, the variables of the first group were transformed with the natural logarithm [log(BAI3), log(BAI5), log(BAI7)]. The log-transformed function was used to lower the weight given to very high values of BAI. We define a growth trend variable as the change of growth increments over a certain period of time. The motivation for this variable class resulted from two observations: (i) some trees died after a fast growth collapse, although growth level was still relatively high, and (ii) some trees were able to survive long periods of low, but stationary growth. The slopes of local linear regressions fitted over the last 5, 10, 15, …, 40 years of BAI (locreg5, …, locreg40) were used to characterize the growth trend, with BAI as the dependent variable. The fit of the regression lines was verified visually and was found to be satisfactory in most cases. Fitting of logi stic m ortali ty models The prediction of a binary response, such as the tree status ‘dead’ or ‘alive’ from continuous growth variables (independent variables), implies a logistic regression model (Cox and Snell 1989, Hosmer and Lemeshow 1989, McCullagh and Nelder 1989, Collett 1991, Hastie and Pregibon 1992). A distinct advantage of logistic regression models is that there are well-established procedures for model fitting and model testing (Collett 1991). The general expression for logistic regression is as follows: [1]

†

Pr(Y = 1 | X) =

e Xb Xb 1+ e

Chapter I

27

In our study, Pr(Y = 1|X) is the survival probability of an individual tree expressed as a function of a matrix X of independent variables; Y is the dependent variable (Y = 1 if the tree is alive, Y = 0 if the tree is dead) and b is a vector containing the regression coefficients. All analyses were performed using the ‘R’ software (Ihaka and Gentleman 1996). A series of models was fitted using the data from the Davos site only, with 59 dead trees and 60 living trees. The data from the other two sites (Table 1) were reserved for validation purposes. A two-stage, stepwise variable selection strategy was applied, and models were fitted by maximum log-likelihood estimation using the Akaike Information Criterion (AIC)1. The significance level of deviance differences served as the criterion for variable selection2. The reduction of deviance in a stepwise process can be assumed to be c2 distributed, even for ungrouped data (McCullagh and Nelder 1989). The starting point for each stepwise regression was the Null model, where only the intercept was included as an independent variable. In a first stage of analysis, the most significant variable in each of the three variable groups was determined using a stepwise selection process (Eq. 1). Thus, a total of 14 growth variables from the three groups were screened (three nontransformed growth level variables, three log-transformed growth level variables, and eight growth trend variables). DBH was not considered as a further independent variable, since pairs of dead and living trees with very similar DBH had been sampled. In a second stage, the best linear combination using the three variables selected at stage one was sought via another logistic regression model. The three selected variables were added stepwise to the Null model (Eq. 1). The resulting main model, which included significant variables only, was used for all further analyses. The simultaneous inclusion of a nontransformed and a log-transformed growth level variable was disallowed. Interpretation of the mortality m odel Since similar proportions of dead and living trees in each DBH class were sampled, the derived mortality models cannot be used to calculate the population level mortality risk, but only the relative mortality risk of an individual tree given the observed values of the

1

The AIC (Venables and Ripley 1999) is used to compare models with a different number of independent variables. The statistical computing software ‘R’ defines AIC = -2⋅(maximized log-likelihood) + 2p, where p is the number of estimated parameters. Generally, the model with the smallest AIC is selected.

2

The deviance D is calculated in the fitting process of generalized linear models (e.g., logistic regression models) and is derived from the maximized likelihood L, which is a measure of how likely a particular model is, given the observed data (Collett 1991): D = -2{log Lˆ - log Lˆ F } . It is a measure of the difference between a particular model of interest (likelihood L) and the full model (likelihood LF), which fits the data perfectly. The deviance difference is the difference between the deviances of two models. †

28


independent variables (Woodward 1999). This restriction has implications for both application and interpretation of the models. The application of our mortality model to a population sample is appropriate only when odds ratios, an approximation of the relative mortality risk between two trees, are used (Hosmer and Lemeshow 1989, Woodward 1999). The odds can be derived from Eq. 1 with odds = pˆ /(1- pˆ ) = e Xb where pˆ is the estimated survival probability Pr(Y = 1|X). The odds that a given tree r will die relative to the odds that another tree s will die can be expressed as the odds ratio k ˆ = expÈ Â bˆ ( x ri - x si)˘ y ÍÎi= 0 i ˙˚

[2]

†

†

where k is the number of independent variables, bˆ i is the estimated coefficient of variable i† in Eq. 1, and (xri – xsi) is the difference of variable i between tree r and tree s. If all variables except i are held constant in Eq. 2, a 95% confidence interval can be approximated ˆ by exp bˆ i ( x ri - x si) ± 1.96( x ri - x si)SEˆ (b† i) , where SE (b i) is the estimated standard error of

[

]

bi (Woodward 1999).

†

Val idation of the mor tality model † Prediction accuracy is a useful criterion for comparing logistic models of tree mortality (Avila and Burkhart 1992, Dursky 1997, Dobbertin and Brang 2001). Comparing the observed with the predicted state of each individual tree allows us to develop a semimechanistic understanding of mortality processes at the scale of the individual. This is a distinct advantage over population-based mortality models, where measured and predicted mortality rates can only be compared at the stand scale, e.g., with respect to DBH classes or some other aggregated variable. A goodness-of-fit evaluation of a logistic model requires that the variables be grouped, i.e., each independent variable has to be divided into intervals (Collett 1991). This was not possible in our case because of the relatively small size of the data sets. Therefore, goodness-of-fit could not be evaluated by applying a c2 test to the deviance. Instead, goodnessof-fit was tested via validation (Hosmer and Lemeshow 1989) and checks of model diagnostics (Collett 1991). Validation is especially important as an assessment tool when the fitted model is used to predict the behavior of independent subjects. Two validation methods were applied to determine the predictive accuracy of the model. Note that the validation methods to be described are appropriate only because the models were fitted and validated with similar proportions of dead and living trees. For both methods, a deterministic approach was used, where the threshold for the response in the logistic model was fixed at 0.5. Thus, a tree was predicted to be dead when Pr(Y = 1|X) ≤ 0.5 and to be alive when Pr(Y = 1|X) > 0.5. The two methods were as follows.

Chapter I

29

(1)

An internal validation was performed where only data from the Davos site were used. A model was fitted with a random sample containing 50% of the trees from Davos and was then applied to the remaining 50% of the data to predict the status (dead or alive) of these trees. This cross-validation with random sub-sampling, i.e., sampling of a fitting data set and validating the model with the remaining data, was done with R = 200 resamplings (Fielding and Bell 1997, Manly 1997, Chernick 1999).

(2)

An external validation was performed by fitting a model for the Davos site using the full data set and testing this model against the data sets from the Bödmeren and Scatlé sites (cf. Fielding and Bell 1997). This second validation method allowed us to assess the extent to which the model can be generalized to Norway spruce populations growing under different environmental conditions (cf. Table 1).

Rel ations hip be tween growth and competi tive s tatus We used a regression modeling approach to estimate the proportion of variability in recent tree growth that is attributable to competition. Distance-independent and distancedependent, size-related competition indices (CIs) were computed for all three sites (Table 2). Only the Davos site was used for relating recent tree growth to competitive status. To select the most significant CI, only living trees from the Davos site were considered. Two different procedures were applied in the process of model selection. First, a stepwise procedure with the AIC (Akaike Information Criterion) as the selection criterion was used, relating the five CIs from Table 2 linearly to log(BAI3): [3]

log(BAI3) = b0 + b1CI

In order to avoid heteroscedasticity, we used the log transform of BAI3 in the model. Second, a separate linear model (Eq. 3) was developed for each of the five CIs in Table 2. The adjusted R2 was used as criterion for model comparison (Zar 1999). The final variable selected was used to calculate a linear model for reliably dated dead trees only that had died after 1985.

Results Fitting a nd interpretation of the mortality m odel Many dead trees at the three study sites showed growth decreases prior to death that lasted up to several decades (Fig. 3). Notably, long periods of relatively low, but stationary growth did not necessarily imply an increased mortality probability (e.g., see the period from 1770 to 1820 of the living tree DAB203 in Fig. 4a). Rather, strongly negative growth

30


trends appear to imply a high mortality probability (e.g., see the dead tree DAB033 in Fig. 4b). In the first stage of the stepwise regression analysis for the Davos data, BAI3 and log(BAI3) best reflected the status of the trees within the groups of growth level variables (Table 3). Within the growth trend variables group, locreg25 had the highest significance and the lowest AIC (Table 3). In the second stage, the above three variables were included in a stepwise logistic regression. In the resulting main model, only the growth level variable log(BAI3) and the growth trend variable locreg25 were significant (Table 4). The internal validation procedure, where a model was fitted with 50% of the Davos data set and applied to the remaining 50% of the data set (described below in more detail for the main model), was used here additionally as a tool to verify the variable selection. Averaged misclassification rates for all combinations of one growth trend variable (locreg) with one log-transformed growth level variable [log(BAI)] are given in Table 5. These results confirmed the selection of the main model that was developed in the two-stage stepwise regression.

Fig. 3. Individual growth curves and medians of dead trees (n = 59) and living trees (n = 60) of the Davos data set.

Fig. 4. Comparisons of two sampled pairs of a living tree and a dead tree from the Davos site.

Chapter I

31

Most of the dead trees had very low BAI during the last three years, whereas the living trees were characterized by larger growth increments (Fig. 5a). The distribution of the growth trend is shifted towards positive or slightly negative values for the living trees, while most dead trees had negative growth trends over the last 25 years prior to death (Fig. 5b). A scatterplot of log(BAI3) versus locreg25 (Fig. 6) further illustrates the discriminatory power of the growth trend variable locreg25 for dead trees with intermediate growth level (-0.5 < log(BAI3) < 3), but a clearly negative growth trend (locreg25 < -0.2). Growth level as the only independent variable would fail to classify these trees correctly. Furthermore, trees exhibiting a very low growth level (log(BAI3) < 0) always showed stationary growth, with locreg25 close to zero. Table 3. Coefficients, p values, and AIC values of logistic regressions with one independent variable for the Davos data set (n = 119).

Coefficient

p >|z|

AIC

BAI3

0.224

4.76 ¥ 10-5 ***

137.0

BAI5

0.164

2.09 ¥ 10-4 ***

145.5

BAI7

0.134

4.30 ¥ 10-4 ***

149.9

log(BAI3)

0.962

1.51 ¥ 10-6 ***

136.0

log(BAI5)

0.851

7.32 ¥ 10-6 ***

142.2

log(BAI7)

0.793

2.11 ¥ 10-5 ***

145.8

locreg5

1.153

1.36 ¥ 10-3 **

152.9

locreg10

1.731

7.66 ¥ 10-4 ***

151.5

locreg15

2.290

1.98 ¥ 10-3 **

154.3

locreg20

3.859

2.45 ¥ 10-4 ***

145.3

locreg25

5.332

1.06 ¥ 10-4 ***

138.1

locreg30

5.326

1.86 ¥ 10-4 ***

142.7

locreg35

5.327

4.17 ¥ 10-4 ***

142.4

locreg40

6.488

3.20 ¥ 10-4 ***

139.5

Note: Values for the intercepts are not shown. **, p < 0.01; ***, p < 0.001.

The response surface of the main model (Fig. 7) shows that trees with a distinct negative growth trend and an intermediate growth level are subject to an increased risk of dying. Trees with a low growth level (log(BAI3) < 0) combined with stationary growth over the last 25 years (cf. Fig. 6) had a similar risk profile. Note that trees with a low growth level (log(BAI3) < 0) combined with a distinctly positive or negative growth trend do not exist

32


in our sample (cf. Fig. 6). According to our model, trees with a high past growth level (log(BAI3) > 2) and a positive or slightly negative growth trend over the past 25 years (locreg25 > -0.2) are now more likely to be alive than dead. The use of the odds ratio for determining the relative mortality risk is exemplified here for two trees. Let us assume that the first tree has a growth level variable of log(BAI3) = 1, the second tree is characterized by log(BAI3) = 1.5. Assuming that both trees have a stationary growth (locreg25 = 0), we find according to Eq. 2 and the coefficients in Table 4 that the odds ratio for these two trees is 1.57 with a 95% confidence interval of (1.26, 1.94), i.e., the first tree, which has a lower growth level, is nearly 1.6 times more likely to die compared to the second tree. Table 4. Mortality model fitted for the Davos data set (n = 119). Intercept

log(BAI3)

locreg25

Coefficient

-0.568

0.898

4.507

SE

0.316

0.220

1.333

z

-1.800

4.082

3.381

p >|z|

7.18 ¥ 10-2

4.46 ¥ 10-5 ***

7.22 ¥ 10-4 ***

Note: The coefficients, standard errors, and z and p values (***, p < 0.001) of the logistic regression with two independent variables are shown.

Table 5. Average percentage of misclassified trees for the internal validation of the Davos data set (n = 119, R = 200 simulations) using various combinations of growth level variables [log(BAI)] and growth trend variables (locreg). "

log(BAI3)

log(BAI5)

log(BAI7)

locreg5

21.58

21.53

22.67

locreg10

21.82

22.75

22.13

locreg15

23.77

24.99

26.36

locreg20

21.48

23.06

24.19

locreg25

20.58*

21.84

21.49

locreg30

21.55

22.46

22.88

locreg35

22.59

24.16

24.9

locreg40

22.47

24.44

25.56

*Main model

Chapter I

33

Val idation The internal validation, based on a random split of the Davos data set, revealed that 19.1% of the dead trees were misclassified as being alive and 21.7% of the living trees were predicted to be dead (Table 6). Overall, 20.6% of the trees were misclassified. The use of only one growth variable would, for the same validation procedure, result in an increase of the misclassification rate to 27.3% if log(BAI3) was the only independent variable and to 31.6% if locreg25 was the only independent variable.

Fig. 5. Frequency distribution of (a) growth level variable log(BAI3) and (b) growth trend variable locreg25 for dead and living trees (Davos data set, n = 119).

In the external validation (Table 6), 22.2% of the dead trees at the Bödmeren site were misclassified, whereas 34.8% of the living trees were predicted to be dead in the model. At this site, 70.7% of all trees were assigned to the correct group. For Scatlé, 25.0% of the dead trees were misclassified, while 13.6% of the living trees were assigned to the wrong group. Overall, 81.0% of all trees were classified correctly at Scatlé. Table 6. Validation of the mortality model with log(BAI3) and locreg25 as independent variables (0 = dead, 1 = living) for internal validation with random subsampling (data from Davos only, n = 119, R = 200 simulations) and external validation with data from Bödmeren (n = 41) and Scatlé (n = 42). Predicted = 0

Predicted = 1

Observed = 0

23.85 ± 2.50

5.62 ± 2.77

Observed = 1

6.63 ± 2.63

23.91 ± 2.39

Observed = 0

14

4

Observed = 1

8

15

Observed = 0

15

5

Observed = 1

3

19

Internal Davos

External Bödmeren

Scatlé

Note: Numbers of observed and predicted (mean ± SD) trees are shown.

34


Fig. 6. Scatterplot of log(BAI3) (growth level) and locreg25 (growth trend), grouped by dead or alive (Davos data set, n = 119). Many dead trees had a low to very low growth level (log(BAI3) < 0) combined with a growth trend around 0 or a growth level of greater than -0.5 in combination with a growth trend of less than -0.2.

Fig. 7. Response surface of logistic mortality model with fitted survival probabilities Pr(Y = 1|X). High values of Pr(Y = 1|X) indicate low mortality probabilities.

Chapter I

35

Rel ations hip be tween growth and competi tive s tatus In the stepwise regression using all five CIs (cf. Table 2), as well as in the comparison of the separate models, CI5 turned out to best reflect recent growth [log(BAI3)] of living trees with respect to both selection criteria, the AIC for the stepwise regression and the adjusted R2 for the separate models. The adjusted R2 values for the five competition indices in the linear models for living trees were 25.9% (CI1), 29.9% (CI2), 23.7% (CI3), 47.7% (CI4), and 51.5% (CI5). Table 7. Linear regression models relating recent growth [log(BAI3)] and competition (CI5) of living trees and trees that died between 1986 and 1999 (Davos data set).

Coefficient (p) Model

Intercept

CI5

R2 (%)

Living trees (n = 60)

2.436 (< 2 ¥ 10-16 ***)

-0.220 (6.59 ¥ 10-11 ***)

52.3

Trees that died between

1.078 (8.82 ¥ 10-4 ***)

-0.201 (2.98 ¥ 10-2 *)

24.9

1986 – 1999 (n = 19) Note: The regression coefficients, p values (*, p < 0.05; ***, p < 0.001), and the coefficients of determination (R2, unadjusted) are shown.

For the living trees, 52.3% of the variability of log(BAI3) could be attributed to competition using CI5 as an independent variable (Table 7), while for the dead trees that died between 1986 – 1999, this amounted to 24.9% (Table 7). The relationship between competition and recent growth is shown in Fig. 8.

Discussion Growth le vels, growth trends, and tree mortal ity Norway spruce trees are able to endure low, stationary growth for many decades, in our case up to 150 years (cf. Kaufmann 1996). Most of the dead Norway spruce trees in our sample were characterized by a continuously decreasing growth trend during the last decades prior to death (Figs. 3 and 4). This growth pattern is likely attributable to competition or to decreasing resources in general. Some trees in our sample showed strong, stairsteplike growth reductions, which often resulted in rapid death. Intense pathogen attacks or severe drought may result in such growth decreases (Pedersen 1998b, Villalba and Veblen 1998).

36


These considerations provided the underpinning for our rationale to consider both growth level variables and growth trend variables: it is the combination of the two types of variables that provides an improved understanding and explanation of the risk of tree death.

Fig. 8. Scatterplot of CI5 versus log(BAI3); regression lines from Table 7. Shown are living trees (n = 60) and trees that died after 1985 (n = 19) from the Davos site.

Log istic mortal ity model and vali dation The stem growth variables that were derived for the mortality model proved to be useful predictors of the risk of tree death. With respect to the growth level variable in the model, we have to consider that small trees always have low values of BAI compared to large trees, but mortality risk is not necessarily smaller for large trees. This discrepancy is addressed by including the growth trend variable, which has a high discriminating power as well. Similarly, ring width tends to be greater in younger trees, diminishing constantly with age. But this trend does not imply that young trees have a smaller mortality probability. One growth level variable, the log-transformed, averaged BAI of the last three years [log(BAI3)], provided a significant contribution to the discrimination between living and dead trees. With respect to the growth trend variables, the slope of the linear regressions of BAI over the last 25 measured years (locreg25) had the highest explanatory power, although the inclusion of a growth trend variable over a shorter period of 5 or 10 years would result in just a small increase of the misclassification rate (Table 5). The importance of considering the growth level in combination with the growth trend for assessing mortality risk of Norway spruce is supported by these findings. The benefit of adding

Chapter I

37

locreg25 to log(BAI3) in the model is a decrease of the misclassification rate from 27.3% to 20.6%. The growth level and growth trend variables that we derived could be biased if many trees had died in the same years owing to climatic factors such as drought. Three reasons argue against the importance, for this study, of interannual growth variations due to climatic effects. First, we could not detect any clusters in the frequency distribution of the last measured year of dead trees; the year of tree death was distributed relatively uniformly (Fig. 2). Second, unlike dendroclimatological studies, which aim to amplify the climate signal (Fritts 1976), our growth curves were not standardized. Third, growth variables were calculated over periods of at least three years. Such aggregated variables are more robust predictors than variables that have been calculated over shorter periods. The internal validation showed a sufficient goodness-of-fit for the Davos data. A close inspection of the misclassified dead trees showed that they were characterized by abrupt negative growth trends. Possible causes could be strong pathogens, drought, rockfall, or other sudden events. A small number of living, but very slow-growing trees were also misclassified, which reduced the goodness-of-fit. Although such trees showed growth characteristics of dead trees, there was no reason to exclude these trees as true outliers. Such trees may be dying in the course of the coming few years, and hence, their classification as being dead in the model may be merely premature. The external validation indicates that the model fitted for the Davos site can be used for predicting growth-dependent mortality of Norway spruce in mountain forests in different regions of the European Alps. Rel ations hip be tween recent growth and competition In dendroclimatology, the high-frequency climatic signal is used after removing the longterm age trend of ring widths in a mean chronology (Fritts 1976, Bräker 1981). In the present dendroecological study, however, we derived growth indices from the raw tree ring data without using standardization procedures. Thus, we did not emphasize climate effects, but focused on biotic stress factors such as competition, which is one of the main factors that influence recent growth and mortality in relatively dense stands (Keister 1972, Szwagrzyk and Szewczyk 2001). Our results showed that a much greater proportion of the variability of recent growth of living trees was related to competition than is the case for trees that had died after 1985 (Table 7). Tree growth over the last three measured years is negatively related to competition, both for living trees and for trees that had died after 1985 (Fig. 8). The relative response to increasing competition is very similar in both groups of trees, as evidenced by the similar slopes of the relationships. However, given the same value of CI, living trees are generally characterized by a higher growth increment than the now dead trees. It can be assumed that the CIs for the now dead trees did not change very strongly for a maxi-

38


mum of the last 14 years. First, initiation of release of neighboring trees can be delayed by several years (Veblen et al. 1991), and second, growth of Norway spruce does not increase very rapidly in high subalpine forests after the death of a single competitor. A study of P. abies in a montane forest supports the latter finding (Szwagrzyk and Szewczyk 2001). Thus, competition is an important factor determining tree growth in the forests that we studied, but additional factors are responsible for predisposing trees to die. Areas of further rese arch Our approach cannot be used directly to predict tree mortality at the stand scale, which would be required to develop more realistic mortality routines in succession models (Shugart 1984, Bugmann 2001, Wyckoff and Clark 2002). In our mortality model, the group of dead trees would be strongly overrepresented, since the model was fitted with equal numbers of dead and living trees (Hosmer and Lemeshow 1989, Fielding and Bell 1997, Woodward 1999). However, model fitting with representative proportions of dead and living trees for each size class would require very large samples, and would be far too costly if long-term growth variables are to be used as predictors. In addition, the approach developed in this study essentially is static, i.e., it cannot readily be applied to predict tree mortality in succession models because the time dependency of growth rates is not taken into account explicitly. The development of mortality models that are based on time-dependent variables would be a further step towards a better understanding of mortality processes. For example, hazard functions might be used to assess the mortality probability for a tree at time t, conditional on the subject having survived to time t (see also Maul 1994, Hosmer and Lemeshow 1999, He and Alfaro 2000). Implementing empirically derived growth-mortality relationships in gap models (Shugart 1984, Bugmann 2001, Keane et al. 2001) could significantly improve their performance. The lack of suitable data for calibrating mortality functions is the main reason why relatively unspecific assumptions about growth-mortality relationships continue to be used in models of long-term forest dynamics (Hawkes 2000, Keane et al. 2001; cf. Wyckoff and Clark 2002).

Conclusions In this study, we evaluated different growth-related variables to discriminate between dead and living Norway spruce trees using a logistic regression model. We also estimated the impact of competition on recent growth of dead and living trees by applying a linear regression model. We draw five major conclusions.

Chapter I

39

(1)

Individual-based mortality models can increase our insight into tree mortality processes. A tree-by-tree evaluation of the observed versus predicted state (dead or alive) allowed us to develop a better understanding of the underlying mechanisms than general comparisons of mortality rates at the stand scale.

(2)

The consideration of long-term growth trends significantly improved the performance of logistic tree mortality models compared to models that are based on ‘classical’ growth level variables (‘recent growth’). The inclusion of a long-term growth trend variable reduced the misclassification rate from 27.3% to 20.6%. The difference was mainly the dead Norway spruce trees with an intermediate growth level, in combination with a distinct negative growth trend prior to death.

(3)

Odds ratios, i.e., an approximation of the relative mortality risk of two trees, allow for a direct interpretation of the logistic mortality model.

(4)

The mortality model developed for Norway spruce is transferable to different climatological and geological areas in the Alps, which supports the generality of the model.

(5)

More than 50% of the variability of recent growth of living trees and nearly 25% of the growth variability of dead trees can be attributed to competition. This implies that neighbor trees play an essential role in predisposing trees to die, at least in the longer term.

Acknowledgments We would like to thank Andi Rigling and Fritz Schweingruber (WSL, Birmensdorf, Switzerland) for valuable discussions. The Seminar for Statistics (ETH, Zurich, Switzerland) provided the necessary statistical advice. During field sampling, we were supported by Kathrin Saner (Zug, Switzerland), Dani Gysin (Lausanne, Switzerland), and Peter Weisberg (Mountain Forest Ecology, ETH Zurich, Switzerland). Jean-François Matter (Chair of Silviculture, ETH Zurich, Switzerland) helped us with the selection of the sites at Bödmeren and Scatlé. Peter Weisberg helped us to improve the manuscript with respect to linguistical problems. Thanks are also due to three anonymous reviewers and one of the Associate Editors of the Journal, who provided numerous helpful comments on an earlier version of the manuscript.

40


References Avila, O. B., and H. E. Burkhart. 1992. Modeling survival of loblolly pine trees in thinned and unthinned plantations. Canadian Journal of Forest Research 22:1878-1882. Badeck, F.-W., H. Lischke, H. Bugmann, T. Hickler, K. Hönninger, P. Lasch, M. J. Lexer, F. Mouillot, J. Schaber, and B. Smith. 2001. Tree species composition in European pristine forests: comparison of stand data to model predictions. Climatic Change 51:307-347. Bebi, P. 1999. Erfassung von Strukturen im Gebirgswald als Beurteilungsgrundlage ausgewählter Waldwirkungen. Ph.D. Dissertation. Eidgenössische Technische Hochschule, Zürich. Bettschart, A., editor. 1994. Urwald-Reservat Bödmeren: Moose - Pilze - Gefässpflanzen - Mollusken. Schwyzerische Naturforschende Gesellschaft, Einsiedeln. Biging, G. S., and M. Dobbertin. 1992. A comparison of distance-dependent competition measures for height and basal area growth of individual conifer trees. Forest Science 38:695-720. Bloom, A. J., F. S. Chapin III, and H. A. Mooney. 1985. Resource limitation in plants - an economic analogy. Annual Review of Ecology and Systematics 16:363-392. Bräker, O. U. 1981. Der Alterstrend bei Jahrringdichten und Jahrringbreiten von Nadelhölzern und sein Ausgleich. Mitt. forstl. Bundesversuchsanst. Wien 142:75-101. Breslow, N. E., and N. E. Day. 1989. The analysis of case control studies, 3rd reimpr. edition. International Agency for Research on Cancer, Lyon. Buchman, R. G., S. P. Pederson, and N. R. Walters. 1983. A tree survival model with applications to species of the Great Lakes region. Canadian Journal of Forest Research 13:601-608. Buford, M. A., and W. I. Hafley. 1985. Probability distribution as models for mortality. Forest Science 31:331-341. Bugmann, H. 1997. Sensitivity of forests in the European Alps to future climatic change. Climate Research 8:35-44. Bugmann, H. 2001. A review of forest gap models. Climatic Change 51:259-305. Burgman, M. A., W. Incoll, P. K. Ades, I. Ferguson, T. D. Fletcher, and A. Wohlers. 1994. Mortality models for mountain and alpine ash. Forest Ecology and Management 67:319-327. Chernick, M. R. 1999. Bootstrap methods: a practitioner's guide. John Wiley & Sons, New York a.o. Coley, P. D., J. P. Bryant, and F. S. Chapin III. 1985. Resource availability and plant antiherbivore defense. Science (Washington, D. C.) 230:895-899. Collett, D. 1991. Modelling binary data. Chapman & Hall, London. Cox, D. R., and E. J. Snell. 1989. Analysis of binary data. Chapman and Hall, London [etc.]. Coyea, M. R., and H. A. Margolis. 1994. The historical reconstruction of growth efficiency and its relationship to tree mortality in balsam fir ecosystems affected by spruce budworm. Canadian Journal of Forest Research 24:2208-2221. Crow, G. R., and R. R. Hicks. 1990. Predicting mortality in mixed oak stands following spring insect defoliation. Forest Science 36:831-841. Daniels, R. F. 1976. Simple competition indices and their correlation with annual loblolly pine tree growth. Forest Science 22:454-456. de Luis, M., J. Raventos, J. Cortina, M. J. Moro, and J. Bellot. 1998. Assessing components of a competition index to predict growth in an even-aged Pinus nigra stand. New Forests 15:223-242.

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Chapter I Ogle, K., T. G. Whitham, and N. S. Cobb. 2000. Tree-ring variation in pinyon predicts likelihood of death following severe drought. Ecology 81:3237-3243. Pedersen, B. S. 1998a. Modeling tree mortality in response to short- and long-term environmental stresses. Ecological Modelling 105:347-351. Pedersen, B. S. 1998b. The role of stress in the mortality of midwestern oaks as indicated by growth prior to death. Ecology 79:79-93. Pedersen, B. S. 1999. The mortality of midwestern overstory oaks as a bioindicator of environmental stress. Ecological Applications 9:1017-1027. Peet, R. K., and N. L. Christensen. 1987. Competition and tree death. BioScience 37:586-595. Price, C. 1989. The theory and application of forest economics. Blackwell, Oxford. Rinn, F. 1996. TSAP - Reference manual. Version 3.0. Rinntech. Heidelberg. Schweingruber, F. H. 1996. Tree rings and environment: dendroecology. Verlag Paul Haupt, Bern. Shugart, H. H. 1984. A theory of forest dynamics. The ecological implications of forest succession models. Springer, New York. Stöckli, V. B. 1996. Tree rings as indicators of ecological processes: the influence of competition, frost, and water stress on tree growth, size, and survival. Ph.D. Dissertation. University Basel, Basel. Szwagrzyk, J., and J. Szewczyk. 2001. Tree mortality and effects of releases from competition in an oldgrowth Fagus-Abies-Picea stand. Journal of Vegetation Science 12:621-626. Veblen, T. T., K. S. Hadley, M. S. Reid, and A. J. Rebertus. 1991. Methods of detecting past spruce beetle outbreaks in Rocky Mountain subalpine forests. Canadian Journal of Forest Research 21:242-254. Venables, W. N., and B. D. Ripley. 1999. Modern applied statistics with S-PLUS. Springer-Verlag, New York. Villalba, R., and T. T. Veblen. 1998. Influences of large-scale climatic variability on episodic tree mortality in northern Patagonia. Ecology 79:2624-2640. Visser, H. 1995. Note on the relation between ring widths and basal area increments. Forest Science 41:297304. Waring, R. H. 1987. Characteristics of trees predisposed to die. BioScience 37:569-574. Waring, R. H., and G. B. Pitman. 1985. Modifying lodgepole pine stands to change susceptibility to mountain pine beetle attack. Ecology 66:889-897. West, P. W. 1980. Use of diameter increment and basal area increment in tree growth studies. Canadian Journal of Forest Research 10:71-77. West, P. W. 1981. Simulation of diameter growth and mortality in regrowth eucalypt forest of southern Tasmania. Forest Science 27:603-616. Woodward, M. 1999. Epidemiology: study design and data analysis. Chapman & Hall/CRC, Boca Raton etc. Wyckoff, P. H., and J. S. Clark. 2000. Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches. Canadian Journal of Forest Research 30:156-167. Wyckoff, P. H., and J. S. Clark. 2002. The relationship between growth and mortality for seven co-occuring tree species in the southern Appalachian Mountains. Journal of Ecology 90:604-615. Zar, J. H. 1999. Biostatistical analysis, fourth edition. Prentice-Hall, Upper Saddle River, New Jersey. Zhang, S., R. L. Amateis, and H. E. Burkhart. 1997. Constraining individual tree diameter increment and survival models for loblolly pine plantations. Forest Science 43:414-423.

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Chapter II

45

Chapter II Predicting the time of tree death using dendrochronological data

Submitted as: Bigler, C., and H. Bugmann. 2003. Predicting the time of tree death using dendrochronological data. Ecological Applications. Mountain Forest Ecology, Department of Forest Sciences, Swiss Federal Institute of Technology (ETH), ETH-Zentrum, CH-8092 Zurich, Switzerland

Manuscript accepted after minor revision on August 1 2003.

Abstract – Complex interactions of various environmental factors result in high variability of tree mortality in space and time. Tree mortality functions that are implemented in forest succession models have been suggested to play a key role in assessing forest response to climate change. However, these functions are based on theoretical considerations, and are likely to be poor predictors of the timing of tree death, since they do not adequately reflect our understanding of tree mortality processes. In addition, these theoretical mortality functions and most empirical mortality functions have not been tested sufficiently with respect to the accuracy of predicting the time of tree death. We introduce a new approach to modeling tree mortality based on different growth patterns of entire tree-ring series. Dendrochronological data from Picea abies (Norway spruce) in the Swiss Alps were used to calibrate mortality models using logistic regression. The autocorrelation of the data was taken into account by a jackknife variance estimator. Model performance was assessed by two criteria for classification accuracy and three criteria for prediction error. The six models with the highest overall performance correctly classified 71 – 78% of all dead trees and 73 – 75% of all living trees, and they predicted 44 – 56% of all dead trees to die within 0 – 15 years prior to the actual year of death. For these six models, a maximum of 1.7% of all dead trees and 5% of all living trees were predicted to die more than 60 years prior to the last measured year. Models including the

46

Predicting the time of tree death

relative growth rate and a short-term growth trend as explanatory variables were most reliable with respect to inference and prediction. The generality of the mortality models was successfully tested by applying them to two independent P. abies data sets from climatologically and geologically different areas. We conclude that the methods presented improve our understanding of how tree growth and mortality are related, which results in more accurate mortality models that can ultimately be used to increase the reliability of predictions from models of forest dynamics. Key words Tree mortality; dendroecology; Picea abies (Norway spruce); growth patterns; models; jackknife variance estimator; prediction; logistic regression; repeated measurements; longitudinal data; validation; model performance

Introduction Due to the longevity of trees and the high variability of tree mortality in space and time, tree death is one of the least understood processes in ecology (Franklin et al. 1987, Villalba and Veblen 1998), even though it is of fundamental importance for understanding and predicting forest dynamics (Veblen 1986, Johnson and Fryer 1989, Oliver and Larson 1996). Tree mortality is closely related to tree growth (Kozlowski et al. 1991), which in turn is affected by complex interactions of various environmental factors such as fire, prolonged droughts, windthrow, or severe insect epidemics (Franklin et al. 1987, Pedersen 1999). These factors often cause episodic or irregular mortality (Michaels and Hayden 1987, Mast and Veblen 1994, Villalba and Veblen 1998). Competition or senescence typically lead to what is termed continuous or regular mortality (Peet and Christensen 1987, Noodén and Leopold 1988, Szwagrzyk and Szewczyk 2001, Lussier et al. 2002). The present paper focuses on continuous, growth-dependent mortality processes of trees, using Picea abies (L.) Karst. (Norway spruce) in the European Alps as a case study. An enhanced understanding of tree mortality provides an improved basis for forest ecology and, ultimately, forest management under current and changed environmental conditions (Franklin et al. 1987, Pedersen and McCune 2002). Mortality processes have been found to play a key role in predicting forest dieback during climate change (Loehle and LeBlanc 1996). Future, climate change-induced increases in intensity and frequency of extreme climate events, such as prolonged drought periods (Beniston and Innes 1998, Houghton et al. 2001), are likely to be accompanied by increased episodic tree mortality, whereas chronic climatic alterations are likely to lead to changes in continuous, regular mortality (see Villalba and Veblen 1998, Ogle et al. 2000). The mortality algorithms that are implemented in many current models of forest dynamics, including forest gap models, have several drawbacks (Loehle and LeBlanc 1996, Hawkes 2000, Bugmann 2001, Keane et al. 2001). Particularly, the lack of empirical data for deriving species-specific growth-

Chapter II

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mortality relationships is a fundamental problem in modeling tree mortality (Hawkes 2000). Therefore, these mortality algorithms rely on theoretical assumptions and do not consider (1) the tolerance of slow growth that is characteristic of very long-lived species (Kaufmann 1996), (2) the behavior of trees growing at climatically extreme sites (Schweingruber 1996), or (3) the survival strategies of shade tolerant, suppressed trees (Canham 1985, 1990, Szwagrzyk and Szewczyk 2001). As pointed out by Hawkes (2000), poor validation procedures are one of the major issues in modeling tree mortality. For example, forest gap models are tested mainly by comparing tree species composition or tree size distribution with empirical data. Hardly ever have the mortality functions of these models been tested rigorously against empirical data (cf. Loehle and LeBlanc 1996, Hawkes 2000). According to Kirchner et al. (1996), critical steps to assess the validity, reliability, and accuracy of a model are (1) to define a performance criterion, and (2) to compare a model against a benchmark, such as alternative model formulations, a null hypothesis, or expert judgment (see also Keane et al. 2001, Bugmann 1996). Reynolds and Ford (1999) recommend to assess model performance by judging simultaneously multiple model criteria, rather than considering only one single criterion, since a single criterion may be satisfied by different models (Oreskes et al. 1994). The most frequent empirical approach for modeling individual-based tree mortality rests upon cross-sectional data, e.g., forest survey data of one year (Dobbertin and Brang 2001). The aim of these models is to predict the status of each individual tree (dead or alive) based on its recent growth pattern and additional variables. Only one measurement per tree is used, and the binary responses of the trees (dead or alive) thus are independent. Multiple logistic regression models are commonly used for this purpose (e.g., Hamilton 1986, Coyea and Margolis 1994, Monserud and Sterba 1999, Yao et al. 2001, Bigler and Bugmann 2003b). Other methods such as discriminant analysis (Monserud 1976, Crow and Hicks 1990), neural networks (Guan and Gertner 1991b, a, Hasenauer et al. 2001), or classification and regression trees (CART; Dobbertin and Biging 1998, Gottschalk 1998) were also applied to model tree mortality. Evidently, such mortality functions are not optimized to predict the time of tree death. The application of models based on crosssectional data to growth curves of slow-growing or suppressed trees can result in large prediction errors (cf. Bigler and Bugmann 2003b). Longitudinal data or repeated measurements from prospective or retrospective studies have much less often been used for modeling individual tree mortality (Fridman and Stahl 2001; for textbooks on the analysis of longitudinal data, cf. Diggle et al. 1994, Hand and Crowder 1996, Lindsey 1999). Longitudinal data such as time series of tree rings can be viewed as multivariate data with autocorrelated responses within tree individuals (Fahrmeir and Tutz 1994). In the longitudinal approach to modeling tree mortality, the aim is to predict the mortality probability for each year of tree life.

48


With this study, we present a new approach to model a tree’s mortality probability across time, and assess the potential of this method for predicting the time of tree death based on longitudinal growth data. Our ultimate aim is to improve the predictive capabilities with respect to growth-dependent tree mortality. Such knowledge in turn improves the understanding of tree mortality processes and increases the reliability of models of long-term forest dynamics. The specific objectives of our study are (1) to optimize the prediction of the time of individual tree death of Norway spruce (Picea abies) based on growth patterns from entire tree-ring series, (2) to define multiple criteria for assessing the performance of the mortality models, (3) to compare the performance of several mortality models, and (4) to validate the mortality models against independent data sets.

Material & methods Study sites Pairs of dead and living trees of Norway spruce (Picea abies (L.) Karst.; see Hess et al. 1991), a very widespread species in the subalpine zone of the European Alps, were sampled in P. abies dominated mountain forests in Switzerland (see Bigler and Bugmann 2003b), at the three study sites Davos, Bödmeren, and Scatlé. Sixty tree pairs were sampled on southwestern aspects between 1600 and 2000 m a.s.l. in two parallel valleys in the Davos area, i.e., the Dischma valley (46°47’ N, 09°53’ E) and the Flüela valley (46°49’ N, 09°52’ E). Annual rainfall in Davos amounts to 1075 mm and average annual temperature is 2.4°C. The area is classified geologically as silicate (Gneiss) (Landolt et al. 1986, Bebi 1999). In the Karst landscape of Bödmeren (46°59’ N, 08°51’ E) (Hantke 1995), 23 pairs of dead and living P. abies trees were sampled. The study area runs from 1500 to 1600 m a.s.l. on western slopes; it is characterized climatically by high amounts of rainfall (≈ 2500 mm/year) and a mean annual temperature of ≈ 3 – 4°C (Bettschart 1994). The third site is situated in Scatlé (46°47’ N, 09°03’ E) on a silicate (Verrucano) bedrock (Hartl 1967, Hillgarter 1971), where 22 tree pairs were considered. The slopes are facing ENE, and trees were sampled between 1500 and 1700 m a.s.l. Climate data were estimated based on Badeck et al. (2001) as 1440 mm annual precipitation and 2.2°C annual mean temperature. Field sam pling and pr ocessi ng of tree-r ing data Pairs of a standing dead tree and a living tree with a minimum DBH (diameter at breast height) of 10 cm were cored twice at breast height using an increment borer. The living tree had to be comparable to the dead tree with respect to size, competition, and microsite (for further details see Bigler and Bugmann 2003b). Dead trees were not included in the sample if they had obviously been killed by strong pathogens, avalanches, wind, fire, or other episodic events.

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Tree rings were measured on a Lintab 3 measuring system (F. Rinn S.A., Heidelberg, Germany) with a resolution of 0.01 mm. The TSAP tree ring program (Rinn 1996) was used to crossdate the cores of all dead and living trees (Fritts 1976, Schweingruber 1988). At each site, the averaged growth curve of 6 – 12 living trees was used as reference. The two cross-dated cores of each tree were averaged and converted to basal area increment (BAI). A small number of trees had to be excluded from the further analyses due to low wood quality of the cores or due to obvious bark beetle attacks (cf. Bigler and Bugmann 2003b). At the Davos site, 119 trees were included in the final sample, 41 trees at the Bödmeren site, and 42 trees at the Scatlé site. Der ivation of m ortali ty mod els We applied logistic regression (Hosmer and Lemeshow 1989, McCullagh and Nelder 1989, Collett 1991) to predict the survival probability Pr(Yi,t = 1|X i,t) of tree i at a given time t, where Y i,t = 1 indicates that tree i is alive at time t (correspondingly, Yi,t = 0 indicates that tree i is dead at time t). The matrix Xi,t contains the independent variables of tree i at time t. The independent variables (covariates) used were separated into three groups, denoted as growth level variables, growth trend variables (cf. Bigler and Bugmann 2003b), and additionally as a relative growth rate variable. The covariates were calculated using time series of BAI (basal area increment) or RW (ring width) of individual trees, as explained below. Growth level variables were defined as the mean annual increment within a given period. Low growth levels are commonly considered as an indicator of increased mortality risk (see e.g. Buchman et al. 1983, Wyckoff and Clark 2000). Two growth level variables over a period of 3 years were considered, since preliminary analyses showed that growth level variables over 3 years had a higher statistical significance than variables calculated over 5 or more years (Bigler and Bugmann 2003b): BAI3 (cm2/year) is the 3-year average of BAI, and RW3 (1/100 mm/year) is the 3-year average of tree ring width. Growth trend variables were defined as the rate of change in mean increment within a given time period (cf. LeBlanc 1992, LeBlanc 1996, Bigler and Bugmann 2003b). Growth trend variables were considered in the variable selection because some trees were observed to die after a rapid growth decrease, although they were growing at a relatively high level, whereas some trees were surviving that showed a very low growth level combined with no significant growth trend. Based on an extensive statistical screening procedure, we decided to consider a short-term growth trend variable and a long-term growth trend variable. The slopes of local linear regressions (locreg) over 5 years (locreg5) and 25 years (locreg25) of BAI were used.

50


Finally, the relative growth variable relbai was calculated as the ratio of BAI and BA (i.e., basal area increment divided by basal area), in order to take the size of the tree into account. Consequently, small trees have a higher value of relbai than larger trees, assuming the same BAI. Combinations of the independent variables were used to fit logistic regression models to the Davos data set, including 14219 to 17075 repeated measurements from the 59 dead and 60 living trees (Table 1). A maximum of one variable within each variable group was entered in any given regression. Under this condition and except for variable RW3, all possible combinations of one, two, or three independent variables were evaluated (Table 1). The variables BAI3 and relbai were transformed with the natural logarithm. The variable RW3 was considered only in model 4, since BAI had been shown to be a better indicator of tree vigor than ring width (LeBlanc 1996, Pedersen 1998). The aim of this comparative model analysis was to assess the performance of models with different variable combinations. Table 1. Independent variables used in mortality models, as represented by the Wilkinson-Rogers notation (Wilkinson and Rogers 1973). Model

Linear combination of independent variables

Number of measurements

Model 1

log(BAI3)

16837

Model 2

locreg5

16599

Model 3

locreg25

14219

Model 4

RW3

16837

Model 5

log(relbai)

17075

Model 6

log(BAI3) + locreg5

16599

Model 7

log(BAI3) + locreg25

14219

Model 8

locreg5 + log(relbai)

16599

Model 9

locreg25 + log(relbai)

14219

Model 10

log(BAI3) + log(relbai)

16837

Model 11

locreg5 + log(BAI3) + log(relbai)

16599

Model 12

locreg25 + log(BAI3) + log(relbai)

14219

Note: Linear combinations of two growth level variables (log(BAI3), RW3), two growth trend variables (locreg5, locreg25), and one relative growth variable [log(relbai)] were included to fit logistic regression models. The accumulated lengths of the time series of the 59 dead trees and the 60 living trees from Davos give the number of measurements that were used to calibrate the models. The values differ due to variables that are calculated over different moving windows (see Material & methods section).

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Estimation of m odel coefficients and corrected vari ances The estimates of the model coefficients were not affected by autocorrelation (Collett 1991), and the systematic component was modeled by applying the same methods as for independent data (cf. Lumley and Heagerty 1999). Logistic regression models were fitted by maximum log-likelihood estimation with the ‘R’ software (version 1.5; Ihaka and Gentleman 1996), applying the function glm() in the library ‘base’. The AIC (Akaike Information Criterion; Venables and Ripley 1999) was used during the model selection procedure to assess the goodness-of-fit of the models. To correct the biased variances due to the correlated data (Cox and Snell 1989, McCullagh and Nelder 1989), we applied the infinitesimal jackknife variance estimator infjack.glm() from the library ‘weave’, written by Thomas Lumley (University of Washington) (cf. Chernick 1999, Lumley and Heagerty 1999). This robust variance estimator re-samples whole individuals within a fitted, generalized linear model. Ass essing model performance The fitted models were applied to each tree, which resulted in individual probability curves of survival with annual resolution. A tree was predicted to be dead as soon as the probability curve fell below a specific threshold, while a tree was predicted to be alive as long as the entire probability curve stayed above the threshold. To illustrate this, some results for model 8 (Table 1) are shown in Figs. 1c and 1d, Figs. 2c and 2d, and Figs. 3c and 3d, along with the tree-ring series in panels a and b of these figures. Large prediction errors typically arose for trees with very slowly declining growth rates, whereas quite precise predictions generally resulted for trees with rapid growth decreases (e.g., tree ‘DAA006’ in Fig. 1, or tree ‘SCA121’ in Fig. 3). In the Davos data set, only 59 measurements out of the 14219 – 17075 measurements stem from trees that were dead at time t (Yi,t = 0). If a threshold of 0.5 was applied a priori, as it is common in ecological models, the strong prevalence of measurements from trees that were alive at time t (Yi,t = 1) would bias the results towards this larger group (Hosmer and Lemeshow 1989, Fielding and Bell 1997). Therefore, the threshold level was varied in steps of 0.005 to adjust it with respect to maximizing model performance. The performance of most models was highest when the threshold level was set at 0.975. Model performance was assessed based on multiple criteria. Two classification accuracy criteria (Fielding and Bell 1997) and three prediction error criteria were used, as explained below. First, it was assessed whether the trees were accurately classified as being dead or alive. The first classification accuracy criterion was defined as the percentage of dead trees that were correctly predicted to be dead (CCd; correctly classified dead trees). The second classification accuracy criterion was defined as the percentage of living trees that were correctly predicted to be alive (CCl; correctly classified living trees).

52


Fig. 1. (a), (b) Ring widths and (c), (d) corresponding survival probabilities of two pairs of a dead tree (black line) and a living tree (gray line) from Davos. The survival probabilities were computed by applying model 8 (locreg5 + log(relbai), see Table 2), fitted with the Davos data set (n = 119). The horizontal, dotted line shows the threshold of 0.975. All four trees were correctly predicted to be alive or dead, respectively. The prediction error for the dead tree ‘DAA006’ was 4 years and for the dead tree ‘DAA008’ 21 years.

Fig. 2. (a), (b) Ring widths and (c), (d) corresponding survival probabilities of two pairs of a dead tree (black line) and a living tree (gray line) from Bödmeren. Further explanations see Fig. 1. The prediction error for the dead tree ‘BOA065’ was 25 years, and for the dead tree ‘BOA073’ 20 years.

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Second, we calculated the prediction error for all the trees as the difference between the last measured year and the predicted year of death. The last measured year was identified as the year of death in the case of dead trees and as the year when the tree was cored in the case of living trees. We denoted the first prediction error criterion as the percentage of actually dead trees that were predicted to die no more than 15 years prior to actual death (PEd,15). The second and third criterion were defined as the percentages of actually dead or living trees that were predicted to die more than 60 years prior to death or prior to the last measured year, respectively (PEd,60, PEl,60). A given model’s performance was assessed to be high when CCd, CCl, and PEd,15 were high, and when PEd,60 and PEl,60 were low. The performance criteria were calculated by applying each model, fitted with the Davos data set, to the Davos data set (n = 119 trees; model verification) and to the two independent data sets Bödmeren (n = 41 trees; model validation) and Scatlé (n = 42 trees; model validation). Finally, the resulting values of the performance criteria were ranked.

Fig. 3. (a), (b) Ring widths and (c), (d) corresponding survival probabilities of two pairs of a dead tree (black line) and a living tree (gray line) from Scatlé. Further explanations see Fig. 1. The prediction error for the dead tree ‘SCA121’ was 0 years, and for the dead tree ‘SCA131’ 9 years.

54


Table 2. Estimates of fitted mortality models using logistic regression (Davos data set, n = 119 trees). Model

Independent variables

Estimates

Uncorrected standard errors (p values)

Corrected standard errors (p values)

AIC

Model 1

(intercept)

5.035

0.136 (< 2e-16 ***)

0.151 (< 2e-16 ***)

748.1

log(BAI3)

0.667

0.098 (1.27e-11 ***)

0.104 (1.25e-10 ***)

(intercept)

5.732

0.136 (< 2e-16 ***)

0.111 (< 2e-16 ***)

locreg5

0.568

0.085 (1.89e-11 ***)

0.065 (< 2e-16 ***)

(intercept)

5.639

0.143 (< 2e-16 ***)

0.122 (< 2e-16 ***)

locreg25

2.917

0.338 (< 2e-16 ***)

0.465 (3.60e-10 ***)

(intercept)

2.925

0.241 (< 2e-16 ***)

0.342 (< 2e-16 ***)

RW3

0.059

0.008 (5.93e-15 ***)

0.013 (2.43e-06 ***)

(intercept)

16.104

0.890 (< 2e-16 ***)

0.934 (< 2e-16 ***)

log(relbai)

2.004

0.143 (< 2e-16 ***)

0.150 (< 2e-16 ***)

(intercept)

5.052

0.138 (< 2e-16 ***)

0.157 (< 2e-16 ***)

log(BAI3)

0.826

0.103 (1.31e-15 ***)

0.112 (2.08e-13 ***)

locreg5

0.846

0.109 (9.93e-15 ***)

0.113 (5.85e-14 ***)

(intercept)

4.917

0.146 (< 2e-16 ***)

0.160 (< 2e-16 ***)

log(BAI3)

0.924

0.117 (3.25e-15 ***)

0.129 (8.51e-13 ***)

locreg25

3.773

0.391 (< 2e-16 ***)

0.582 (9.02e-11 ***)

(intercept)

16.003

0.904 (< 2e-16 ***)

0.934 (< 2e-16 ***)

locreg5

0.431

0.135 (1.45e-03 **)

0.092 (3.00e-06 ***)

log(relbai)

1.965

0.145 (< 2e-16 ***)

0.149 (< 2e-16 ***)

(intercept)

15.680

0.912 (< 2e-16 ***)

0.913 (< 2e-16 ***)

locreg25

0.872

0.515 (9.00e-02)

0.540 (1.06e-01)

log(relbai)

1.915

0.151 (< 2e-16 ***)

0.148 (< 2e-16 ***)

(intercept)

15.646

1.071 (< 2e-16 ***)

1.192 (< 2e-16 ***)

log(BAI3)

0.104

0.140 (4.57e-01)

0.138 (4.54e-01)

log(relbai)

1.938

0.167 (< 2e-16 ***)

0.187 (< 2e-16 ***)

(intercept)

14.688

1.064 (< 2e-16 ***)

1.098 (< 2e-16 ***)

locreg5

0.577

0.145 (6.94e-05 ***)

0.096 (1.57e-09 ***)

log(BAI3)

0.319

0.150 (3.32e-02 *)

0.127 (1.22e-02 *)

log(relbai)

1.769

0.168 (< 2e-16 ***)

0.174 (< 2e-16 ***)

(intercept)

14.528

1.132 (< 2e-16 ***)

1.152 (< 2e-16 ***)

locreg25

1.290

0.572 (2.42e-02 *)

0.632 (4.13e-02 *)

log(BAI3)

0.244

0.154 (1.13e-01)

0.149 (1.01e-01)

log(relbai)

1.736

0.184 (< 2e-16 ***)

0.186 (< 2e-16 ***)

Model 2 Model 3 Model 4 Model 5 Model 6

Model 7

Model 8

Model 9

Model 10

Model 11

Model 12

760.1 723.0 652.7 548.1 704.2

664.8

541.2

546.9

549.5

538.8

546.4

Note: Shown are the estimated regression coefficients, uncorrected standard errors (p values), corrected standard errors (p values) using the infinitesimal jackknife variance estimator, and the AIC (Akaike Information Criterion) values. The uncorrected standard errors are nominal values assuming independent observations, the corrected standard errors account for the dependency of the data within individuals. Low values of AIC imply a better goodness-of-fit.

Chapter II

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Results Growth pa tterns of de ad and living trees Dying Norway spruce trees at the sites Davos, Bödmeren, and Scatlé were generally characterized by declining growth, i.e., negative growth trends for several years up to several decades prior to death. At the time of death, the growth level of most dead trees was low or very low (for examples, see Figs. 1a and 1b, Figs. 2a and 2b, Figs. 3a and 3b; cf. Bigler and Bugmann 2003b). Strongly negative growth trends in combination with relatively low growth levels often resulted in rapid tree death (see e.g. growth decrease of tree ‘SCA121’ prior to death, Fig. 3a), while slowly decreasing growth rates resulted in tree death after several decades only (see e.g. tree ‘BOA073’ in Fig. 2b, or tree ‘SCA131’ in Fig. 3b). The relative growth rate allowed us to differentiate between low growth levels of small trees, when relative growth rate is still high, and low growth levels of larger trees, when relative growth rate is low. This is exemplified by tree ‘SCA121’ (Fig. 3a), which survived the first growth decrease before 1750, but died after the growth decrease in the 1970s. Suppressed trees with a low growth level combined with a stationary growth trend were often able to recover, even after more than 100 years of suppression (see e.g. tree ‘BOA066’ in Fig. 2a, or the trees ‘SCA121’ and ‘SCA122’ in Fig. 3a). Inferences from mortality m odels The mortality models that were fitted using the Davos data set are shown in Table 2. The uncorrected, nominal standard errors were slightly biased. The application of the infinitesimal jackknife variance estimator corrected the standard errors. However, inference would not have been affected seriously without the adjustment (Table 2). When the corrected, actual standard errors are considered, model 1 to model 8 only include independent variables with very highly significant coefficients (p < 0.001). Models 9 to 12 had at least one variable with a p value > 0.01. The lowest AIC values were found for model 5 and models 8 to 12, with values ranging between 538.8 (model 11) and 549.5 (model 10). Mod el ver ification Regarding the first performance criterion (CCd) of the model verification (Table 3), model 5 and models 8 to 12 correctly predicted the status of 71.2 – 78.0% (model 11) of the dead trees. The highest number of living trees (CCl) was predicted correctly according to the models 1, 2, 3, 6, and 7 (83.3 – 93.3%), with model 2 achieving the highest value. According to the models 5 and 8 to 12, between 44.1% (model 8) and 55.9% (models 10 and 12) of all actually dead trees turned out to have a prediction error between 0 and 15 years (PEd,15). With model 1, 5.1% of all dead trees were predicted to die more than 60 years prior to the actual year of death (PEd,60), while in models 2 to 12, either no trees or one out of 59 trees died more than 60 years too early. In models 2, 3, 5, and 8 to 12, 0% (model 3) to 5% of all actually living trees was predicted to die more than 60 years prior to the last

56


measured year (PEl,60). Models 5 and 8 to 12 showed the highest overall performance, as indicated by the average ranks. Table 3. Verification of the models fitted to the Davos data set with the Davos data set (n dead = 59 trees, n alive = 60 trees). CCd

CCl

PEd,15

PEd,60

PEl,60

Average rank

Model 1

6.8 (12)

88.3 (3)

1.7 (12)

5.1 (12)

10.0 (10.5)

9.9

Model 2

11.9 (11)

93.3 (1)

5.1 (11)

1.7 (8)

3.3 (2)

6.6

Model 3

13.6 (10)

91.7 (2)

6.8 (10)

1.7 (8)

0.0 (1)

6.2

Model 4

50.8 (7)

75.0 (6.5)

35.6 (7)

0.0 (2.5)

11.7 (12)

7.0

Model 5

71.2 (5.5)

73.3 (10)

54.2 (3)

0.0 (2.5)

5.0 (5.5)

5.3

Model 6

20.3 (9)

83.3 (5)

13.6 (9)

1.7 (8)

10.0 (10.5)

8.3

Model 7

37.3 (8)

86.7 (4)

28.8 (8)

1.7 (8)

6.7 (9)

7.4

Model 8

72.9 (3.5)

73.3 (10)

44.1 (6)

0.0 (2.5)

5.0 (5.5)

5.5

Model 9

71.2 (5.5)

75.0 (6.5)

50.8 (4.5)

0.0 (2.5)

5.0 (5.5)

4.9

Model 10

74.6 (2)

73.3 (10)

55.9 (1.5)

1.7 (8)

5.0 (5.5)

5.4

Model 11

78.0 (1)

73.3 (10)

50.8 (4.5)

1.7 (8)

5.0 (5.5)

5.8

Model 12

72.9 (3.5)

73.3 (10)

55.9 (1.5)

1.7 (8)

5.0 (5.5)

5.7

Note: Shown are the five model performance criteria, which were defined as: CCd = percentage of correct classification of dead trees, CCl = percentage of correct classification of living trees, PEd,15 = percentage of actually dead trees with prediction error ≤ 15 years, PEd,60 = percentage of dead trees with prediction error > 60 years, PEl,60 = percentage of living trees with prediction error > 60 years. The values of the performance criteria were computed using a threshold of 0.975. The ranking for each performance criterion is indicated in brackets, with highest performances having lowest ranks. Tied ranks were averaged (Zar 1999).

Model val idation The performance criteria of the most reliable models (models 5 and 8 to 12) as validated with the data sets Bödmeren (Table 4) and Scatlé (Table 5) did not differ markedly to those of the verification with the Davos data set (Table 3). The percentage of correctly classified dead trees (CCd) increased or decreased slightly for these models at Bödmeren, while all CCd values increased at Scatlé. The percentage of correctly classified living trees (CCl) increased for these six models at Bödmeren, while they tended to decrease at Scatlé. The fraction of dead trees predicted with a low prediction error (PEd,15) was consistently higher at Davos than at the sites Bödmeren and Scatlé, except for model 8 at Scatlé, where the value slightly increased. At the site Davos, fewer dead trees were predicted to die more than 60 years prior to the actual year of death (PEd,60) than at the sites Bödmeren and Scatlé. Regarding the percentage of living trees that were predicted to die more than 60 years prior to the last measured year (PEl,60), the six models consistently achieved a higher performance at Bödmeren and a lower performance at Scatlé compared to Davos.

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Table 4. Validation of the models fitted to the Davos data set with the Bödmeren data set (n dead = 18 trees, n alive = 23 trees). CCd

CCl

PEd,15

PEd,60

PEl,60

Average rank

Model 1

27.8 (10)

78.3 (7.5)

0.0 (10.5)

27.8 (10)

21.7 (10.5)

9.7

Model 2

5.6 (11.5)

91.3 (2)

0.0 (10.5)

0.0 (1.5)

0.0 (4.5)

6.0

Model 3

5.6 (11.5)

100.0 (1)

0.0 (10.5)

0.0 (1.5)

0.0 (4.5)

5.8

Model 4

61.1 (7)

69.6 (11.5)

27.8 (4.5)

27.8 (10)

17.4 (9)

8.4

Model 5

72.2 (4)

82.6 (4)

27.8 (4.5)

11.1 (4.5)

0.0 (4.5)

4.3

Model 6

38.9 (9)

78.3 (7.5)

0.0 (10.5)

33.3 (12)

21.7 (10.5)

9.9

Model 7

44.4 (8)

69.6 (11.5)

11.1 (8)

27.8 (10)

26.1 (12)

9.9

Model 8

72.2 (4)

78.3 (7.5)

27.8 (4.5)

11.1 (4.5)

0.0 (4.5)

5.0

Model 9

72.2 (4)

82.6 (4)

27.8 (4.5)

11.1 (4.5)

0.0 (4.5)

4.3

Model 10

72.2 (4)

82.6 (4)

27.8 (4.5)

11.1 (4.5)

0.0 (4.5)

4.3

Model 11

72.2 (4)

73.9 (10)

27.8 (4.5)

16.7 (7.5)

0.0 (4.5)

6.1

Model 12

77.8 (1)

78.3 (7.5)

33.3 (1)

16.7 (7.5)

0.0 (4.5)

4.3

Note: Further explanations see Table 3.

Table 5. Validation of the models fitted to the Davos data set with the Scatlé data set (n dead = 20 trees, n alive = 22 trees). CCd

CCl

PEd,15

PEd,60

PEl,60

Average rank

Model 1

30.0 (9)

68.2 (7.5)

5.0 (10)

25.0 (8.5)

27.3 (10.5)

9.1

Model 2

10.0 (11)

95.5 (2)

5.0 (10)

5.0 (1.5)

0.0 (1.5)

5.2

Model 3

5.0 (12)

100.0 (1)

0.0 (12)

5.0 (1.5)

0.0 (1.5)

5.6

Model 4

70.0 (7)

63.6 (11.5)

25.0 (7.5)

35.0 (11.5)

27.3 (10.5)

9.6

Model 5

80.0 (4.5)

72.7 (4)

35.0 (5.5)

25.0 (8.5)

18.2 (6)

5.7

Model 6

25.0 (10)

68.2 (7.5)

5.0 (10)

15.0 (3)

27.3 (10.5)

8.2

Model 7

50.0 (8)

68.2 (7.5)

25.0 (7.5)

20.0 (5)

27.3 (10.5)

7.7

Model 8

85.0 (2.5)

68.2 (7.5)

45.0 (1.5)

25.0 (8.5)

18.2 (6)

5.2

Model 9

80.0 (4.5)

77.3 (3)

45.0 (1.5)

20.0 (5)

13.6 (3)

3.4

Model 10

85.0 (2.5)

68.2 (7.5)

40.0 (3.5)

25.0 (8.5)

18.2 (6)

5.6

Model 11

90.0 (1)

63.6 (11.5)

40.0 (3.5)

35.0 (11.5)

18.2 (6)

6.7

Model 12

75.0 (6)

68.2 (7.5)

35.0 (5.5)

20.0 (5)

18.2 (6)

6.0

Note: Further explanations see Table 3.

58


A comparison of the entire distribution of the prediction errors is illustrated for the models 4, 5, 8, and 11 in Fig. 4. The percentage of dead trees with high prediction errors (> 60 years) was higher for the sites Bödmeren and Scatlé than for Davos (Figs. 4a, 4c, 4e, 4g). According to the four selected models, relatively a high fraction of living and dead trees at the site Scatlé died more than 100 years prior to the last measured year. Model 4 had the highest fraction of dead and living trees with a prediction error > 100 years (Figs. 4a and 4b). On average over the three sites, model 4 predicted more dead trees to be alive (39.3%, see Fig. 4a) than the other three models (19.9 – 25.5%), while the highest classification accuracy of dead trees was achieved by model 11 (Fig. 4g). The classification accuracy for the living trees was on average highest for model 5 (76.2%, Fig. 4d) and lowest for model 4 (69.4%, Fig. 4b). Models 5, 8, and 11 predicted the time of tree death on average more precisely than model 4, i.e., more dead trees were predicted to die within 10 years prior to death (Figs. 4a, 4c, 4e, 4g).

Discussion Growth pa tterns of de ad and living tree s Low growth levels are often characteristic of stressed or dying trees, and it is well known that prolonged periods of strongly reduced stem growth increase a tree’s risk of dying (Kozlowski et al. 1991, Pedersen 1998, Monserud and Sterba 1999, Wyckoff and Clark 2002). In addition to growth rates that are commonly used to model tree mortality, the consideration of growth trends has been shown to be of high relevance in detecting growth patterns of dying trees (LeBlanc et al. 1992, LeBlanc 1996, Bigler and Bugmann 2003b). In the longitudinal approach presented here, we have shown that a third type of variable, the relative growth rate, is necessary to achieve a high model performance. In the study by Bigler and Bugmann (2003b), a considerable amount of the recent growth variability of the investigated trees in Davos could be related to the negative impact of competition, which affected living and dying trees in a similar manner. More than 50% of the recent growth variability of living trees was attributable to the influence of neighbor trees, while the competitive influence explained only 25% of the growth variability shortly before tree death. This implies that additional environmental factors may affect tree growth prior to death, but competition acts in the long term as an important predisposing factor (Manion 1981), as confirmed by several studies (Kenkel 1988, Szwagrzyk and Szewczyk 2001, Lussier et al. 2002). Fig. 4 (next page). Histograms of prediction errors for four selected models (models 4, 5, 8, and 11) fitted with the Davos data set and applied to the sites Davos (n dead = 59 trees, n alive = 60 trees), Bödmeren (n dead = 18 trees, n alive = 23 trees), and Scatlé (n dead = 20 trees, n alive = 22 trees). The class ‘alive’ contains dead or living trees that were predicted to be alive, the other classes contain prediction errors of dead or living trees that were predicted to be dead.

Chapter II

59

60


The ability of trees to adapt to low resource availability enables them to survive one or several periods of suppression (Canham 1985, 1990, Veblen et al. 1991, Szwagrzyk and Szewczyk 2001). Such suppression periods, defined here as periods of low growth level in combination with no growth trend, can last more than 100 years (Kaufmann 1996, Villalba and Veblen 1998). Trees are permanently exposed to the risk of dying, but the allocation of resources to either growth or defenses (Loehle 1988, Herms and Mattson 1992) allows them to minimize mortality risk. During periods of limited resources, slowgrowing, adapted trees may be favored over those with fast growth rates (Coley et al. 1985). Furthermore, suppressed trees may exploit the resources that become available when dominating neighbors die, due to e.g., pathogens, a windthrow, or other disturbances. Release effects in the growth curves of trees reflect a successful survival strategy of suppressed trees (see e.g. Fig. 3a). If the objective of a mortality model is to predict the timing of tree death, it is crucial to consider entire growth curves, including persistent periods of low growth, when calibrating and validating the model. Trade-offs of m ortali ty mod els The development of mortality models for predicting when trees die involves finding a suitable combination of predictor variables and optimizing the trade-offs between different model performance criteria. Notably, lowering or raising the threshold that we fixed at 0.975 affects the performance criteria in different ways. Increasing the threshold results in a higher percentage of correctly classified dead trees (CCd), whereas the other four performance criteria (CCl, PEd,15, PEd,60, PEl,60) tend to be influenced negatively. Decreasing the threshold results in an increased percentage of correctly classified living trees (CCl) and a lower percentage of dead and living trees that are predicted to die more than 60 years prior to the last measured year (PEd,60, PEl,60). The remaining two criteria (CCd, PEd,15) are influenced negatively. Thus, we conclude that using a single performance criterion would ignore the effects of the other performance criteria. Accordingly, our results strongly support the suggestion by Reynolds and Ford (1999) to use multiple criteria for model assessment. With regard to the performance of a model, there are different implications for dead trees that were erroneously predicted to be alive than for living trees that were misclassified as being dead (Monserud 1976), as discussed below. The probability curve of a dead tree that is predicted to be alive up to the year of death may have approached the fixed threshold, but without crossing it. If the growth curve of this dead tree could be continued, e.g., by autoregressive modeling, the tree might be predicted to die in some years (see Hasenauer et al. 2001), which would result in a (possibly small) negative prediction error. However, the mortality models presented in this study only compute positive prediction errors, which means that a dead tree either dies prior to the actual year of death, or it survives.

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61

Living trees that were erroneously predicted to be dead cannot recover according to the mortality model. However, in reality such stressed trees might die some years in the future (Bigler and Bugmann 2003b). Thus, the prediction error of a living tree that was predicted to die reflects a minimum prediction error, which is always smaller or equal to the true prediction error. To calculate the true prediction error, the tree would need to be observed until it dies. Inferences from mortality m odels Most standard errors in the mortality models were inflated after adjusting for the autocorrelation between observations using the jackknife variance estimator, but some standard errors actually decreased. In a study with correlated data, Lumley and Heagerty (1999) suggested that such patterns are not unusual. Specifically, they showed that some corrected standard errors of a Poisson regression model increased considerably compared to the uncorrected standard errors, whereas some decreased if the correlation was taken into account. Below, we refer to the corrected standard errors, but our inference is consistent between the uncorrected and the corrected standard errors. All models that contain only one independent variable (models 1 to 5 in Table 2) have p values smaller than 0.001. However, in combination with additional variables (models 6 to 12), some of the former variables turned out to be less significant. Among the variables that were used in combination with one or two other variables, i.e., all variables except for RW3, only the variables locreg5 and relbai proved to always have p values smaller than 0.001. The short-term growth trend variable (locreg5) and particularly the relative growth variable (relbai), which takes into account the current growth rate as well as the size of the tree, seem to have a high predictive power in this longitudinal approach of modeling tree mortality. If the model is to be evaluated with respect to inference, only models with significant variables (p < 0.05) should be considered, which is satisfied by models 1 to 8 and 11. Mod el per formance In the verification process of the twelve models, model 5 and models 8 to 12 performed best with respect to maximizing classification accuracy, which was balanced between CCd and CCl, and minimizing prediction errors (Table 3). The reliability of these models was supported by validating them with two independent data sets from Bödmeren and Scatlé (Tables 4 and 5, Fig. 4), which differ climatologically and geologically from the Davos area. Regarding the application of the mortality models to individual trees, it has to be considered that the models developed for Norway spruce should only be applied to trees larger than 10 cm DBH, since the minimum DBH in the calibration data set was 10 cm. Model 4 with RW3 as the single variable was used in our comparative analysis to demonstrate its qualities and shortcomings in a longitudinal study. Many mortality models, which are based on cross-sectional data, still rely on ring width as the only independent

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variable (see LeBlanc 1996). Compared to model 1 with BAI3 as the single independent variable, all performance criteria of model 4 achieved a better ranking, except for CCl and PEl,60 (Table 3). Yet, model 4 proved to have a lower overall performance than model 5 (relbai) (Table 3, Fig. 4). Therefore, we conclude that ring width alone is an insufficient predictor of the risk of tree mortality in longitudinal studies. The classification accuracy for dead and living trees for the two sites Bödmeren and Scatlé was comparable to the Davos site. Approximately 60% of the trees from Scatlé experienced a noticeable release effect after 1850 (see e.g. Fig. 3a), maybe owing to a disturbance such as a windthrow or bark beetle epidemics. The high number of dead and living trees at Scatlé with a prediction error of more than 100 years (Fig. 4) can be explained by the prolonged suppression period before the event around the year 1850. Thus, these findings suggest that the site-specific results for P. abies at the Davos site can be extended to other areas in the European Alps. Yet, persistent periods of suppression might affect the precision of the predictions, resulting in increased prediction errors. A recent study supports the substantially higher performance of the empirical mortality functions presented in this study compared to theoretical mortality functions that are currently implemented in forest gap models (Bigler and Bugmann 2003a). The theoretical mortality functions mainly failed for trees with suppressed growth, e.g., at the Scatlé site and, less pronounced, at the Bödmeren site.

Conclusions A novel approach is introduced to model tree mortality based on longitudinal data. Treering series of dead and living Norway spruce (Picea abies) trees were used to develop logistic regression models that calculate the mortality probability for every year of the life of a tree. The objectives of this study were to predict the time of tree death based on growth patterns, to define criteria for assessing model performance, to compare the different mortality models, and to validate the models against independent data sets. We draw the following major conclusions from our study: (1)

Longitudinal data in the form of entire growth curves should be considered in the model calibration process if the objective is to predict the time of individual tree death. Cross-sectional studies, which have been used extensively in the past, use one measurement per tree and thus are appropriate only for predicting tree status (dead or alive) at one single point in time, typically at the time when the last measured tree ring was formed.

(2)

Logistic mortality models including the relative growth rate (basal area increment divided by basal area) and the short-term growth trend over 5 years as independent variables proved to perform best with respect to inference and prediction.

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(3)

The assessment of model performance by considering multiple criteria is crucial for model evaluation. Relying on a single performance criterion can be highly misleading and may mask counteracting effects that need to be captured by complementary criteria.

(4)

The level of the threshold that converts the modeled mortality probability to a binary response (dead or alive) may affect some performance criteria in an undesirable way, if it is set inappropriately. Thus, the threshold has to be adjusted in order to achieve a trade-off between maximizing classification accuracy and minimizing prediction errors.

(5)

Validating the mortality models with independent data sets from geologically and climatologically different areas supports the reliability of our models for predicting tree death. The generality of the models gives us confidence that they can be applied to P. abies trees growing at a wide range of ecologically different sites.

This study is a further step towards an improvement of our understanding of the linkages between tree growth and tree mortality and, ultimately, towards an improved modeling of tree mortality. The potential and the feasibility of the methods have been demonstrated for one species. Studies with other species are in progress (Bigler and Bugmann, unpublished data), but obviously, we would need data on more species, and also on small trees (DBH < 10 cm) to corroborate the applicability of this kind of mortality models. We conclude that the longitudinal approach presented here for predicting the time of tree death should be applicable in several fields. An improved understanding of how tree growth and mortality are related may be relevant in forest management for assessing tree mortality risks at the individual tree and population levels, particularly in forest stands that are observed continually by forest managers. Another example that may hold even more promise deals with improving the realism and validity of forest gap models. The advantage of empirical mortality functions that were presented in this study over theoretical mortality functions that are commonly implemented in gap models has recently been shown by Bigler and Bugmann (2003a).

Acknowledgments We would like to thank Jim Lindsey at Limburgs University (Belgium) as well as Roman Lutz and Hansruedi Künsch at the Seminar for Statistics at ETH Zurich (Switzerland) for their statistical advice. Andi Rigling at the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL, Birmensdorf Switzerland) assisted us during the laboratory analyses. We also would like to thank the field crew (Kathrin Saner, Dani Gysin) for their support, and Peter Weisberg (Mountain Forest Ecology, Zurich Switzerland) for his critical review on an earlier version of this article.

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Pedersen, B. S. 1999. The mortality of midwestern overstory oaks as a bioindicator of environmental stress. Ecological Applications 9:1017-1027. Pedersen, B. S., and B. McCune. 2002. A non-invasive method for reconstructing the relative mortality rates of trees in mixed-age, mixed-species forests. Forest Ecology and Management 155:303-314. Peet, R. K., and N. L. Christensen. 1987. Competition and tree death. BioScience 37:586-595. Reynolds, J. F., and E. D. Ford. 1999. Multi-criteria assessment of ecological process models. Ecology 80:538-553. Rinn, F. 1996. TSAP - Reference manual. Version 3.0. Rinntech. Heidelberg. Schweingruber, F. H. 1988. Tree rings: basics and applications of dendrochronology. Kluwer Academic Publishers, Dordrecht. Schweingruber, F. H. 1996. Tree rings and environment: dendroecology. Verlag Paul Haupt, Bern. Szwagrzyk, J., and J. Szewczyk. 2001. Tree mortality and effects of releases from competition in an oldgrowth Fagus-Abies-Picea stand. Journal of Vegetation Science 12:621-626. Veblen, T. T. 1986. Age and size structure of subalpine forests in the Colorado Front Range. Bulletin of the Torrey Botanical Club 113:225-240. Veblen, T. T., K. S. Hadley, M. S. Reid, and A. J. Rebertus. 1991. Methods of detecting past spruce beetle outbreaks in Rocky Mountain subalpine forests. Canadian Journal of Forest Research 21:242-254. Venables, W. N., and B. D. Ripley. 1999. Modern applied statistics with S-PLUS. Springer-Verlag, New York. Villalba, R., and T. T. Veblen. 1998. Influences of large-scale climatic variability on episodic tree mortality in northern Patagonia. Ecology 79:2624-2640. Wilkinson, G. N., and C. E. Rogers. 1973. Symbolic description of factorial models for analysis of variance. Applied Statistics 22:392-399. Wyckoff, P. H., and J. S. Clark. 2000. Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches. Canadian Journal of Forest Research 30:156-167. Wyckoff, P. H., and J. S. Clark. 2002. The relationship between growth and mortality for seven co-occuring tree species in the southern Appalachian Mountains. Journal of Ecology 90:604-615. Yao, X. H., S. J. Titus, and S. E. MacDonald. 2001. A generalized logistic model of individual tree mortality for aspen, white spruce, and lodgepole pine in Alberta mixedwood forests. Canadian Journal of Forest Research 31:283-291. Zar, J. H. 1999. Biostatistical analysis, fourth edition. Prentice-Hall, Upper Saddle River, New Jersey.

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Chapter III

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Chapter III Assessing the performance of theoretical and empirical tree mortality models using tree-ring series

Submitted as: Bigler, C., and H. Bugmann. 2003. Assessing the performance of theoretical and empirical tree mortality models using tree-ring series. Ecological Modelling. Mountain Forest Ecology, Department of Forest Sciences, Swiss Federal Institute of Technology (ETH), ETH-Zentrum, CH-8092 Zurich, Switzerland

Manuscript re-submitted after moderate revision in August 2003. Abstract – Successional dynamics of forests under current and changed climate are often investigated using gap models, a subset of forest succession models that simulate establishment, growth, and mortality of trees. However, the mortality submodels of gap models are largely based on theoretical assumptions, and have not been tested in detail. In the present study, we compared the performance of a range of theoretical mortality functions (TMFs) that are commonly used in gap models with several empirical mortality functions (EMFs) that were derived using logistic regression from growth patterns of treering series as predictor variables. Data from dead and living Norway spruce (Picea abies (L.) Karst.) trees from subalpine forests at three study sites in Switzerland were used to this end. Three of the four EMFs consistently performed better at all three sites, while three of the four TMFs performed worse than the remaining mortality functions. At one site, these three EMFs correctly classified 71 – 78% of the dead trees (48 – 72% for the three TMFs), and 73% (49 – 64%) of the living trees. 44 – 54% (21 – 25%) of the dead trees were predicted to die within 15 years prior to death. 0 – 2% (7 – 10%) of the dead trees and 5% (19 – 31%) of the living trees were predicted to die more than 60 years prior to the last measured year. We conclude that, unless the parameters of the TMFs are optimized for individual species, the TMFs are not appropriate to predict the time of tree death, in spite of their widespread use. A substantial change in the simulated forest succession is to be expected if the currently implemented TMFs in gap models are replaced by species-specific EMFs.

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Assessing the performance of theoretical and empirical tree mortality models

Key words Tree mortality; gap models; mortality functions; prediction; validation; model performance

Introduction Long-term forest succession, such as the dynamics of stand structure, biomass, and species composition under current and changed climate are commonly investigated using forest succession models (cf. Shugart 1984). In this context, the issue of the potential effects of climate change on forest dynamics is of increasing concern (Gates 1990, Bugmann 1994, Loehle and LeBlanc 1996, Beniston and Innes 1998, Lindner et al. 1999, Bolliger et al. 2000, Houghton et al. 2001, Theurillat and Guisan 2001). Predicting the impacts of natural or anthropogenic climate changes on forest succession requires (i) a sound understanding of the fundamental relationships between environmental factors, establishment, tree growth, and mortality (Foster and LeBlanc 1993, Pedersen 1999), and (ii) tools (i.e., models) that synthesize this information and thus provide reliable projections of forest responses under current and changed climates (Shugart et al. 1992, Loehle and LeBlanc 1996, Bugmann and Solomon 2000). Forest gap models, a subset of forest succession models (Shugart and West 1980), have been formulated and developed since 1969. These models simulate the establishment, growth, and mortality of individual trees on patches of 100 – 1000 m2 as a function of abiotic factors (e.g., temperature, soil water availability, nutrients), and species-specific, biotic factors (e.g., competition, age) (Shugart 1984, Urban and Shugart 1992, Botkin 1993, Bugmann 2001). Over the past decades, the early gap models JABOWA (Botkin et al. 1972) and FORET (Shugart 1984) have been improved considerably (cf. review by Bugmann 2001). However, two of the main shortcomings of gap models are the poor parameterization and the lack of testing of the mortality submodels (Loehle and LeBlanc 1996, Hawkes 2000, Keane et al. 2001). These submodels are largely based on theoretical assumptions, though, improving the simulation of tree mortality in gap models requires species-specific, empirically derived formulations (Keane et al. 2001). As a critical issue, Hawkes (2000) suggests to test the mortality algorithms of succession models against field-measured mortality data. Validation procedures for mortality functions that are developed to predict the timing of tree death have recently been introduced by Bigler and Bugmann (2003b), using multiple model performance criteria. Most current gap models simulate tree mortality as a combination of (i) an intrinsic mortality (tree-level process), (ii) a growth-dependent mortality (stand-level process), and occasionally (iii) an exogenous mortality (landscape process) (Keane et al. 2001).

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The intrinsic mortality is usually formulated as a species-specific, constant probability of death, which is dependent only on the maximum longevity of a tree species. It accounts for random mortality factors that kill single trees such as lightning strikes, non-epidemic pathogens, or windthrow. The growth-dependent mortality is related to competition and climate variability, and is commonly represented as a stochastic function of growth increment at breast height. The parameters of the first mortality algorithm used in JABOWA, which were often adopted in subsequent gap models, were based on theoretical assumptions without any empirical support (Hawkes 2000). Some follow-up mortality formulations emerged from this initial, simple formulation, which tried to more closely reflect known mortality processes (cf. Keane et al. 2001). The exogenous mortality is included in some models only, and is used to incorporate the effects of large-scale disturbances such as fire, severe windstorms, major pathogen epidemics, or harvesting. Recent, promising advances in modeling growth-dependent tree mortality are mainly based on species-specific, empirical relationships between mortality and growth (Guan and Gertner 1991b, a, Pacala et al. 1993, Kobe et al. 1995, Kobe 1996, Kobe and Coates 1997, Monserud and Sterba 1999, He and Alfaro 2000, Wyckoff and Clark 2000, Hasenauer et al. 2001, Bigler and Bugmann 2003b). Implementing these empirically derived mortality functions or altering existing theoretical mortality algorithms in gap models may result in considerable changes of modeled succession (Hawkes 2000, Keane et al. 2001), as documented for several gap models (Pacala et al. 1996, Bugmann 2001, Wyckoff and Clark 2002). What is lacking, however, is an assessment of the relative performance of the various mortality formulations that have been or could be implemented in forest succession models. Therefore, the objective of the present study is to compare the performance of a range of theoretical mortality functions commonly used in gap models, and empirical mortality functions derived from dendrochronological time series (Bigler and Bugmann 2003b). The mortality functions are applied to predict the time of tree death using measured tree-ring data of dead and living Norway spruce (Picea abies) trees from the European Alps.

Material & methods Study sites and sampl ing of trees Dead and living trees of Norway spruce (Picea abies (L.) Karst.), a dominant species in many forests of the European Alps, were sampled in the three subalpine study areas Davos, Bödmeren, and Scatlé (Switzerland). The three areas differ considerably with respect to climatic and geological conditions. Only trees with a minimum DBH (diameter at breast height) of 10 cm were considered. From each tree, two cores were taken with an incre-

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ment borer at breast height. The ring widths (RW) of the cores were measured, cross-dated (Fritts 1976), and converted to basal area increment (BAI). The final data set contained 59 dead and 60 living trees from the Davos area, 18 dead and 23 living trees from Bödmeren, and 20 dead and 22 living trees from Scatlé. For a more detailed description of the study sites and the field sampling, see Bigler and Bugmann (2003a). The Davos data set was used to fit and verify the empirical mortality models (Bigler and Bugmann 2003b) and to validate the theoretical mortality functions. The data sets Bödmeren and Scatlé were used to validate the empirical and theoretical mortality functions. Empirical mortality functions Four deterministic, empirical mortality functions were selected based on the analyses by Bigler and Bugmann (2003b). The parameters were fitted using logistic regression (Hosmer and Lemeshow 1989, Collett 1991): [1]

Pr(Y i,t = 1 | X i,t ) =

1 1 + exp (Xi,t b ) -1

with Yi,t = status of tree i at time t (Y = 1 means the tree is alive, Y = 0 means the tree is † dead). Pr(Yi,t = 1|Xi,t) is a survival probability in the interval [0, 1], and Xi,tb is a linear combination of the independent variables (X) and the regression coefficients (b). Time series of growth-related variables, derived from BAI or RW of individual trees, were considered as independent variables (for a detailed description, see Bigler and Bugmann 2003a, 2003b). Standard fitting methods were used to estimate the regression coefficients (Collett 1991). The infinitesimal jackknife variance estimator (Chernick 1999, Lumley and Heagerty 1999) was applied to estimate the variances, thus accounting for the autocorrelation in the data (for further details, see Bigler and Bugmann 2003b). In the four EMFs, a tree is predicted to die as soon as the survival probability Pr(Yi,t=1|Xi,t) falls below a threshold, which was fixed at 0.975 (Bigler and Bugmann 2003b). Note that the application of the functions is illustrated for one particular tree in Fig. 1. [2]

EMF1: Pr(Y i,t = 1 | X i,t ) =

1 1 + exp [ 2.925 + 0.059 ¥ RW 3,i,t ] -1

where RW3 (1/100 mm/year) is the average of the last three ring widths (Fig. 1b). † 1 [3] EMF2: Pr(Y i,t = 1 | X i,t ) = -1 1 + exp [16.104 + 2.004 ¥ log(relbai i,t )] where log(relbai) is the log-transformed ratio of BAI (basal area increment; cm2/year) and 2 BA (basal † area; cm ) (Fig. 1b).

Chapter III

Fig. 1. Application of empirical mortality functions (EMFs) and theoretical mortality functions (TMFs) to growth curve of single, dead tree. The last ring of tree ‘DAA029’ was formed in 1995. Circles in (b) – (e) indicate the predicted year of death according to the corresponding mortality function, the dots in (d) and (e) indicate one simulation of a uniformly distributed random number. The probability scale is indicated between 0.9 – 1.0 for the EMFs in (b) and (c), and between 0 – 1 for the TMFs in (d) and (e). (a) Measured ring widths, 10% curve of theoretical maximum growth (parameterized for Norway spruce: G = 171 cm/yr, Hmax = 58 m, Dmax = 210 cm; see Moore 1989) used in TMFrel, 0.3 cm threshold used in TMFstress and TMFsev, and 0.1 cm threshold used in TMFabs. The predicted year of death is (b) 1981 for EMF1 (prediction error = 14 years), and 1960 for EMF2 (prediction error = 35 years), (c) 1960 for EMF3 (prediction error = 35 years), and 1963 for EMF4 (prediction error = 32 years), (d) tree survives according to TMFabs, 1981 for TMFrel (prediction error = 14 years), (e) 1967 for TMFstress (prediction error = 28 years), and 1948 for TMFsev (prediction error = 47 years).

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[4]


EMF3:

Pr(Y i,t = 1 | X i,t ) =

1 1 + exp [16.003 + 0.431¥ locreg 5,i,t + 1.965 ¥ log(relbai i,t )]

-1

where locreg5 is the slope of a local, linear regression (locreg) over the last five years, and log(relbai) is the log-transform of the ratio of BAI and BA (Fig. 1c). † [5]

EMF4:

Pr(Y i,t = 1 | X i,t ) =

†

1 1 + exp[14.688 + 0.577 ¥ locreg 5,i,t + 0.319 ¥ log(BAI 3,i,t ) + 1.769 ¥ log(relbai i,t )]

where locreg5 is the slope of a local, linear regression (locreg) over the last five years, log(BAI3) is the log-transformed BAI over the last three years, and the relative growth variable log(relbai) is the log-transform of the ratio of BAI and BA (Fig. 1c).

Theoretical mor tality functions The following four stochastic, theoretical mortality functions (TMFs) were selected. In all these models, a tree dies if a uniformly distributed random number (in the interval [0, 1]) is larger than the survival probability Pr(Yi,t = 1). The ring width of the previous year is expressed as RWi,t-1. Again, an example of the application of the TMFs to a single tree is shown in Fig. 1. The first function, TMFabs, was introduced in JABOWA (Botkin et al. 1972). It was based on the observation that slow-growing (often, suppressed) trees have an increased mortality probability. In the model, this was taken into account by assuming an absolute, age- and species-independent threshold (Fig. 1d): the survival probability drops to 0.632 whenever the annual diameter increment falls below a threshold of 0.1 mm (see Fig. 1a; Eq. 6). The reason for this parameter value was that Botkin et al. (1972) considered it highly unlikely that a tree would survive 10 consecutive years of such low growth ([0.632]10 ≈ 0.01). [6]

TMFabs: Pr(Yi,t = 1 | RWi,t < 0.1 mm) = 0.632, Pr(Yi,t = 1 | RWi,t ≥ 0.1 mm) = 1

Note that the threshold in TMFabs is not species-specific, and the increased mortality acts as soon as low growth occurs. For the FORENA model, Solomon (1986) changed this formulation to improve these two aspects by (1) introducing a lag between low growth and the stress-induced mortality, and (2) considering the realized growth rate relative to the

-1

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maximum species-specific growth rate at the respective age of the tree (Eq. 7). Solomon (1986) assumed that a tree has a lower survival probability (Pr[Yi,t = 1] = 0.632) as soon as the annual growth increment of two consecutive years is below 10% of the age-specific theoretical maximum growth (see Figs. 1a and 1d; Moore 1989). To calculate the theoretical maximum growth of Norway spruce, we adopted the parameterization of the species used in the gap model FORCLIM 2.9.1 (Bugmann and Solomon 2000). Each measured tree ring was assigned to the corresponding age corrected by the estimated number of missing rings between pith and the first tree ring, which resulted from imprecise coring. Trees with more than 10 missing rings between pith and first measured tree ring were excluded from the data set, i.e., only trees with a reliable estimation of age were considered. [7]

TMFrel: Pr(Yi,t = 1 | RWi,t Ÿ RWi,t-1 < 10% maximum growth) = 0.632, Pr(Yi,t = 1 | RWi,t Ÿ ⁄ RWi,t-1 ≥ 10% maximum growth) = 1

Keane et al. (1996) intended to further improve Solomon’s (1986) formulation by taking into account that different tree species have very different capabilities of surviving periods of low growth. That is, the mortality risk does not increase to 99% after 10 years of slow growth for all species, and one year of vigorous growth after a stress period may not be sufficient to reduce the mortality risk to “normal” levels. We consider these ideas through TMFstress, which is a slightly modified version of the mortality algorithm from FIRE-BGC (Keane et al. 1996) (Fig. 1e; Eq. 8). A stress counter (SC) is incremented by 1 (= ∆SCi,t) every time when RWi,t < threshold (see Fig. 1a). Stressed trees become healthy (SC = 0) after experiencing three consecutive years of RW above the threshold. The stress counter is used in a three-parameter Weibull probability function with the parameters being dependent on the shade tolerance of the tree species. We assumed P. abies to be a medium shade tolerant tree species (Bugmann 1994, Ellenberg 1996) (parameters in Eq. 8: a = 0.15, b = 0.15, c = 2.5; threshold = 0.3 mm). [8]

TMFstress: Pr(Yi,t = 1) = 1 – a [1 - exp(-b SCi,t)]c

Bugmann (2001) tried to further improve the realism of the Keane et al. (1996) formulation. The reasoning was that a simple distinction between “stress” and “no stress” is not entirely satisfactory; rather, the severity of the stress should be important as well (e.g., growth just below the threshold should imply a different mortality risk compared to nearzero growth in a given year). Hence, one year of severe stress may weigh as much as several years of light stress with respect to determining the stress-induced mortality probability. Therefore, our TMFsev (Eq. 9) is based on TMFstress, but it accounts for stress severity (Fig. 1e), as follows: the stress counter SC is incremented by a linearly interpolated value ( DSC i,t = 10 ¥ [ threshold - RW i,t ] / threshold ) in the interval (0, 10], when RWi,t < threshold. Otherwise, the same parameterization as for TMFstress holds. †

76

[9]


TMFsev: Pr(Yi,t = 1) = 1 – a [1 - exp(-b SCi,t)]c

Model per formance cri teria The four EMFs and four TMFs were compared against the measured Norway spruce data based on multiple performance criteria (Reynolds and Ford 1999). Two classification accuracy criteria (CC) and three prediction error criteria (PE) were considered, as defined in Bigler and Bugmann (2003b). In each year, the mortality functions were applied to the corresponding growth variables of individual dead and living trees from the three study sites Davos, Bödmeren, and Scatlé. Due to the stochasticity of the TMFs, simulation runs over R = 200 repetitions were averaged. First, we assessed how many dead trees were correctly predicted to be dead (CCd) and how many living trees were correctly predicted to be alive (CCl). Second, we calculated the prediction error for dead and living trees as the difference between the last measured year and the predicted year of death. The last measured year was defined as the year when the last tree ring was formed. We calculated the percentage of dead trees that were predicted to die no more than 15 years prior to actual death (PEd,15), the percentage of dead trees that were predicted to die more than 60 years prior to death (PEd,60), and the percentage of living trees that were predicted to die more than 60 years prior to the year of sampling (PEl,60).

Results Dis tribution of predi ction errors The distributions of the prediction errors of the EMFs and TMFs are summarized for the three sites in Fig. 2, Fig. 3, and Fig. 4. On average over the three sites, the highest percentage of correctly classified dead trees in the class ‘0 – 10’ resulted from EMF4 (33.7%), EMF3 (33.1%), and EMF2 (31.5%), and the lowest fraction of dead trees that were erroneously predicted to be alive was achieved by EMF4 (19.9%), TMFrel (20.9%), and EMF3 (23.3%). At all three sites, the highest correct classification of living trees resulted for the models EMF2 (76.2%), EMF3 (73.3%), and TMFabs (73.2%). The highest mean percentage of dead trees that were predicted to die more than 100 years prior to death resulted from TMFrel (35.4%), TMFsev (33.3%), and TMFstress (28.8%). The highest number of living trees that were predicted to die more than 100 years prior to the last measured year resulted from the models TMFrel (35.3%), TMFsev (34.9%), and TMFstress (28.9%), with a particularly high fraction at Scatlé (Fig. 4b).

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Fig. 2. Distribution of prediction errors for (a) dead trees and (b) living trees, applying theoretical mortality functions (TMFs) and empirical mortality functions (EMFs) to the Davos data set (n dead = 59 trees, n alive = 60 trees; reduced data set of trees with reliably estimated age only for TMFrel with n dead = 43 trees, n alive = 47 trees). The class ‘alive’ contains the fraction of trees that were predicted to be alive, the other classes contain the fraction of trees with the corresponding prediction errors.

Mod el per formance A comparison of the five model performance criteria calculated for the EMFs and TMFs with the Davos data set is shown in Table 1. The highest percentage of correctly classified dead trees (CCd) was achieved by TMFrel, EMF2, EMF3, and EMF4 (range: 71.2 – 78.0%). TMFabs and all four EMFs showed a higher correct classification rate of the living trees (CCl; 73.3 – 79.0%) than the other three TMFs. The highest precision in predicting the time of tree death (PEd,15) resulted from EMF2, EMF3, and EMF4 (44.1 – 54.2%). Only a low fraction of dead trees was predicted to die more than 60 years prior to the last measured year (PEd,60) by TMFabs and all four EMFs (0.0 – 1.7%), while TMFabs, EMF2, EMF3, and EMF4 showed the best performance with respect to the same criterion for the living trees (PEl,60; 5.0 – 7.9%).

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Fig. 3. Distribution of prediction errors for (a) dead trees and (b) living trees, applying theoretical mortality functions (TMFs) and empirical mortality functions (EMFs) to the Bödmeren data set (n dead = 18 trees, n alive = 23 trees; reduced data set of trees with reliably estimated age only for TMFrel with n dead = 12 trees, n alive = 15 trees). Further explanations see Fig. 2.

At the Bödmeren site (Table 2), the best performance with regard to the fraction of correctly classified dead trees (CCd) was achieved by TMFrel, TMFsev, EMF2, EMF3, and EMF4 (range: 72.2 – 74.4%), while for the living trees (CCl), the highest percentage was found for TMFabs, EMF2, EMF3, and EMF4 (73.9 – 82.6%). As in Davos, all four EMFs predicted more dead trees to die within a maximum of 15 years prior to actual death (PEd,15; 27.8%) than the TMFs. The lowest fraction of dead or living trees that were predicted to die more than 60 years prior to the last measured year (PEd,60, PEl,60) resulted from TMFabs, EMF2, EMF3, and EMF4. At the Scatlé site (Table 3), TMFrel, TMFstress, TMFsev, EMF3, and EMF4 were most reliable with respect to correctly classifying the dead trees (CCd; 84.4 – 91.2%). As in Davos, TMFabs and the four EMFs proved to behave best regarding the classification of living trees (CCl; 63.6 – 72.7%). With respect to the remaining three performance criteria (PEd,15, PEd,60, PEl,60), TMFabs and all four EMFs showed a better performance than the remaining TMFs.

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With respect to the overall performance (average ranks in Tables 2, 3, and 4), EMF2, EMF3, and EMF4 consistently performed best at all three sites, while TMFrel, TMFstress, and TMFsev performed worst.

Fig. 4. Distribution of prediction errors for (a) dead trees and (b) living trees, applying theoretical mortality functions (TMFs) and empirical mortality functions (EMFs) to the Scatlé data set (n dead = 20 trees, n alive = 22 trees; reduced data set of trees with reliably estimated age only for TMFrel with n dead = 17 trees, n alive = 16 trees). Further explanations see Fig. 2.

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Table 1. Comparison of performance criteria of TMFs (theoretical mortality functions) and EMFs (empirical mortality functions) for the Davos area. Model

CCd

CCl

PEd,15

PEd,60

PEl,60

Average rank

TMFabs

44.2 (8)

79.0 (1)

32.2 (5)

1.3 (4)

7.9 (4)

4.4

TMFrel

71.7 (3)

48.6 (8)

24.6 (6)

10.0 (8)

31.3 (8)

6.6

TMFstress

48.2 (7)

64.3 (6)

21.4 (8)

6.7 (6)

18.5 (6)

6.6

TMFsev

59.1 (5)

59.0 (7)

24.5 (7)

9.6 (7)

21.3 (7)

6.6

EMF1

50.8 (6)

75.0 (2)

35.6 (4)

0.0 (2)

11.7 (5)

3.8

EMF2

71.2 (4)

73.3 (4)

54.2 (1)

0.0 (2)

5.0 (2)

2.6

EMF3

72.9 (2)

73.3 (4)

44.1 (3)

0.0 (2)

5.0 (2)

2.6

EMF4

78.0 (1)

73.3 (4)

50.8 (2)

1.7 (5)

5.0 (2)

2.8

Note: Shown are the five model performance criteria using the Davos data set (n dead = 59 trees, n alive = 60 trees; reduced data set for TMFrel with n dead = 43 trees, n alive = 47 trees). The criteria were defined as: CCd = percentage of correct classification of dead trees, CCl = percentage of correct classification of living trees, PEd,15 = percentage of actually dead trees with prediction error ≤ 15 years, PEd,60 = percentage of dead trees with prediction error > 60 years, PEl,60 = percentage of living trees with prediction error > 60 years. The values for the EMF were computed using a threshold of 0.975. The ranking for each performance criterion is indicated in brackets, with highest performances having lowest ranks. Tied ranks were averaged (Zar 1999).

Discussion Qua litati ve ass essment of m ortali ty functions A qualitative assessment of the time series of survival probabilities derived from the empirical and theoretical mortality functions (EMFs and TMFs, respectively) reveals that the TMFs generally show simpler patterns (Figs. 1d and 1e), while the EMFs are more sensitive to small changes of the growth rate (Figs. 1b and 1c). One reason for this difference is the pseudo-probabilistic nature of the TMFs, which are based on theoretical considerations concerning the decrease of vitality in stress periods, whereas the EMFs rest upon statistical, species-specific relationships between tree status (dead or alive) and one or several growth patterns as predictor variables. A related reason is that within the group of the TMFs, thresholds are applied to measured ring widths before survival probabilities are derived, while in the group of the EMFs, the thresholds are applied to survival probabilities. Yet, some features concerning the calculated survival probabilities are common to all mortality functions, as illustrated by the tree ‘DAA029’ (see Fig. 1): all TMFs and EMFs identify the years or some of the years within 1960 – 1963 and 1980 – 1987 as periods of increased mortality risk (Figs. 1b – 1e). Also, the stress release after ca. 1986 is shown by

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all models with increased survival probabilities, however with some delay by TMFstress and TMFsev (Fig. 1e). We infer that all mortality functions qualitatively agree about “stress” versus “non-stress” periods, but their quantitative predictions diverge strongly. Table 2. Comparison of performance criteria of TMFs (theoretical mortality functions) and EMFs (empirical mortality functions) for the Bödmeren area.

Model

CCd

CCl

PEd,15

PEd,60

PEl,60

Average rank

TMFabs

53.3 (8)

74.7 (3)

18.5 (5)

18.7 (4)

13.7 (4)

4.8

TMFrel

74.4 (1)

45.9 (8)

18.4 (6)

44.9 (8)

45.5 (8)

6.2

TMFstress

63.9 (6)

58.8 (6)

9.8 (8)

36.5 (6)

28.5 (6)

6.4

TMFsev

73.3 (2)

50.0 (7)

11.8 (7)

43.9 (7)

36.9 (7)

6.0

EMF1

61.1 (7)

69.6 (5)

27.8 (2.5)

27.8 (5)

17.4 (5)

4.9

EMF2

72.2 (4)

82.6 (1)

27.8 (2.5)

11.1 (1.5)

0.0 (2)

2.2

EMF3

72.2 (4)

78.3 (2)

27.8 (2.5)

11.1 (1.5)

0.0 (2)

2.4

EMF4

72.2 (4)

73.9 (4)

27.8 (2.5)

16.7 (3)

0.0 (2)

3.1

Note: Shown are the five model performance criteria using the Bödmeren data set (n dead = 18 trees, n alive = 23 trees; reduced data set for TMFrel with n dead = 12 trees, n alive = 15 trees). For further explanations see Table 1.

Table 3. Comparison of performance criteria of TMFs (theoretical mortality functions) and EMFs (empirical mortality functions) for the Scatlé area. Model

CCd

CCl

PEd,15

PEd,60

PEl,60

Average rank

TMFabs

71.8 (7)

66.1 (3)

25.9 (4)

31.2 (3)

25.3 (4)

4.2

TMFrel

91.2 (1)

27.3 (7)

10.0 (8)

68.2 (8)

56.6 (7)

6.2

TMFstress

84.4 (5)

29.9 (6)

11.7 (6)

60.7 (6)

48.8 (6)

5.8

TMFsev

89.0 (3)

24.8 (8)

11.2 (7)

65.0 (7)

57.0 (8)

6.6

EMF1

70.0 (8)

63.6 (4.5)

25.0 (5)

35.0 (4.5)

27.3 (5)

5.4

EMF2

80.0 (6)

72.7 (1)

35.0 (3)

25.0 (1.5)

18.2 (2)

2.7

EMF3

85.0 (4)

68.2 (2)

45.0 (1)

25.0 (1.5)

18.2 (2)

2.1

EMF4

90.0 (2)

63.6 (4.5)

40.0 (2)

35.0 (4.5)

18.2 (2)

3.0

Note: Shown are the five model performance criteria using the Scatlé data set (n dead = 20 trees, n alive = 22 trees; reduced data set for TMFrel with n dead = 17 trees, n alive = 16 trees). For further explanations see Table 1.

82


TMFabs performs relatively well for the investigated P. abies trees compared to the remaining three TMFs. However, one would expect its performance to be worse in two cases: (i) species that are tolerant of very low growth, or species that are able to survive long periods of suppression (Canham 1985, 1990, Kaufmann 1996, Schweingruber 1996, Szwagrzyk and Szewczyk 2001), which would result in low CCl, high PEd,60, and high PEl,60, and (ii) species that are intolerant of low growth and thus have a high risk of dying when growth falls below a threshold that is substantially higher than 0.1 mm (for examples, see Buchman et al. 1983, Guan and Gertner 1991a, Kobe et al. 1995, Kobe 1996, Wyckoff and Clark 2000), resulting in low CCd and low PEd,15. Thus, we conclude that TMFabs should only be used with species-specific thresholds. We found that the mortality functions TMFstress and TMFsev are quite sensitive regarding the choice of an appropriate combination of the growth threshold and the parameterization of the Weibull function (results not shown), but they behave least sensitive with regard to small changes of growth compared to TMFabs and TMFrel (Figs. 1d and 1e). The dominant effect of the inclusion of stress severity in TMFsev is an earlier decrease of the survival probability following stress compared to TMFstress, whereas after many stress years, both TMFs attain the same level of the survival probability (Fig. 1e). Many EMFs in the literature are based on RW alone, although its use in mortality studies has been criticized (LeBlanc et al. 1992, LeBlanc 1996, Pedersen 1998, Keane et al. 2001, Bigler and Bugmann 2003b). Trees that are suppressed when young are likely to be predicted to die too early by EMF1, although BAI as the single independent variable has similar effects, even for non-suppressed trees (see Bigler and Bugmann 2003b). Therefore, our results suggest that besides RW or BAI, tree size should be taken into account in tree mortality models. This can be accomplished by considering the relative growth increment, log(relbai). The functions EMF2, EMF3, and EMF4 have a very similar behavior with respect to the resulting survival probabilities (Figs. 1b and 1c). The strong predictive power of log(relbai) as independent variable in mortality models that aim at predicting the time of tree death has been shown by Bigler and Bugmann (2003b). Our main criticism regarding the TMFs does not concern the relatively simple structure of the mortality algorithms, but rather that a thorough examination of their benefits and shortcomings has not been addressed to date (Hawkes 2000). We suggest that a detailed analysis of the success or failure of any mortality algorithm is a crucial prerequisite for its implementation in a forest model (Korzukhin et al. 1996). For example, adapting the TMF parameters for individual species, be it the absolute threshold in TMFabs, the relative threshold in TMFrel, or the parameters in TMFstress or TMFsev, and the validation of these formulations against e.g. tree-ring series or forest inventory data would very likely lead to improved mortality predictions. We acknowledge that our comparison of TMFs with EMFs did not include a parameter fitting procedure for the TMFs, whereas the parameters of the EMFs were optimized for the present application. Thus, it is conceivable that optimized TMFs may perform as well

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as the EMFs. As they were used in the past in many modeling studies, however, they were probably subject to considerable error. The process of iteratively changing the parameters of mortality functions and verifying the results would lead to an optimization of the trade-offs between the different model performance criteria (Bigler and Bugmann 2003b). Grouping the tree species into functional groups with similar shade tolerance and growth-mortality relationships would facilitate the adaptation of the TMFs for many tree species, particularly for those species where data are lacking (Franklin et al. 1987). Quantitative model comparis on At all three sites, the three mortality functions EMF2, EMF3, and EMF4 showed the best average performance, as expressed by their low average ranks (Tables 1 – 3), while the three mortality functions TMFrel, TMFstress, and TMFsev showed the poorest performance. The models EMF2, EMF3, and EMF4 assign dead and living trees approximately equally well to the correct group (CCd, CCl), and have generally a higher precision regarding the prediction of the time of tree death (PEd,15, PEd,60) than the TMFs. Since the EMFs were fitted with the Davos data set, it has to be taken into account that better results for the model performance criteria of the EMFs are expected for this site (Table 1). Among the four TMFs, TMFabs performs best (Tables 1 – 3), but many dead trees are erroneously predicted to remain alive (Figs. 2a, 3a, and 4a). TMFrel classifies relatively few dead trees to be alive (CCd), but it performs poorly with regard to CCl, PEd,60, and PEl,60. The models TMFstress and TMFsev are characterized by generally higher values of CCl, and lower values of PEd,60 and PEl,60 compared to TMFrel. The consideration of stress severity (TMFsev) results in higher CCd, lower CCl, slightly higher PEd,15, and higher PEd,60 and PEl,60 than in the case of TMFstress. Among the empirical mortality functions, EMF2, EMF3, and EMF4 perform approximately equally well (Tables 1 – 3), but EMF4 has a tendency to predict more dead trees to die more than 60 years prior to death (PEd,60). The effect of different stand histories on the predictions of the mortality models is illustrated by the large performance differences that exist between the sites, particularly between Davos and Scatlé (Figs. 2 and 4). At Scatlé, a high fraction of dead and living trees is predicted to die more than 100 years prior to the last measured year (Figs. 4a and 4b), while PEd,15 as well as CCl are lower (Tables 1 and 3). This drawback is particularly pronounced in the case of TMFrel, TMFstress, and TMFsev that predicted many trees to die during a period of persistent suppressed growth prior to 1850, which was followed by a release of about 60% of the sampled trees (see Bigler and Bugmann 2003b). This period of intense competition constituted an apparent high mortality risk, which was not adequately mirrored by these models. The release effect after the suppression period is probably attributable to a natural, external disturbance that killed many trees in the stand.

84


By contrast, the forests in Davos were over-utilized particularly during the 19th century, with a strong decrease of forest use after 1950 (Bebi 1999). These management activities were likely the reason why relatively few trees suffered growth suppressions in the 19th century, which in turn decreased the values for PEd,60 and PEl,60 in the mortality models at this site. Finally, the relatively high fraction of trees in Bödmeren that are predicted to die more than 60 or 100 years prior to the last measurement (Fig. 3) can perhaps be ascribed to periods of suppression or low growth. Similar to Scatlé, the stands in Bödmeren have primeval character (Bettschart 1994), and we surmise that the lack of management activities led to relatively dense stands more than 100 years ago. Implicati ons of clima te change for observed and pre dicted tree mor tality Three of the four EMFs presented in this study showed a substantially higher performance under the current climate than the TMFs that are implemented in many current gap models. However, the question arises whether the TMFs as well as the EMFs might show a lower performance under an altered climate with respect to predicting the timing of tree death. Since our three study sites are climatically and geologically quite diverse (see Bigler and Bugmann 2003a), we believe that the EMFs examined here should have some predictive power under a changing climate in the 21st century. Global climate change is likely to result in an increase of the frequency and intensity of extreme climate events, which tend to be more important in driving forest dynamics than average climatic conditions (Beniston et al. 1997, Innes 1998, Bugmann and Pfister 2000, Houghton et al. 2001). Climate-induced tree mortality might increase as a consequence of short-term or long-term growth decreases, triggered directly by climate extremes (e.g., exceptionally cold temperatures in winter, extremely hot temperatures in summer, persistent droughts), or indirect climate impacts (e.g., pathogen epidemics) (Gates 1990, LeBlanc and Foster 1992, Innes 1998, Pedersen 1998). The factors that likely will affect tree mortality most strongly under the projected climate changes are higher maximum temperatures and risk of summer droughts (Houghton et al. 2001). The existence of a close relationship between short- and long-term drought periods and subsequent increased tree mortality has been reported for various bioclimatic regions (Tainter et al. 1983, Clinton et al. 1993, Elliott and Swank 1994, Condit et al. 1995, Jenkins and Pallardy 1995, Villalba and Veblen 1998, Ogle et al. 2000, Martinez-Vilalta and Piñol 2002). The observed high variability of tree mortality under the current climate (Franklin et al. 1987) is reflected in a high uncertainty of quantifying tree mortality under a changed climate (Keane et al. 2001). On the one hand, altered mortality functions have been shown to affect considerably the outcome of the simulated succession in some gap models (SORTIE: Pacala et al. 1996; FORCLIM: Bugmann 2001; LINKAGES: Wyckoff and Clark 2002). On the other hand, some gap models were reported to be relatively insensitive to

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changes of the mortality parameters (FORMIX: Bossel and Krieger 1991; FORSKA: Leemans 1991; JABOWA: Botkin and Nisbet 1992). In any case, most model-based projections of forest succession under a changed climate indicate high tree mortality and transitions to different forest types (e.g., Solomon 1986, Prentice et al. 1991, Bugmann 1997). It is not clear at the present time whether these vegetation changes are realistic, or if they might be an artifact of the mortality functions that are used in these models (Loehle and LeBlanc 1996). Increased mortality leads to the more frequent formation of canopy gaps (Clinton et al. 1993, Bugmann 2001), on which many local tree species rely to regenerate. Gap formation also allows the replacement of local species with immigrating species (Shugart 1987, Lertzman 1995), which results in changed vegetation composition. The question arises whether the current EMFs and TMFs are appropriate to simulate tree mortality under a changed climate (Keane et al. 2001). Increased occurrence of e.g. drought does not necessarily imply long-term elevated mortality rates, despite strong empirical indications about the impact of drought on tree mortality, as shown before. Long-lived tree individuals experience several periods of changing environmental conditions during their life, and they are likely to be able to survive many cycles of extreme conditions such as drought that may have been more intense or more persistent than those known for the 20th century (Hughes and Funkhouser 1998). The resilience of forest ecosystems to environmental changes (Loehle and LeBlanc 1996, Innes 1998) might be explained by the presence of plasticity within tree individuals and within species (Kuiper and Kuiper 1988, Kramer 1995, Monserud and Sterba 1999). Thus, we suggest that tests should be conducted to evaluate the sensitivity and appropriateness of TMFs and EMFs under a wide variety of climatic conditions; our study was a first attempt in this direction, but it is clear that further work is required.

Conclusions Four different theoretical mortality functions (TMFs) that are being used in forest succession models were compared to four empirical mortality functions (EMFs) with respect to predicting the timing of tree death. The TMFs are based on theoretical assumptions and include a stochastic component. The EMFs rely on deterministic, statistical relationships between tree status (dead or alive) and different growth-related variables, based on dendrochronological time series. These eight mortality functions were applied to measured tree-ring series of dead and living Norway spruce (Picea abies) trees from three subalpine areas in Switzerland. For both groups of mortality functions (TMFs and EMFs), thresholds were used to determine the time of individual tree death. The site-specific distributions of prediction errors were used to derive different model performance criteria (two classification accuracy criteria and three prediction error criteria) that allowed us to compare the models. The following conclusions can be drawn from this study:

86


(1)

The resulting curves of survival probabilities of the EMFs presented react in a more sensitive manner to small changes in the growth rate, whereas the TMFs show simpler patterns. Yet, periods of severe stress are generally identified by both EMFs and TMFs as periods of increased mortality probability.

(2)

At all three sites, three of the four EMFs show a substantially higher performance than the TMFs. This implies that species-specific, empirically derived mortality functions predict the time of tree death more accurately. We expect considerable changes in the modeled forest succession when the currently implemented TMFs are replaced by EMFs.

(3)

The TMFs investigated here predict many dead or living trees to die in periods of persistent growth suppression, which leads to large prediction errors and a low performance of these mortality models. Optimizing the TMFs, i.e., adapting the thresholds and parameters to individual species might result in improved mortality predictions.

(4)

Testing EMFs and TMFs against field-measured mortality data from different sites is a crucial step in assessing and improving tree mortality functions. However, the applicability of EMFs and TMFs to predict tree death under changed climate is not known at the present time. The large prediction errors arising from most TMFs under the current climatic conditions in our study indicate that forest ecosystems might be less sensitive under the anticipated climate changes than earlier model projections suggested. We recommend that further studies should be conducted to investigate the sensitivity of forest succession models in general and the behavior of the tree mortality submodels in particular, with a focus on changing and changed climatic conditions.

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Hasenauer, H., D. Merkl, and M. Weingartner. 2001. Estimating tree mortality of Norway spruce stands with neural networks. Advances in Environmental Research 5:405-414. Hawkes, C. 2000. Woody plant mortality algorithms: description, problems and progress. Ecological Modelling 126:225-248. He, F., and R. I. Alfaro. 2000. White pine weevil attack on white spruce: a survival time analysis. Ecological Applications 10:225-232. Hosmer, D. W., and S. Lemeshow. 1989. Applied logistic regression. Wiley Interscience Publication, New York. Houghton, J. T., Y. Ding, D. J. Griggs, M. Noguer, P. J. van der Linden, and D. Xiaosu, editors. 2001. Climate change 2001: the scientific basis. Cambridge University Press, Cambridge, UK. Hughes, M. K., and G. Funkhouser. 1998. Extremes of moisture availability reconstructed from tree rings for recent millennia in the Great Basin of Western North America. Pages 99-108 in M. Beniston and J. L. Innes, editors. The impacts of climate variability on forests. Springer, Berlin etc. Innes, J. L. 1998. The impact of climatic extremes on forests: an introduction. Pages 1-18 in M. Beniston and J. L. Innes, editors. The impacts of climate variability on forests. Springer, Berlin etc. Jenkins, M. A., and S. G. Pallardy. 1995. The influence of drought on red oak group species growth and mortality in the Missouri Ozarks. Canadian Journal of Forest Research 25:1119-1127. Kaufmann, M. R. 1996. To live fast or not: growth, vigor and longevity of old-growth ponderosa pine and lodgepole pine trees. Tree Physiology 16:139-144. Keane, R. E., M. Austin, C. Field, A. Huth, M. J. Lexer, D. Peters, A. Solomon, and P. Wyckoff. 2001. Tree mortality in gap models: application to climate change. Climatic Change 51:509-540. Keane, R. E., P. Morgan, and S. W. Running. 1996. FIRE-BGC - a mechanistic ecological process model for simulating fire succession on coniferous forest landscapes of the northern Rocky Mountains. USDA Forest Service Research Paper INT-RP-484. Kobe, R., and K. D. Coates. 1997. Models of sapling mortality as a function of growth to characterize interspecific variation in shade tolerance of eight tree species of northwestern British Columbia. Canadian Journal of Forest Research 27:227-236. Kobe, R. K. 1996. Intraspecific variation in sapling mortality and growth predicts geographic variation in forest composition. Ecological Monographs 66:181-201. Kobe, R. K., S. W. Pacala, J. A. Silander, and C. D. Canham. 1995. Juvenile tree survivorship as a component of shade tolerance. Ecological Applications 5:517-532. Korzukhin, M. D., M. T. Ter-Mikaelian, and R. G. Wagner. 1996. Process versus empirical models: which approach for forest ecosystem management. Canadian Journal of Forest Research 26:879-887. Kramer, K. 1995. Phenotypic plasticity of the phenology of seven European tree species in relation to climatic warming. Plant Cell and Environment 18:93-104. Kuiper, D., and P. J. C. Kuiper. 1988. Phenotypic plasticity in a physiological perspective. Acta Oecol. Plant. 9:43-59. LeBlanc, D. C. 1996. Using tree rings to study forest decline: an epidemiological approach based on estimated annual wood volume increment. Pages 437-449 in J. S. Dean, D. M. Meko, and T. W. Swetnam, editors. Tree rings, environment and humanity. Radiocarbon, Department of Geosciences, University of Arizona, Tucson, Arizona. LeBlanc, D. C., N. S. Nicholas, and S. M. Zedaker. 1992. Prevalence of individual-tree growth decline in red spruce populations of the southern Appalachian Mountains. Canadian Journal of Forest Research 22:905-914.

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LeBlanc, D. G., and J. R. Foster. 1992. Predicting effects of global warming on growth and mortality of upland oak species in the midwestern United States: a physiologically based dendroecological approach. Canadian Journal of Forest Research 22:1739-1752. Leemans, R. 1991. Sensitivity analysis of a forest succession model. Ecological Modelling 53:247-262. Lertzman, K. P. 1995. Forest dynamics, differential mortality and variable recruitment probabilities. Journal of Vegetation Science 6:191-204. Lindner, M., H. Bugmann, W. Cramer, and P. Lasch. 1999. Impact of climate change on forests: application of forest succesion models across central and eastern Europe. Pages 165-178 in K. Vancura and V. Sramek, editors. Effect of global climate change on boreal and temperate forests, Jiloviste, Czech. Loehle, C., and D. LeBlanc. 1996. Model-based assessments of climate change effects on forests: a critical review. Ecological Modelling 90:1-31. Lumley, T., and P. Heagerty. 1999. Weighted empirical adaptive variance estimators for correlated data regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61:459-477. Martinez-Vilalta, J., and J. Piñol. 2002. Drought-induced mortality and hydraulic architecture in pine populations of the NE Iberian Peninsula. Forest Ecology and Management 161:247-256. Monserud, R. A., and H. Sterba. 1999. Modeling individual tree mortality for Austrian forest species. Forest Ecology and Management 113:109-122. Moore, A. D. 1989. On the maximum growth equation used in forest gap simulation models. Ecological Modelling 45:63-67. Ogle, K., T. G. Whitham, and N. S. Cobb. 2000. Tree-ring variation in pinyon predicts likelihood of death following severe drought. Ecology 81:3237-3243. Pacala, S. W., C. D. Canham, J. Saponara, J. A. Silander, R. K. Kobe, and E. Ribbens. 1996. Forest models defined by field measurements: II. Estimation, error analysis and dynamics. Ecological Monographs 66:1-43. Pacala, S. W., C. D. Canham, and J. A. Silander. 1993. Forest models defined by field measurements: I. The design of a northeastern forest simulator. Canadian Journal of Forest Research 23:1980-1988. Pedersen, B. S. 1998. The role of stress in the mortality of midwestern oaks as indicated by growth prior to death. Ecology 79:79-93. Pedersen, B. S. 1999. The mortality of midwestern overstory oaks as a bioindicator of environmental stress. Ecological Applications 9:1017-1027. Prentice, I. C., M. T. Sykes, and W. Cramer. 1991. The possible dynamic response of northern forests to global warming. Global Ecology and Biogeography Letters 1:129-135. Reynolds, J. F., and E. D. Ford. 1999. Multi-criteria assessment of ecological process models. Ecology 80:538-553. Schweingruber, F. H. 1996. Tree rings and environment: dendroecology. Verlag Paul Haupt, Bern. Shugart, H. H. 1984. A theory of forest dynamics. The ecological implications of forest succession models. Springer, New York. Shugart, H. H. 1987. Dynamic ecosystem consequences of tree birth and death patterns. BioScience 37:596602. Shugart, H. H., T. M. Smith, and W. M. Post. 1992. The potential for application of individual-based simulation models for assessing the effects of global change. Annual Review of Ecology and Systematics 23:15-38. Shugart, H. H., and D. C. West. 1980. Forest succession models. BioScience 30:308-313.

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Solomon, A. M. 1986. Transient response of forests to CO2-induced climate change: simulation modeling experiments in eastern North America. Oecologia 68:567-579. Szwagrzyk, J., and J. Szewczyk. 2001. Tree mortality and effects of releases from competition in an oldgrowth Fagus-Abies-Picea stand. Journal of Vegetation Science 12:621-626. Tainter, F. H., T. M. Williams, and J. B. Cody. 1983. Drought as a cause of oak decline and death on the South Carolina coast. Plant Disease 67:195-197. Theurillat, J.-P., and A. Guisan. 2001. Potential impact of climate change on vegetation in the European alps: a review. Climatic Change 50:77-109. Urban, D. L., and H. H. Shugart. 1992. Individual-based models of forest succession. Pages 249-292 in D. C. Glenn-Lewin, R. K. Peet, and T. T. Veblen, editors. Plant succession theory and prediction. Chapman and Hall, London. Villalba, R., and T. T. Veblen. 1998. Influences of large-scale climatic variability on episodic tree mortality in northern Patagonia. Ecology 79:2624-2640. Wyckoff, P. H., and J. S. Clark. 2000. Predicting tree mortality from diameter growth: a comparison of maximum likelihood and Bayesian approaches. Canadian Journal of Forest Research 30:156-167. Wyckoff, P. H., and J. S. Clark. 2002. The relationship between growth and mortality for seven co-occuring tree species in the southern Appalachian Mountains. Journal of Ecology 90:604-615. Zar, J. H. 1999. Biostatistical analysis, fourth edition. Prentice-Hall, Upper Saddle River, New Jersey.

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Chapter IV Drought as an inciting mortality factor in Scots pine stands of the Valais, Switzerland

Manuscript: Bigler1, C., O. U. Bräker2, H. Bugmann1, M. Dobbertin2, and A. Rigling2. 2003. Drought as an inciting mortality factor in Scots pine stands of the Valais, Switzerland. 1

Mountain Forest Ecology, Department of Forest Sciences, Swiss Federal Institute of Technology (ETH),

ETH-Zentrum, CH-8092 Zurich, Switzerland 2

Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Zürcherstr. 111,

CH-8903 Birmensdorf, Switzerland

Abstract – During the 20th century, high mortality rates of Scots pine (Pinus silvestris L.) were observed over large areas in the Rhône valley (Valais, Switzerland) and in other dry valleys of the European Alps. Until the 1980s, fluorine emissions were suggested to be the main cause of Scots pine decline in the Valais, however, recent observations argue for other major stress factors being involved in the mortality process. In our study, a complex of multiple stress factors such as increasing competition due to invading tree species, drought, and insect infestations is suggested to cause Scots pine decline. In the present study, the decline disease theory is applied to provide a framework for relating reduced tree growth and increased mortality rates to a series of short- and long-term environmental stresses that occur sequentially in time. The main focus was on the verification of drought as an inciting factor of Scots pine decline. Averaged tree-ring widths, standardized tree-ring series, and estimated mortality risks were evaluated with respect to two conceptually differing drought indices. Linear relationships between recent growth and a competition index were calculated to assess the long-term effect of competition on tree growth of living trees and growth prior to death, respectively.

92

Drought as an inciting mortality factor

Competition had a highly significant effect on recent growth of living Scots pine trees. Growth rates of dying trees were less affected by competition, and we conclude that additional environmental factors must be taken into account to explain low growth prior to death. Correlations between drought indices and standardized tree-ring series from eleven sites showed a moderate association. Several drought years and drought periods could be detected since 1864 that coincided with decreased growth. While single, extreme drought years had generally a short-term, reversible effect on tree growth, multi-year drought initiated prolonged growth decreases that increased a tree’s long-term risk of death. After a persistent drought period (1956 – 1974), dying trees benefited less of the improved moisture availability and the relaxation of competition compared to surviving trees. Tree death occurred generally several years or decades after the drought, probably as a result of increasing competition in combination with drought-insect interactions that acted as the final lethal factors. In conclusion, competition is one of the factors that acts in the long term and predisposes trees to die. Drought has a limiting effect on tree growth and acts very likely as a bottleneck event that triggers Scots pine decline in the Valais. Key words Drought; tree mortality; Scots pine (Pinus silvestris L.); air pollution; mortality risk; statistical models; potential evapotranspiration; tree rings; climate; competition; decline disease theory

Introduction Hig h Scots pine morta lity i n the Valais Since the beginning of the 20th century, occurrences of high Scots pine (Pinus silvestris L.) mortality have been observed in irregular intervals in the Rhône valley (Valais, Switzerland), one of the main valleys of the Central Alps (Fig. 1) (Innes 1993, Dobbertin 1999, Rigling and Cherubini 1999). The decline of Scots pine in forests of the Valais is not a local phenomenon; from other central alpine dry valleys of the European Alps, high mortality rates of Scots pine trees have been documented as well, e.g., from Austria (Inntal) and Italy (Valle d’Aosta, Valle di Susa, Vintschgau) (Rigling et al. 1999b). The Scots pine decline in the Valais was distributed over a large area between Martigny and Brig, with the highest occurrence until the 1980s in the areas of Charrat/Saxon, Pfynwald (east of Chippis), and Visp (Flühler et al. 1981, Kienast 1985b), and from the 1990s in the area from Salgesch (north-east of Chippis) to Brig (Fig. 1). Within a site, declining or dead trees are standing besides living, vigorous trees, resulting in a regular scatter of

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dead Scots pine trees (Scherrer et al. 1981). The causes that led to the death of these diffusely distributed trees are not obvious (Rigling and Cherubini 1999). It is unlikely that the regular scattering of dead trees could have been caused only by heavy insect outbreaks, which generally kill groups of trees or entire stands. Since about 1995, however, infestation fronts with dead Scots pine trees have been observed locally, where most of the trees were infested with the pine shoot beetle (Tomicus piniperda L. or Tomicus minor Hart.) (Rigling and Cherubini 1999).

Fig. 1. Map of the Rhône valley in the Valais, south-west of Switzerland. Codes: 1 = Martigny, 2 = Les Arbepins, Boutieu, Eponde, Creux du Dailley, Torrent des Croix, (Charrat/Saxon), 3 = Sion, 4 = LWF Lens, 5 = Chippis, 6 = Turtmann, 7 = Steg, 8 = Raron, 9 = LWF Visp, 10 = Visp, 11 = Rohrberg Eyholz, Gliswald Gamsen, 12 = Brig. Study sites are indicated with white numbers on black circles. DHM25, reproduced by permission of swisstopo (BA035522).

Pos sible causes of Scots pi ne decline Between the 1920s and the early 1980s, scientific investigations on Scots pine decline in the Valais largely focused on fluorine emissions of nearby aluminum smelters that were built 1907 in Martigny, 1908 in Chippis, and later, 1962 in Steg (Fig. 1) (Faes 1921, Wille 1922, Bolay and Bovay 1965, Flühler 1981, Kontic et al. 1986). Damages of Scots pine trees were shown to be greatest downwind (west – east) of pollution sources (Flühler 1983) and in the zone of atmospheric inversions (Kontic et al. 1986). Scots pine is as-

94


sumed to be one of the most sensitive conifers with regard to the impact of acid deposition and air pollutants (Bolay and Bovay 1965, Richardson and Rundel 1998). After the installation of emission reduction technologies in the aluminum smelters in the early 1980s, necrosis as a symptom of fluorine injury disappeared, and the mortality rates in the most severely affected areas were reduced (Rigling et al. 1999a). However, mortality rates in the other areas remained high, or even increased, e.g., in the area of Visp in the early 1990s, or again in 1996 (Dobbertin 1999, Rigling and Cherubini 1999, Rigling et al. 1999a), although the fluorine charge has never been very high in this area (Rigling et al. 1999b). The climate of the Valais indicates that drought stress could be an important cause of Scots pine decline (Flühler 1981, Kienast 1985b, Rigling and Cherubini 1999, Rigling et al. 2002), which would be in line with the findings of Manion (1981) and Innes (1993), who suggested that drought is one of the most important factors in triggering forest declines. There is substantial evidence that drought stress promotes outbreaks of fungal diseases and secondary insects (Mattson and Haack 1987, Wargo 1996, de Groot and Turgeon 1998). Insect calamities often occur during or after unusually warm and dry weather, which decreases the resistance of stressed trees and provides favorable conditions for the population development of insects (Berryman 1989). In the Scots pine stands of the Valais, there is a latent presence of insects, including the common and lesser pine shoot beetle (Tomicus piniperda L., T. minor Hart.), the pine processionary moth (Thaumetopoea pityocampa Denis & Schiff.), the six-toothed bark beetle (Ips sexdentatus Boern.), or the engraver beetle (Ips acuminatus Gyll.) (Rigling and Cherubini 1999, NierhausWunderwald and Forster 2000). Besides pollutants, drought, and insects, stand ageing and invading tree species might impose an additional stress on the shade-intolerant Scots pine (Rigling and Cherubini 1999). Due to century-long management activities in the Valais, the extent of Scots pine forests has increased to currently 11% of the forested area, which is probably much larger than their natural range (Plumettaz Clot 1988, Rigling and Cherubini 1999). The changed forest utilization after 1950 is one reason why many Silver fir (Abies alba Mill.), Norway spruce (Picea abies (L.) Karst.), downy oak (Quercus pubescens Willd.) trees, and several shrub species currently invade Scots pine stands (Rigling and Cherubini 1999, Rigling et al. 1999b, Kienast et al. 2003). Decline d isease theor y The description of environmental factors above suggests that a combination of multiple stress factors is very likely to cause Scots pine decline (Flühler 1981, Innes 1993, Rigling and Cherubini 1999). The decline disease theory, a general conceptual model for complex, stress-induced forest decline, provides a framework to relate tree death or the deterioration of a tree’s vigor to a sequence of interchangeable environmental factors (Sinclair 1967,

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95

Manion 1981, Houston 1984). A three-step process of predisposing, inciting, and contributing factors that occur sequentially in time underlies the decline disease theory. Predisposing factors such as competition or air pollutants impact a tree during years or decades. These long-term factors are often expressed as lowered growth rates (Pedersen 1998b), and they increase a tree’s susceptibility to short-term, inciting stresses, such as insect defoliation or drought. Such inciting factors affect the physiological functioning of a tree, and considerably reduce its vigor and potential for pathogen defense (Manion 1981, Loehle 1988, Herms and Mattson 1992), resulting in rapid growth decreases (Pedersen 1998a). Finally, a tree’s fate often depends on the presence or absence of further, contributing stress factors that act over the short or long term. Examples are secondary, opportunistic insects, fungi, or further climatic events, which ultimately may kill stressed trees (Schoeneweiss 1986, Mattson and Haack 1987, Cherubini et al. 2002). Objective s and resear ch que stions The main objective of this study is to evaluate drought as a potential inciting factor of Scots pine decline in the Valais. Drought years are extracted from long-term time series of two conceptually differing drought indices. At eleven sites, three different methods are used to assess past tree responses to drought years: (i) the association between ring widths or standardized tree-ring indices, respectively, and drought indices is evaluated, (ii) the impact of drought on tree growth prior to death is assessed, and (iii) a method to compute a tree’s annual mortality probability is applied to estimate the relative mortality risk. In addition, to estimate the impact of competition as a predisposing factor in the mortality process of Scots pine, the effect of competition on recent growth of living trees and on tree growth prior to death is quantified using linear models. The following six questions are relevant in the present study: (1) To what extent do single drought years and drought periods affect tree growth? (2) How strong is the correlation between standardized tree-ring indices and drought indices? (3) What is the effect of drought on tree growth prior to death? (4) What is the lag of the mortality response after a drought period? (5) How is the distribution of the mortality risk related to drought? (6) What is the effect of competition on growth of living and dying trees?

Material & methods Des cripti on of study sites and tr ee species Eleven study sites were selected in the Rhône valley, an inner alpine valley in the Valais, Switzerland (Table 1, Fig. 1). The valley is characterized by a dry-subcontinental climate with high insolation, low precipitation (between Visp and Sion, less than 600 mm precipitation per year), an annual mean temperature of about 9.5 °C, and a pronounced wind system from west to east (Kienast 1985a, Lingg 1986).

46°17’52’’, 7°51’33’’

Gliswald Gamsen (11)

LWF Visp (9)

Turtmann (6)

Raron (8)

Les Arbepins (2)

Boutieu (2)

Eponde (2)

1

2

3

3

4

4

4

46°7’19’’, 7°11’12’’ 46°16’14’’, 7°26’18’’

4

Torrent des Croix (2)

5

LWF Lens (4)

46°7’56’’, 7°11’14’’

Creux du Dailley (2)

46°8’16’’, 7°10’41’’

46°8’4’’, 7°9’59’’

46°8’6’’, 7°9’50’’

46°18’11’’, 7°47’24’’

1050

1540

1240

880

880

840

700

650

680

950

850

Altitude (m a.s.l.)

SE

W

SW

SW

NW

SW

N

N

N

NW

NNW

Aspect

90%

47%

47%

27%

18%

27%

70%

75%

80%

46%

50%

Slope

Limestone

Calcareous schist

Calcareous schist

Calcareous schist

Calcareous sediments

Calcareous sediments and schist

Bündnerschiefer (schist)





Bedrock

20

13

15

20

16

12

16

32

23

58

59

Number of trees

11 (18)

- (15)

- (13)

- (10)

- (15)

- (12)

- (-)

- (-)

8 (12)

10 (17)

10 (14)

Mean tree height (maximum)

1820 – 1997

1833 – 1979

1746 – 1979

1826 – 1979

1843 – 1979

1846 – 1979

1874 – 1976

1817 – 1976

1912 – 2000

1882 – 2001

1869 – 2000

Range

Note: Data were collected by Bigler1, Rigling2, Schweingruber3, Kienast (1985a)4, Rigling et al. (2003)5. Site: the numbers in brackets correspond to the codes in Fig. 1; number of trees: number of trees sampled; mean tree height (maximum): mean tree height and maximum tree height of sampled trees (where available); range: range of years covered by reliably dated trees.

L

CT

ABE

4

46°17’49’’, 7°57’13’’

Rohrberg Eyholz (11)

46°18’8’’, 7°43’7’’

46°17'59’’, 7°56’49’’

1

RGV

TR

Coordinates (N, E)

Site

Data set

Table 1. Description of study sites.

96 Drought as an inciting mortality factor

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97

The eleven sites were combined to five data sets, according to geographic location and altitude (Table 1): RGV (Rohrberg Eyholz, Gliswald Gamsen, LWF1 Visp), TR (Turtmann, Raron), ABE (Les Arbepins, Boutieu, Eponde), CT (Creux du Dailley, Torrent des Croix), L (LWF1 Lens). The bedrock at all sites belongs to the penninic, and all stands grow on relatively shallow Rendzic Leptosols (FAO soil classification system). Scots pine (Pinus silvestris L.) is the dominant or one of the dominating tree species at all study sites. Pinus silvestris, the most widely distributed species of all pines (MartinezVilalta and Piñol 2002), is a fast colonizing, light demanding pioneer tree, which establishes on wet as well as on dry sites, and grows on acid and also on calcareous soils (Ellenberg 1996, Rigling and Cherubini 1999). Scots pine is resistant to frost and drought (Leibundgut 1991, Ellenberg 1996). Due to its low competitiveness, P. silvestris is typically restricted to excessively wet, nutrient poor, or dry sites. Drought i ndices Climate data from the SMI (Swiss Meteorological Institute) from the eastward-located climate station Visp (measurement period: 1901 – 2001) and the westward-located climate station Sion (1864 – 2001) were used (Fig. 1). Since both climate stations were moved in the 20th century, and due to incomplete measurement series for precipitation or temperature, additional meteorological data of adjacent climate stations had to be used to bridge the missing climate series. For this purpose, monthly mean values and variances of the overlapping periods were adjusted to homogenize the data (O. U. Bräker, unpublished report). The homogenization procedure was more adapted to the approximately normally distributed temperature data and less to the skewed distribution of the precipitation data. Two different drought indices were calculated based on the homogenized climate data. The first drought index (DRI1) is based on the formulation for calculating the potential evapotranspiration (PET) according to Thornthwaite (1948), and requires monthly mean temperatures and precipitation sums: [1]

DRI1 = P – PET

with P = precipitation sum of August (previous year) to July (current year), and PET = sum of estimated potential evapotranspiration of August (previous year) to July (current year) as a function of monthly mean temperatures and geographical latitude. This 12month period was chosen because Rigling et al. (2001) found that ring width of Scots pine on dry sites is more affected by water availability of the previous August than of the current August.

1

LWF = Langfristige Waldökosystem-Forschung (Long-term Forest Ecosystem Research)

98


The second drought index (DRI2) is an adapted version of the more mechanistic model by Bugmann and Cramer (1998), which – unlike DRI1 (Eq. 1) – explicitly considers the amount of water transpired by the trees relative to the evaporative demand drawing on soil water: [2]

DRI2 = 1 – ∑DRI2i/9

with ∑DRI2i = sum of monthly drought indices (September to November of previous year and March to August of current year). Low values for both drought indices indicate moisture deficits. The drought indices from Visp were used to analyze data from the sites RGV and TR, which are located in the east of the Valais, and the drought indices from Sion were used in combination with the more westerly sites ABE, CT, and L (see Fig. 1 and Table 1). Sam pling of tre es and processing of tre e-ring series The Scots pine trees at the sites RGV (n = 140) (Table 1) were sampled in 2001. Here, pairs of a standing dead tree and a similar living tree with a DBH (diameter at breast height) larger than 10 cm were selected. The living trees were selected with regard to similar DBH, competition, and microsite conditions (cf. Bigler and Bugmann 2003a). Two cores were taken at breast height (1.3 m). Tree rings were measured using a Lintab 3 measuring system (F. Rinn S.A., Heidelberg, Germany) and the TSAP tree-ring program (Rinn 1996). Two trees from the Gliswald Gamsen, one tree from Rohrberg Eyholz, and one tree from LWF Visp had to be excluded subsequently from further analyses because of low wood quality of the cores. The two cores of the remaining trees were cross-dated and averaged. Cross-dating constitutes the dendrochronological method that assigns each tree ring to a calendar year, based on the comparison of growth patterns of individual trees with the average growth pattern of dominant trees in the stand (Fritts 1976). Fifty-five percent of the reliably dated dead trees of the data set RGV died in 1998, only one tree died in the sampling year 2001 (Fig. 2). At the study sites Gliswald Gamsen and Rohrberg Eyholz, the DBH of each cored tree was measured as well as the distance to and the DBH of neighboring trees larger than 10 cm DBH within a radius of 5 m. These data allowed to calculate tree competition indices (see below). The tree-ring data of the data sets TR (n = 48), ABE (n = 48), CT (n = 28), and L (n = 20) were available from the dendrochronological database at WSL (Swiss Federal Institute for Forest, Snow and Landscape Research, Birmensdorf, Switzerland). These Scots pine trees had been sampled in 1977 (TR), 1980 (ABE, CT), and 1998 (L). From each tree, tree-ring widths from one or two cross-dated cores are available. When two cores per tree were

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available, the ring widths were averaged. It can be assumed that all data sets except for L contained a few dead trees, since some sampled trees developed their last tree ring prior to the year of sampling. However, the exact number of dead trees in these data sets could not be reconstructed any more, since a couple of trees might have died in the year of sampling.

Fig. 2. Annual mortality rates from the sites RGV (Rohrberg Eyholz, Gliswald Gamsen, LWF Visp). Only reliably dated dead trees were considered.

The ring widths of the cross-dated and averaged tree-ring series of all five data sets were (i) converted to BAI (basal area increments; see next section), and (ii) detrended and transferred to standardized, site-specific tree-ring chronologies. The individual tree-ring series of the reliably dated trees (RGV, n = 124; TR, n = 48; ABE, n = 48; CT, n = 28; L, n = 20) were standardized, i.e., the observed values were divided by the expected values to remove the non-climatic low-frequency variability which is due to tree ageing and stand dynamics (Fritts 1976). The ARSTAN software (Cook and Holmes 1984) was used, applying a double-detrending standardization (Holmes et al. 1986, Cook et al. 1990). Treering indices were estimated by sequentially fitting a negative exponential or linear function, followed by fitting a cubic smoothing spline (with 50% variance reduction using a 128-yr spline) through the tree-ring indices to remove any residual growth trend. Finally, the individual series of tree-ring indices were averaged using a biweight robust mean within each of the five combined data sets to get a site-specific mean series of tree-ring indices. Der ivation of the rel ative mortal ity ri sk The method of Bigler and Bugmann (2003b) was adopted to calculate a tree’s annual mortality probability along time and to derive an estimator of the population-level mortality risk. Entire growth curves of the data set RGV (n dead trees = 70, n living trees = 70) were used with a total of n = 9254 measurements to fit a logistic mortality model, based on the growth patterns of individual tree-ring curves:

100

[3]


Pr(Y i,t | X i,t ) =

1 1 + exp[11.415 + 0.816 ¥ locreg5,i,t + 1.456 ¥ log(relbaii,t )] -1

where Pr(Yi,t|Xi,t) is the survival probability of tree i at time t, given the independent variables † X. Locreg5 is the slope of a local linear regression over the last 5 years, and the relative growth rate log(relbai) is the log-transformed ratio of BAI (basal area increment) and BA (basal area), respectively (cf. Bigler and Bugmann 2003b). To take the autocorrelation of the dependent variable into account, an infinitesimal jackknife variance estimator (Lumley and Heagerty 1999) was applied to correct the biased variances. All regression coefficients turned out to be very highly significant (p < 0.0001). In the following, this mortality model was applied to all reliably dated trees of the five data sets (RGV, n = 124; TR, n = 48; ABE, n = 48; CT, n = 28; L, n = 20), resulting in time-dependent, individual probability curves of survival that are bounded by 0 and 1 (cf. Bigler and Bugmann 2003b). For each calendar year, the percentage of trees with an increased mortality risk was estimated. This was achieved by estimating the percentage of trees with a survival probability falling below a fixed threshold of 0.975 (Bigler and Bugmann 2003b). Decreasing or increasing this threshold resulted in reducing or amplifying the signal of the mortality risk, without strongly affecting the overall pattern of the mortality risk. Therefore, the precise choice of the threshold is of no key importance for this application. However, the computed annual mortality risk is valid for the sampled trees only and has to be considered as a relative mortality risk, since some trees in the population may have died, but were not considered in the sample. Growth-competition re lationships To assess the effect of neighboring trees on the current growth rate of a subject tree, a simple distance-dependent competition index (CI) was used, as described in Daniels (1976): [4]

n

2

2

DBH j DBH i j =1 DIST ij

CI i = Â

where DBHi designates the DBH of subject tree i, DBHj designates the DBH of neighbor † j, and DISTij is the distance between subject tree i and neighbor tree j. tree Linear regression models between CI as independent variable and the recent growth for dead or living trees as dependent variable were calculated: [5]

log(BAI3,i) = b0 + b1 CIi

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where log(BAI3,i) is the log-transformed, averaged BAI of tree i over the last three years, and CIi is the competition index of tree i (Eq. 4). For this calculation, the data sets Rohrberg Eyholz and Gliswald Gamsen were combined (Table 1), and the models were calculated separately for living trees and reliably dated dead trees that died between 1996 and 2001 (cf. Bigler and Bugmann 2003a).

Fig. 3. Comparison of drought indices (DRI1, DRI2) and standardized tree-ring indices for (a) Visp (sites RGV, TR), and (b) Sion (sites ABE, CT, L). Lines indicate linear regressions, dotted lines indicate the lower 5%, 10%, and 15% confidence limits (Zar 1999). Circles specify the intensity of drought years (5%, big circles; 10%, medium circles; 15%, small circles). Only tree-ring indices of reliably dated trees with n ≥ 5 trees are shown.

102


Results Ass ociati on between d rought and tree gr owth The agreement between drought (Eqs. 1 and 2) and ring width indices (including mid- to high-frequency growth variability) or averaged ring widths (including low- to highfrequency growth variability) is shown in Figs. 3 and 4. In the Visp area, single drought years such as 1921, 1933, 1944, 1947, 1974, and 1998 considerably decreased tree-ring indices in the short term (Fig. 3a); this was more pronounced for the sites RGV than for the sites TR. Persistent periods of moisture deficits affected ring widths negatively in the long term, e.g., 1943 – 1950, 1956 – 1974, and 1996 – 2000 (Fig. 4a).

Fig. 4. Drought indices (DRI1, DRI2) and averaged ring widths for (a) Visp (sites RGV, TR), and (b) Sion (sites ABE, CT, L). The hatched areas in the upper panels show the values above respectively below the fitted regression lines. Only averaged ring widths of reliably dated trees with n ≥ 5 trees are shown.

Chapter IV

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In the Sion area, the negative impact of extreme drought on ring width indices is at least partially evident for the years 1865, 1870, 1893, 1894, 1909, 1921, 1944, and 1976 (Fig. 3b). Similarly as in the case of Visp, series of drought years had a more sustained effect on tree growth than single drought years, as exemplified by the periods 1880 – 1887, 1899 – 1909, and (1933 –) 1942 – 1950 (Fig. 4b). The non-parametric Spearman rank correlations rs (Zar 1999) between the overlapping periods of ring width indices and drought indices (cf. Fig. 3), calculated with the statistical software “R” (version 1.5; Ihaka and Gentleman 1996), indicate a moderate association using all data (Table 2a). For both drought indices and all five data sets, there was consistently a higher association between below average drought indices and ring width indices (Table 2b) than between above average drought indices and ring width indices (Table 2c). The statistical significance of the correlation coefficients was not calculated, because the ring width indices were autocorrelated up to a lag of 3 to 4 years. Table 2. Spearman rank correlations (rs) between drought indices (DRI1, DRI2) and ring width indices.

(a) all data

(b) below average

(c) above average

Data set

DRI1

DRI2

RGV

0.46 (100)

0.52 (100)

TR

0.49 (75)

0.45 (75)

ABE

0.43 (115)

0.44 (115)

CT

0.42 (115)

0.43 (115)

L

0.61 (133)

0.55 (133)

RGV

0.57 (51)

0.46 (48)

TR

0.25 (40)

0.33 (39)

ABE

0.39 (61)

0.28 (59)

CT

0.45 (61)

0.40 (59)

L

0.66 (70)

0.38 (69)

RGV

0.40 (49)

0.24 (52)

TR

0.08 (35)

0.25 (36)

ABE

0.17 (54)

0.24 (56)

CT

0.14 (54)

0.21 (56)

L

0.20 (63)

0.36 (64)

Note: Shown are the correlation coefficients for the overlapping periods (number of measurements in brackets). The correlation coefficients were calculated (a) for all data, (b) for drought indices below the average, and (c) for drought indices above the average.

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Impact of droug ht on tree g rowth prior to death At the three sites RGV, the averaged growth curves of dead and living trees decreased between 1951 and 1974, between 1978 and 1990, and after 1995 (Fig. 5). The decreasing growth curves coincided with moisture deficits (1956 – 1974, 1996 – 2000) or with decreasing moisture availability (1980 – 1990), as represented by DRI1 in Fig. 5. At the site Rohrberg Eyholz (Fig. 5a), the growth curves of dead and living trees started diverging after about 1978. Eighty-one percent of the reliably dated dead trees died between 1996 and 1998 (see Fig. 2), during or shortly after the single drought years 1996 and 1998. At the site Gliswald Gamsen (Fig. 5b), the growth curves of dead and living trees started deviating from each other after 1990. At this site, 64% of the dead trees died between 1996 and 1998 (see Fig. 2). At the site LWF Visp (Fig. 5c), the now dead trees showed a higher growth than the living trees between 1974 and 1998, but the growth curves again approached each other in the drought years 1996 and 1998. The average growth of the living trees decreased from 1.26 mm in 1995 to 0.40 mm in 1998, while in the same period the growth of the now dead trees was reduced from 2.20 mm to 0.45 mm. Eight of the 10 dead trees died in 1998 (see Fig. 2). Dis tribution of the r elative mortality risk The impact of moisture availability on the temporal distribution of the estimated relative mortality risk according to the mortality model (Eq. 3) is represented in Fig. 6. For the sites RGV, an increased number of trees was subject to a high risk of dying in the years 1973 – 1976, 1987 – 1993, and 1996 – 2000 (Fig. 6a). The first of these three risk periods occurred after the drought period 1971 – 1974, while the last period coincided with the moisture deficit 1996 – 2000. The decreasing moisture availability from 1980 – 1990 allows us to explain the increased mortality risk between 1987 and 1993. The trees at the next two sites further west (TR) suffered mainly in 1921, owing to the very strong drought year (Fig. 6b). Less accentuated were the late 1940s and 1972 – 1976; still, both periods of increased mortality risk coincide with series of drought years. At the sites ABE (Fig. 6c), 1921, 1944, and particularly 1972 – 1978 reflected years with a relatively high number of stressed trees. Strong drought coincides with the first two stress years only. The trees at the high-elevation sites CT (Fig. 6d) experienced stress in the years 1858, 1893/94, 1921, 1934, less pronounced in the 1940s, and strongly between 1971 and 1979. For the site L (Fig. 6e), the years 1858, 1874, 1894, 1921, 1944/45, 1949/50, 1972 – 1976, and 1992 could be identified as stress years, and most of them are related to the occurrence of drought. Impact of competition on gr owth of dead and l iving trees The linear regression models (Eq. 5) for the data sets Rohrberg Eyholz and Gliswald Gamsen revealed a strong, negative impact of competition (CI; Eq. 4) on current growth [log(BAI3)] of living trees, which explained 35.5% of the growth variability (Table 3a). The effect of neighbor trees was weaker for growth prior to death, as shown by the higher

Chapter IV

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coefficient for CI (Table 3a). In this case, CI explained 28.8% of the growth variability (Table 3a). After removing two strongly suppressed trees (CI > 7) from the data sets, the coefficients for the intercept and slope did not change considerably (Fig. 7). However, the R2 for the model with the living trees as well as for the dead trees dropped to 25.9% and 8.1%, respectively, and competition turned out to have no significant effect on growth prior to death any more (Table 3b).

Fig. 5. Averaged ring widths of reliably dated dead and living trees (black lines: living trees, gray lines: dead trees) and drought index (DRI1; hatched areas) for (a) Rohrberg Eyholz (n alive = 29, n dead = 26), (b) Gliswald Gamsen (n alive = 26, n dead = 22), and (c) LWF Visp (n alive = 11, n dead = 10). Only averaged ring widths with n ≥ 5 trees are shown.

106


Fig. 6. Annual relative mortality risks and drought index (DRI1; hatched areas) of the five combined data sets RGV, TR, ABE, CT, and L. Only mortality risks of reliably dated trees with n ≥ 5 trees are shown.

Discussion Drought can exert a major impact on the vegetation structure and species composition in a variety of biomes, such as grasslands (Clark et al. 2002), tropical forests (Condit et al. 1995, Nakagawa et al. 2000, Aiba and Kitayama 2002), or temperate forests (Hursh and Haasis 1931, Tainter et al. 1983, Clinton et al. 1993, Elliott and Swank 1994, Jenkins and

Chapter IV

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Pallardy 1995, Orwig and Abrams 1997, Villalba and Veblen 1998, Ogle et al. 2000). The results presented in this study suggest that drought has a limiting effect on tree growth and that it acts very likely as a bottleneck event that triggers Scots pine decline in the Valais. However, other factors besides the direct climate impacts need to be considered to better understand short- to long-term periods of low growth and the related mortality response. The impact of the investigated stress factors drought and competition on tree growth, as well as observations of insects occurrences are discussed in the context of the decline disease theory. Table 3. Linear regression models relating recent growth rate [log(BAI3)] and competition (CI) of living trees and reliably dated dead trees that died between 1996 and 2001. The models were calculated combining the data sets Rohrberg Eyholz and Gliswald Gamsen; (a) full data sets, (b) restricted data sets (trees with CI ≤ 7). For details, see text. Coefficient (p)

(a)

Model

Intercept

CI

R2 (%)

R2adj (%)


1.754 (< 2 ¥ 10-16 ***)

-0.359 (6.44 ¥ 10-7 ***)

35.5

34.4


1.051 (3.22 ¥ 10-11 ***)

-0.128 (2.96 ¥ 10-4 ***)

28.8

27.0


1.736 (< 2 ¥ 10-16 ***)

-0.342 (4.49 ¥ 10-5 ***)

25.9

24.6


1.075 (1.29 ¥ 10-8 ***)

-0.147 (7.5 ¥ 10-2)

8.1

7.5

1996 and 2001 (n = 41)

(b)

1996 and 2001 (n = 40) Note: The regression coefficients, p values (***, p < 0.001), and the coefficients of determination (unadjusted R2, adjusted R2adj) are shown. To compare the goodness-of-fit of linear models that contain different numbers of measurements or independent variables, R2adj should be considered (Zar 1999).

Drought a s an i nciting mortality factor Although they are drought-adapted, Scots pine trees in the arid climate of the Valais tend to live close to the limit of their hydraulic capacity and therefore might react sensitively to drought, particularly on dry, shallow soils (Flühler 1981, Kienast 1985a; cf. Hill 1993). Recently, Martinez-Vilalta and Piñol (2002) have compared three pine species in northeastern Spain in terms of their physiological reaction to drought. Only P. silvestris stands were affected by drought-induced mortality, and the hydraulic conductivity per unit of leaf area has been shown to be lowest for the most strongly affected population. Generally, pine species seem to be more vulnerable to xylem embolism than other conifers (Piñol and Sala 2000, Martinez-Vilalta and Piñol 2002, but see Irvine et al. 1998). The absence of Scots pine decline outside the main wind trajectories in the Valais (Flühler 1983) indicates that wind is likely to act as an additional desiccating factor, which might intensify the effects of drought (Telewski 1995, Ennos 1997).

108


Drought indices and ring width indices of the combined Scots pine data sets are moderately correlated (rs = 0.42 – 0.61) (Table 2). For all five data sets and for both drought indices, there were higher correlation coefficients between below average drought indices compared to above average drought indices. This indicates that during periods of moisture surplus, additional limiting factors than moisture availability affect tree growth, such as early or late frosts that occur frequently in the Valais due to the high terrestrial radiation (Lingg 1986, Z'Graggen 1992).

Fig. 7. Competition index (CI) versus recent growth rate [log(BAI3)]. Shown are dead trees that died between 1996 and 2001 (n = 41) and living trees (n = 59) from the sites Rohrberg Eyholz and Gliswald Gamsen. Regression lines from Table 3 (black: full data set, gray: restricted data set with CI ≤ 7).

Single drought years reduced tree growth in the investigated Scots pine stands in the short term, generally in the year of drought (Fig. 3), while periods of drought years often initiated prolonged growth decreases (Figs. 4 and 5). The mortality model interpreted years or periods of low growth commonly as increased mortality risk, particularly with increasing tree size (Fig. 6; cf. Eq. 3). In the context of the decline disease theory, it is noteworthy that extreme drought years such as 1921, 1944, or 1974/76 had a less sustained negative effect on tree growth compared to series of medium drought years such as those during the 1940s for Visp and Sion, or 1956 – 1974 for Visp (Figs. 3 and 4) (cf. Kienast et al. 1981). Generally, extreme events such as drought tend to be crucial in initiating changes in forest ecosystems, much more than average climatic conditions (Oliver and Larson 1996, Innes 1998). The negative impact of drought on tree growth or the onset of declining growth prior to death has been observed for a wide range of tree species (Stahle et al. 1985, LeBlanc and Foster 1992, Elliott and Swank 1994, Orwig and Abrams 1997, Hughes and Funkhouser 1998, Pedersen 1998b, Villalba and Veblen 1998, Ogle et al. 2000). However, the significance of multi-year drought having much more adverse and decisive effects on tree growth than single-year drought has been emphasized only by a few studies (Stringer et al. 1989, Biocca et al. 1993, Jenkins and Pallardy 1995, LeBlanc 1998), which is underlined by the present study. What might be the reasons for the prolonged growth decreases of Scots pine after multiyear drought? In a retrospective study on needle retention of Scots pines felled in 1996, Pouttu and Dobbertin (2000) found for the Region Visp several periods with reduced nee-

Chapter IV

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dle amount and increased needle loss. These periods coincide mostly with the end of drought periods found in this study (i.e., 1946 – 1949, 1973 – 1976, and 1990 – 1992). Drought not only leads to increased needle loss but also to reduced needle length and to reduced shoot length with fewer needle pairs in the following year (Clements 1969). This explains why foliage amount is reduced over several years following a drought. As foliage amount affects both tree growth (Solberg 1999) and tree mortality (Dobbertin 1999, Dobbertin and Brang 2001) longer lasting effects of multi-year drought on growth and mortality can be expected. Consistently over the five combined data sets, the 1970s are revealed by the standardized tree-ring series as below-average growth (Fig. 3), and by the mortality model as a period of increased mortality risk (Fig. 6), which is related to the growth decrease in the same decade (Fig. 4). These results agree with historical reports of accumulating forest damages in the 1970s in the Valais (Kienast 1985b). In the Visp area (sites RGV), an increase of forest damages was observed again at the beginning of the 1990s and after 1996 (Dobbertin 1999, Rigling and Cherubini 1999), which matches the estimations of the mortality model fairly well (Fig. 6a). In a stand nearby the site LWF Visp, the observed annual mortality rates increased after 1996 and reached in 1998 a maximum of more than 25% (Dobbertin 1999). For the sites RGV and TR, the low growth rates in the 1970s and the related increased mortality risk coincide with drought periods (Figs. 3a and 6a). Unlike Visp, the climate station Sion does not show a longer period of drought in the 1970s, which could explain the growth depression at the sites ABE, CT, and L (Figs. 3b and 4b) and the related mortality risks (Figs. 6c – 6e). We strongly suppose that the climate data, particularly the temperature values, are biased for this period, since the original climate data from Sion (1864 – 1977) were homogenized with two overlapping climate series that covered the periods 1971 – 1982 and 1978 – 2001, respectively (O. U. Bräker, unpublished report). Despite some agreement between the standardized ring widths and the relative mortality risk, some differences are striking, which point at the fundamental difference between the two approaches. For example, the standardized ring widths identify the periods 1893 – 1895 and 1973 – 1976 as approximately equally stressful for all five data sets (Fig. 3). The mortality model, however, mainly identifies the 1970s as a period of increased stress, and suggests that the trees had no or only a low risk of dying in the 1890s (Fig. 6). A similar pattern is visible at the sites RGV, where the standardized ring widths point at several stress years between 1890 and 1970 (Fig. 3a), whereas the mortality model does not detect any increased mortality risks in this period (Fig. 6a). This is because the mortality model assumes the trees not to be stressed as long as their relative growth rate, which takes into account the current growth rate and the size of the tree, is relatively high and their growth rate does not decrease rapidly (Eq. 3) (Bigler and Bugmann 2003b). In conclusion, standardized tree-ring indices reflect a mean growth response of stressed and non-stressed trees considering the relative vigor of the trees. The mortality model returns the percentage of stressed trees in a population taking into account the absolute vigor of the trees.

110


Elucidating stress-induced mortality by deriving standardized tree-ring series and reconstructing mortality risks is based on the assumption that stress is mirrored in the growth patterns of living and dead trees. However, the over- or underrepresentation of stressed or dying trees in the sample as well as the overrepresentation of young trees may bias the tree-ring indices as well as the distribution of the modeled mortality risk. The overrepresentation of dead trees towards the upper (recent) range limit of each chronology (see Table 1) is likely to result in underestimated standardized ring widths and overestimated mortality risks, e.g., during the 1990s for the sites RGV (Figs. 3a and 6a). At these sites, 50% dead trees were used in the sample, while the actual proportion of lying or standing dead trees in the population was about 30% at the sites Rohrberg Eyholz and Gliswald Gamsen, and 50% at the site LWF Visp. Likewise for the sites RGV, TR, ABE, and CT, the mortality risk might be underestimated towards the lower range limit, since only a few dead trees were sampled that had died several decades ago. The initial underrepresentation of stressed and dead trees in the sample leads to an increase of the estimated mortality risk along time (Figs. 6a – 6d). The data set L can be considered as representing the entire tree population (Figs. 3b and 6e) for a longer time than at the other sites, since no lying or standing dead trees or stumps could be detected in the field. In spite of these limitations, we believe that the combination of standardized tree-ring indices and modeled mortality risks is a powerful means to reconstruct past growth responses to stress factors. The question whether there is a direct link between climatic variability, particularly drought, and tree mortality rates has been addressed by other studies, supplying evidence of a strong association between extreme single drought years and tree mortality (Clinton et al. 1993, Hill 1993, Condit et al. 1995, Villalba and Veblen 1998). However, if the mortality response does not occur immediately in the year of stress or within a lag of one or two years, the association between environmental stress and tree mortality is likely to be weak and difficult to elucidate (Clinton et al. 1993, Pedersen 1999). At the sites RGV in the Valais, drought periods (1956 – 1974, 1996 – 2000) or decreasing moisture availability (1980 – 1990) preceded the mortality response by several years or decades and were likely one of the major mortality factors (Fig. 5). The agreement between reconstructed mortality rates at the sites RGV and drought in the period after 1990 (Figs. 2 and 5) does not necessarily imply a simple cause-effect relationship. Rather, the drought in 1996 and 1998 can be considered as further contributing mortality factors (Fig. 5). In a stand near Saxon (Fig. 1), 50% of the Scots pine trees died 25 – 30 years after the drought period in the 1940s (Kienast et al. 1981). A lagged mortality response up to several decades after severe drought was also detected by Tainter et al. (1984), Pedersen (1998b), and Jenkins and Pallardy (1995). These studies support our findings of considerably lagged mortality responses after persistent drought periods, where further short-term drought might ultimately kill the previously stressed trees.

Chapter IV

111

Com petiti on as a pred isposi ng mor tality factor The changed management activities in the Valais after 1950 might be a reason for the increasing stand densities. The currently invading Silver fir, Norway spruce, downy oak, and shrub species (Kienast et al. 2003) are more shade-tolerant than Scots pine and – besides stand ageing – additionally increase competition in the stands, which is a disadvantage for the shade-intolerant Scots pine (Ellenberg 1996, Ott et al. 1997). The scattered distribution of dead Scots pine trees observed until the mid-1990s is likely to be related to competition (cf. Dobbertin et al. 2001). While neighbor trees were found to exert a highly significant impact on recent growth rates of living Scots pine trees, the effect of competition on growth prior to death is less pronounced (Table 3). Competition can reduce tree growth or initiate growth declines of living trees, but as soon as a tree is in the stage of dying, further factors have to be taken into account that determine tree growth prior to death (Fig. 7). Although two outliers (two suppressed trees of 10 cm and 11 cm DBH) had a substantial impact on the explained growth variability and on the inference particularly for the dead trees (Table 3), the regression coefficients changed only slightly after removing these measurements (Fig. 7). We assume that growth rates of Scots pine trees in the Valais will decrease further with increasing shading, due to stand ageing and invading tree species, which will ultimately increase the individual mortality risk. In a similar study with dead and living Norway spruce trees from Davos (Switzerland) where the same competition index was used (Eq. 4), Bigler and Bugmann (2003a) showed that the effect of competition on recent growth of living trees (log(BAI3) = 2.436 – 0.220 CI) was comparable to the effect on growth prior to death (log(BAI3) = 1.078 – 0.201 CI). Although the Scots pine stands in the Visp area were less dense and younger than the Norway spruce stands in the Davos area, our results clearly show the different reaction of vigorous versus dying Scots pine trees to competition. Increasing growth rates after single, extreme drought years, such as in 1921, 1944, and 1974/76, might be partly explained climatically by the improved moisture availability after these drought years (Fig. 4). From an ecological point of view, a further factor contributing to the increasing growth rates may be release effects due to a relaxation of competition, since it is likely assumed that a certain fraction of the trees in these stands died during or after the drought years (cf. Innes 1993, Orwig and Abrams 1997, Villalba and Veblen 1998, Martinez-Vilalta and Piñol 2002). At the sites Rohrberg Eyholz and Gliswald Gamsen, the surviving trees benefited more strongly from the release of resources after the drought period 1956 – 1974 as compared to the stressed trees that ultimately died (Figs. 5a and 5b), while at the site LWF Visp, the trees that eventually died showed an increased growth until 1995 (Fig. 5c). These results corroborate earlier findings by Hill (1993), who demonstrated that in combination with climate effects, non-dominant trees suffered con-

112


siderably higher mortality rates in drought years or one year after such events compared to dominant Scots pine trees (see also Elliott and Swank 1994). Ins ects-drought inter actions as contributing mortal ity factor The century-long human impact in the forests of the Valais has led currently to an overrepresentation of Scots pine compared to its natural distribution. This relatively high abundance might contribute to the increased likelihood of insect epidemics in the 20th century, since insect populations more easily propagate from one stand to another than between isolated stands (Berryman 1982). Among the native tree species, Scots pine is a host for a larger number of harmful insect species compared to the other European tree species (Leibundgut 1991; cf. de Groot and Turgeon 1998). The locally observed change from a regular scattering of single dead Scots pine trees to a clustering into groups or entire stands of dead trees during the 1990s (Rigling and Cherubini 1999, Rigling et al. 1999a) suggests that the importance of insects might has increased in some stands during the last decade. The significantly rising mean temperatures since about 1980 (data not shown) have likely favored insect outbreaks in the Valais. The compilation of historical forest damages in Switzerland until 1960 reveals for the years 1910, 1919/20, 1931/32, and 1946 – 1956 several local to regional bark beetle infestations in Scots pine stands of the Valais (Bütikofer 1987a, b). All of these infestations, except for 1919/20, can be related to drought in the current or previous years (Fig. 3). For P. silvestris, severe water stress results in a reduction of the length of the induced defense reaction and a lower resin content (Croisé and Lieutier 1993), which later facilitates insect infestations in the affected stands (Hill 1993, Cobb et al. 1997, Czokajlo et al. 1997). More detailed data are available for the Gliswald Gamsen, where the Forest Service of the canton of Valais reported 50 Scots pine trees being infested in 1992 (reports from 1984 – 2002) by Thaumetopoea pityocampa Denis & Schiff. (pine processionary moth). These infestations occurred two years after the growth curves of dead and living trees started to diverge (Fig. 5b), which in turn was probably caused by the decreasing precipitation before 1990; thus, this complex of factors suggests that this infestation was stress-induced, conforming to the decline disease theory. No documented insect outbreaks from the site Rohrberg Eyholz are available. At the site LWF Visp, the dying trees have been growing better than the surviving trees since 1974 (Fig. 5c), and most of the dead trees died in 1998 (Fig. 2). The rapid growth decrease of the dying trees after 1995 points at insect infestations, which are likely related to the drought years 1996 and 1998. In 1998, mainly the occurrence of Tomicus sp. (pine shoot beetle), but also other insect species were recorded (observation period 1984 – 2002, PBMD2). In the years 1997/98, Phaenops cyanea Fabr. (blue pine wood borer) was ob-

2

Phytosanitärer Beobachtungs- und Meldedienst (WSL; Birmensdorf, Switzerland)

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served in the field as a potential lethal factor (M. Dobbertin and A. Rigling, personal observations). Phaenops cyanea was observed to also attack non-stressed trees (cf. Hill 1993). These observations show that in some cases vigorous trees may have the same or an even higher risk of being attacked by insects than stressed trees (Lorio et al. 1982, Price 1991, Czokajlo et al. 1997). It may partially explain why at the site LWF Visp larger trees had higher mortality rates (Dobbertin 1999).

Conclusions The widespread occurrence of high Scots pine mortality in the Valais and in several other central alpine dry valleys of the European Alps suggests that this phenomenon is caused by regional-scale factors and not by local anomalies. A multitude of biotic and abiotic stress factors, some of which changed in the course of time is currently assumed to be involved in the decline of Scots pine. The shade-intolerance of Scots pine, a pioneer tree, renders this tree species more vulnerable to high competition than other dominant tree species in the Valais. Changed management activities after 1950 resulted in the invasion of more shade-tolerant and competitive tree species such as Silver fir, Norway spruce, downy oak, and shrubs, which increase stand density and thus the competition-related mortality risk, particularly for Scots pine. The observed scattered distribution of dead Scots pine trees is likely to be attributable to intra- and inter-specific shading of neighbor trees, not to primary insect infestations. Our results show a highly significant effect of competition on recent growth rates of living Scots pine trees, which is stronger than e.g. for Norway spruce. However, the growth rates of dying Scots pine trees are less affected by competition, and additional environmental factors must be taken into account to explain their low growth prior to death. In addition to competition as predisposing factor, shallow soils, i.e., low soil water holding capacity, and wind as a desiccating factor impose a permanent stress on the Scots pine trees in the Valais, which intensifies the effects of drought. Although this was not investigated in our study, fluorine emissions and other pollutants might have acted as further predisposing factors, which affected particularly Scots pine. In this paper, we have presented strong evidence of the limiting effect of drought on tree growth and of the impact of drought on Scots pine mortality. While it is plausible to assume that drought could play a major role for tree growth and mortality in this continental climate, the relative importance of single-year and multi-year drought has not been studied explicitly to date. Our results suggest that single, extreme drought years have a short-term, reversible effect on tree growth, but there are no strong indications about single drought years acting as an inciting factor for tree mortality. However, multi-year drought has been shown to reduce tree growth for several years or decades, thus increasing a tree’s risk to die. Increased growth after drought periods is probably caused by the improved moisture availability as well as by release effects due to drought-induced mortality of neighbor trees. Lagged mortality responses several years or decades after drought events complicate

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the analysis of cause-effect relationships. Predisposing factors such as competition and a previous extended drought period impaired trees in the long term and made them more vulnerable to following contributing factors, such as further strong drought years in combination with secondary insect infestations that could be detected locally. At one site, not only stressed trees, but also vigorous trees were attacked by insects. The recent shift from scattered single dead trees to clusters of dead Scots pine trees points at a stronger impact of insects, which superposes the effects of drought and competition. We suggest that further investigations should focus on detailed analyses of tree-insect interactions on the individual tree and stand level. In addition, examining competition relationships between Scots pine and the main tree species will provide a sound foundation to better understand future dynamics in the Scots pine forests of the Valais.

Acknowledgments We would like to thank Bärbel Zierl (Mountain Forest Ecology, Zurich, Switzerland) and Esther Hegglin (Zug, Switzerland) for their support in the field. We are also indebted to Felix Kienast and Fritz Schweingruber (both WSL, Birmensdorf, Switzerland) for using their tree-ring data. Thanks are due to Ludger Wenzelides (Mountain Forest Ecology, Zurich, Switzerland) for creating the GIS map, and to Franz Meier (WSL, Birmensdorf, Switzerland) for the query in the insects data base. We would also like to thank the Seminar for Statistics (ETH, Zurich, Switzerland) for statistical advice. Finally, we are grateful to the Forest Service of the canton of Valais for their generous support.

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Synthesis The fundamental aim of this thesis was to show how tree mortality is interrelated to tree growth. In the case of growth-dependent tree mortality, the mortality inducing factors act primarily upon ecophysiological processes and reduce tree vigor, while tree death occurs as a lagged response to decreasing vigor. The factors that ultimately kill a tree are at the end of a chain of multiple mortality factors that act on the short to the long term and thus affect a tree over a few years or several decades. This synthesis chapter is structured into four sections, as follows: Relating environmental stress factors to growth rates of living and dying trees allows us to reveal the causes that affect tree growth prior to death. I showed that the vigor of trees with a strongly increased mortality risk has previously been lowered by predisposing and inciting factors. These weakened trees may eventually die when an ultimate mortality factor is present. Knowing the complex of dominating stress factors and their timing in a particular stand leads to an improved understanding of the mortality processes of individual trees. In this study, impending tree death was found to be characterized by particular, speciesspecific tree-ring patterns. Investigating these different growth patterns provided a means to reconstruct the mortality process of individual trees. In spite of the large individualspecific growth variability, the growth patterns prior to death that were detected at one site generally turned out to be transferable to other sites. The ecological interpretation of the growth patterns of living and dying trees that are growing at different sites allows us to better understand species-specific growth and survival strategies. These decisive growth patterns were incorporated in tree mortality models, which may be applied in diverse fields such as forest ecology, forest management, and succession research. The significance of the growth patterns was assessed in terms of their predictive power for modeling tree mortality. In a first step, this was addressed using a crosssectional modeling approach for one time point, and in a second step using a longitudinal approach along time. These two fundamentally different approaches were shown to emphasize different aspects of tree mortality processes. Accurate predictions of forest succession under current and changed climate rely on appropriate species-specific mortality functions. Assessing and validating mortality functions under different climate regimes gives us some confidence about the extent to which these functions may be applied under changed climate. This in turn will allow us to more reliably project forest dynamics in time and space using forest succession models that incorporate improved mortality algorithms.

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Mortality inducing factors Although the impact of environmental stress factors on tree growth can be quantified fairly well, the event ‘tree death’ is comparatively difficult to predict due to the randomness of the involved stress factors in time and space, e.g., the occurrence of multiple drought years or attacks by insects from adjacent, infested forest stands. This circumstance is exemplified by the estimated mortality risks of the Scots pine (Pinus silvestris L.) trees in the Valais (chapter IV, Fig. 6). Although many Scots pine trees that we sampled exhibited a short-term increased mortality risk in the year 1921, none of them died during or shortly after this drought year. This was probably due to the lack of contributing mortality factors, such as pathogens or further drought. However, it can be assumed that many trees died at this time, which are not included in the sample due to the decay of wood or due to the removal of these dead trees. Only later in 1998, many of the Scots pine trees sampled in the Visp area died, triggered by a longer period of moisture deficit that was followed by further drought and pathogens as lethal factors (chapter IV, Figs. 2 and 5). Unlike in the case of Scots pine, the mortality predictions for Norway spruce (Picea abies (L.) Karst.) turned out to be relatively precise (chapter II, Fig. 4), which can probably be attributed to the higher impact of competition and the lower impact of randomly occurring mortality factors, as discussed below. The fate of a tree that is at high risk of dying depends on the presence of such additional contributing factors that ultimately kill a tree, but it also depends on forest dynamics in the direct neighborhood of this tree. For example, dominating neighbor trees may have a higher risk of dying due to windthrow or snow breakage, and due to their increased vigor they may be more attractive for some specialized insect species that infest particularly vigorous trees (e.g. chapter IV, Fig. 5c). The death of these dominating trees makes additional resources available (light, nutrients, water) that allows the formerly dominated trees to recover (see chapter II, Fig. 3a). Therefore, the temporal predictability of tree mortality also depends on the ecological and climatological factors that govern forest dynamics at a given site. The results of this thesis show that the high mortality rates in the Scots pine stands of the arid Valais are more likely related to drought than to competition, while competition is rather a dominating, decisive factor for the relatively low mortality rates in the more humid Norway spruce stands of Davos, Bödmeren, and Scatlé. This is supported by the growth-competition models (chapter I, Table 7, and chapter IV, Table 3), where competition explained a higher percentage of the recent growth variability of living Norway spruce trees than of Scots pine trees. Within each species, a higher amount of recent growth variability of living trees was related to competition than in the case of growth prior to death. However, there was a stronger effect of competition on tree growth of living Scots pine trees than on living Norway spruce trees as indicated by the slope of the regressions, but the effect of neighbor trees on tree growth prior to death was weaker for Scots pine than for Norway spruce (cf. chapter I, Table 7, and chapter IV, Table 3). For Norway spruce, competition had a similar effect on growth of living trees and on growth prior to death (chapter I, Fig. 8), while for Scots pine, the impact on tree growth attenuates as soon as a tree is in the process of dying (chapter IV, Fig. 7). Thus, living Scots pine

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trees suffer stronger competition-induced growth decreases than Norway spruce trees, but the remaining environmental factors such as climate effects or insects explain a higher amount of the overall growth variability in the Scots pine stands than in the Norway spruce stands. A complex of multiple stress factors has to be considered to understand the Scots pine decline in the Valais (chapter IV). Changed management activities over the last 50 years must have resulted in increasing stand densities due to stand ageing and invading tree species, which affect the shade-intolerant Scots pine more than other tree species in the Valais. Competition has a highly significant effect on recent growth rates of living Scots pine trees (as mentioned before), and acts as a long-term stress factor that predisposes trees to die. Shallow soils and wind as a desiccating factor are likely to impose a permanent stress on trees in the Valais. Overall, drought has a limiting effect on tree growth and very likely acts as a “bottleneck event” triggering Scots pine decline in the Valais. Single, extreme drought years were found to have a short-term, reversible effect on tree growth, whereas multi-year drought initiated prolonged growth decreases that increased a tree’s risk of dying in the long term. It is likely that drought-insect interactions often are the final lethal factors in these Scots pine stands. Notably, the mortality response generally occurred with a lag of several years or even decades after the drought periods. The detailed analyses of the mortality processes in the Scots pine stands of the Valais suggest that it is crucial to consider multiple environmental stress factors for a relatively long time period that goes much beyond the last few years prior to death. Although the methods presented in this thesis are not powerful enough to demonstrate detailed cause-effect chains, I was able to detect and quantify some of the main factors that cause the mortality of Norway spruce and Scots pine. To provide an improved mechanistic understanding of the mortality processes of trees, a large number of vigorous and dying trees would need to be studied using ecophysiological methods over several years or even decades. Also, the associated mortality factors would need to be monitored in detail. Such a comprehensive approach would be very costly, whereas the approach used in the present thesis is relatively simple, but still quite effective.

Growth patterns of dying trees Impending tree death of the investigated species was often indicated by characteristic, species-specific growth patterns. The differences between the ecological properties of Norway spruce and Scots pine, and the presence of different stand-specific mortality factors in Davos, Bödmeren, Scatlé, and in the Valais are quite evident when the growth curves over several decades prior to death are compared. On average, growth decreases of now dead Norway spruce trees started more than 50 years prior to death (chapter I, Fig. 3), while growth divergences between dead and living Scots pine trees started only 10 to 20 years prior to death (chapter IV, Fig. 5). Different combinations of long-term and shortterm stress factors act upon tree growth in the Norway spruce stands (chapter II, Figs. 1 –

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3) compared to the Scots pine stands (chapter IV, Figs. 4 and 5), as discussed above. These species- and site-specific differences have to be taken into account when the growth patterns prior to death are interpreted. The significance of different intra-specific growth patterns as an indicator of the mortality risk was evaluated for Norway spruce. A closer inspection of the recent growth patterns of living and dying Norway spruce trees in Davos showed that growth levels (i.e., recent growth rates) and growth trends (i.e., changes of growth rates) of dead trees are shifted to lower values compared to living trees (chapter I, Fig. 5). Low to very low growth levels generally indicate an increased risk of dying (chapter I, Figs. 6 and 7). However, particularly those periods that are characterized by intermediate to low growth levels have to be interpreted carefully when we try to assess the current mortality risk based on growth patterns. While trees with low to intermediate growth levels, but stationary or slightly positive growth trends do not necessarily have an increased mortality risk, trees with low to intermediate growth levels in combination with rapid growth decreases (strongly negative growth trends) are at high risk of dying. Persistently reduced but stationary growth may indicate an adaptation to low resource availability such as light, nutrients, and water (see chapter II, Fig. 3a). This may be considered as a strategy to minimize mortality risk, since slow-growing trees may be favored eventually over those with fast growth rates, e.g., when the latter die due to windthrow or pathogen infestations (chapter IV, Fig. 5c). Even trees that are growing on a high to very high growth level can have an increased mortality risk if they experience rapid growth decreases (see chapter I, Fig. 4b, or chapter II, Fig. 3a). A high to very high growth level and increasing growth rates (positive growth trends), however, suggest a very low mortality risk. These empirical findings were the rationale to consider a growth trend variable in the mortality models of the cross-sectional approach in addition to a short-term growth level variable, and this helped considerably to improve the identification of dead trees with an intermediate to low growth level and a distinctly negative growth trend. Growth levels as the only predictor variable would fail to correctly predict the status (dead or alive) of trees with an intermediate to low growth level. Thus, a major finding of this thesis is that if the current mortality risk of a tree has to be assessed reliably, one should consider the growth trend over the last few years in addition to the recent growth level, because this additional variable significantly improves the performance of mortality models. This finding is valid at least in the case of Norway spruce and Scots pine in the European Alps, and it should be applicable to other tree species as well. The significant growth patterns resulting from chapter I were considered in the mortality models of the longitudinal approach. These variables and the relative growth rate turned out to be highly significant for determining the time of tree death of Norway spruce (chapter II), and to assess the relative mortality risk for Scots pine (chapter IV). The relative growth rate not only reflects the growth rate of one year, but it also accounts for the current tree size. This variable allowed to differentiate between low absolute growth rates

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of small trees when the relative growth rate is still high and thus mortality risk is low, and low absolute growth rates of larger trees when the relative growth rate is low.

Cross-sectional versus longitudinal mortality models Two fundamentally different approaches of modeling tree mortality were used in this thesis. Depending on the research question or the field of application, either the crosssectional approach to discriminate between dead and living trees or the longitudinal approach to predict the time of tree death provide a suitable solution. For both modeling approaches, I have shown that appropriate verification and validation methods are crucial to assess model performance. The commonly applied cross-sectional approach for modeling tree mortality offers basically a static view and does not allow any statements about changes in time (chapter I). This approach is sufficient e.g., when forest managers or forest ecologists wish to assess the current mortality risk of individual trees based on recent growth patterns. The growth patterns that were selected as predictor variables, i.e., combinations of growth level and growth trend variables, proved to be useful to discriminate between dead and living Norway spruce trees. In the verification, 80% of the trees at the site Davos were classified correctly as being dead or alive, which was confirmed in the validation with a correct classification of 71% in Bödmeren and 81% in Scatlé. Using Norway spruce as a case study of the cross-sectional modeling approach, these findings support the broad applicability of the selected growth patterns as an indicator of the current mortality risk for this species. The novel approach of longitudinal mortality models presented in chapter II provides a dynamic view with a methodologically similar, but conceptually different approach than the cross-sectional study (see chapter I). The longitudinal models are optimized to assess the mortality risk over time at the individual tree level (chapter II). The models may be applied to improve mortality predictions of individual trees that can be used in forest succession models (chapter III), or to reconstruct mortality risks at the population level (chapter IV). In spite of the autocorrelated responses (dead or alive) within the tree individuals, the regression coefficients can be estimated using standard regression methods, which allows us to make correct predictions. Combinations of growth levels, growth trends, and the relative growth rate as predictor variables resulted in a high performance of the best six models with regard to maximizing two classification accuracy criteria and minimizing three prediction error criteria (chapter II). In the verification using the Norway spruce trees in Davos, 71 – 78% of all dead trees and 73 – 75% of all living trees were classified correctly, and 44 – 56% of all dead trees were predicted to die within 0 – 15 years prior to the actual year of death. Only a low percentage of all dead and living trees was predicted to die more than 60 years prior to the last measured year. The generality of the mortality models for Norway spruce was supported by the validation with two independent data sets from geologically and climatically different areas.

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Although the mortality models of the longitudinal approach were not optimized exclusively to maximize the correct classification of dead and living trees, the performance of the Norway spruce models with regard to the classification accuracy criteria is fairly high compared to the mortality models of the cross-sectional approach. The comparison of the correct classification rates of Norway spruce trees at the three sites Davos, Bödmeren, and Scatlé reveals that for both, the dead and living trees, the longitudinal approach (see chapter II, e.g. model 8 in Tables 3 – 5) performs better at one of three sites than the crosssectional approach (chapter I, Table 6), but it performs somewhat less satisfactorily at two of three sites.

Predictions of tree mortality under current and changed climate Ultimately, the accurate mortality predictions based on the longitudinal modeling approach (chapter II) should allow us to improve the mortality submodel in forest succession models (chapter III). Under current climate, the deterministic, empirical mortality functions (EMFs) developed for Norway spruce were found to perform better than several stochastic, theoretical mortality functions (TMFs) that are commonly used in forest gap models, a widely used subset of forest succession models (chapter III). Three of the four EMFs performed consistently better at all three sites (Davos, Bödmeren, and Scatlé), i.e., they predicted the time of tree death more accurately, while three of the four TMFs performed worse than the remaining mortality functions. From this I conclude that the TMFs are not appropriate models to predict the time of tree death, in spite of their widespread use in gap models, unless the parameters and thresholds of the TMFs are optimized for individual species. The implementation of species-specific, empirically derived mortality functions that have been validated with tree-ring data would be quite likely to result in substantial changes of simulated forest succession, and would increase the reliability of projections under current climate. Under a changed climate, there is a high uncertainty in quantifying tree mortality, which reflects the high variability of tree mortality under current climate. Although most modelbased projections of forest succession indicate high tree mortality and transitions to different forest types under a changed climate, the applicability of EMFs and TMFs to predict the time of tree death under changed climates is uncertain at the present time. However, since the three sites of the Norway spruce study conducted in this thesis are climatically quite diverse, this gives us confidence that the EMFs developed for this species (chapter II) should have some predictive power, even under a changing climate in the 21st century (chapter III). However, further tests should be conducted to evaluate the sensitivity and appropriateness of TMFs and EMFs under a wider variety of climatic conditions.

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Fig. 1. Group of dead Norway spruce trees surrounded by living trees. Primeval forest Bödmerenwald, central Switzerland (picture: Christof Bigler).

A changing climate will have direct impacts on ecophysiological processes of individual trees, which may result in altered growth-mortality relationships at the stand level. However, due to the physiological adaptability of tree species and the resilience of forest ecosystems to environmental changes, these direct impacts might have comparatively small effects. Instead, I would expect that altered climate-pathogen interactions and increases of climate-related extremes such as windthrow, snow breakage, fire, or intensive drought periods have more decisive effects on tree mortality and future species composition. An improved understanding of mortality processes at the individual tree level, at the stand level, and at the landscape level provides more accurate mortality predictions, which will ultimately allow us to make more reliable projections of forest succession under current and changed climate.

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Acknowledgments

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Acknowledgments

First of all, I would like to express my gratitude to my supervisor and mentor Prof. Dr. Harald Bugmann1, who guided me in the last more than three years through the scientific space. Many short and long discussions provided me with the necessary feedback on my work. Thanks due to his innumerable and helpful comments in my manuscripts, I learnt to more critically structure and formulate my thoughts and research results. He more and more gave me the freedom to pursue my own ideas and to explore different research approaches. I am indebted to Prof. Dr. Fritz Schweingruber2, who taught me to ask questions about the nature of trees, and to discover relationships between trees and environmental factors. He introduced me to the fascinating field of tree rings and dendrochronological methods as a tool to answer questions about growth strategies of trees. His networked thinking allowed me to recognize patterns beyond the local scale. Many thanks are due to Prof. Dr. Brian Pedersen3, who accepted to serve as a co-advisor of my thesis, despite the geographical distance. He supported me with many useful and important hints on conceptual and technical issues of my work. I am very grateful to Dr. Andreas Rigling2, Dr. Otto Ulrich Bräker2, and Dr. Matthias Dobbertin2 for their many stimulating discussions and their collaboration, particularly during the last, intensive period of my thesis. Thanks also to Werner Schoch2, who kept my increment borers in good shape. A special thanks to Dr. Veronika Stöckli4 and JeanFrançois Matter5 for providing help with the selection of the study sites. My thesis would not have been possible without the professional advice of many statisticians. Prof. Dr. Jim Lindsey6 was patient with answering many questions, and he allowed me to dive into the concepts of longitudinal data analysis during my stay at Limburgs University. The Seminar for Statistics7, notably Prof. Dr. Hansruedi Künsch, Dr. Georg

1

Mountain Forest Ecology, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

2

Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland

3

Dickinson College, Carlisle (Pennsylvania), USA

4

Swiss Federal Institute for Snow and Avalanche Research (SLF), Davos, Switzerland

5

Chair of Silviculture, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

6

Limburgs University, Diepenbeek, Belgium

7

Seminar for Statistics, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

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Acknowledgments

Kralidis, Roman Lutz, and Bruno Tona, supported me in regular intervals, when I got stuck. The R community8 solved many of my statistical problems literally over night. A big thanks is addressed to the internal and external members of the Mountain Forest Ecology Group1. They provided a friendly and stimulating atmosphere during the vital coffee breaks, at lunchtime, or on the occasion of scientific beer drinking. I also want to thank our diploma students to keep me on the trot, my field assistants, my friends, Esther Thalmann9 and Caroline Heiri1 for the fine tuning of some chapters, and all the helpful people at the Department of Forest Sciences (ETH) and at WSL2 that I did not mention. I am indebted to the Swiss Federal Institute of Technology (ETH) for the financial support. Finally, I want to thank my parents, who supported me during my studies.

8

The R Project for Statistical Computing: http://www.r-project.org

9

Chair of Forest Policy and Forest Economics, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

Curriculum vitæ

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Curriculum vitæ

Christof J. Bigler born March 26, 1972 in Rüti, Switzerland citizen of Worb (BE), Switzerland

1992

Matura Type C, Kantonsschule Zug, Switzerland

1993 – 1998

Studies of systematic and ecological biology in the Department of Biology, Swiss Federal Institute of Technology Zurich (ETH)

1994 – 1996

Field assistant at the chair of Silviculture, Department of Forest Sciences (ETH)

1997

Diploma thesis (M. Sc.): “Impacts of ungulates on the reforestation dynamics of three subalpine meadows in the Swiss National Park” (in German), under the supervision of Dr. B. O. Krüsi and Dr. M. Schütz, WSL (Birmensdorf)

1998

Practical work (GIS modeling) for five months in the Landscape Modeling Group of PD Dr. F. Kienast, WSL (Birmensdorf)

1998 – 1999

Master degree in Statistics (Statistics Group, University of Neuchâtel, Switzerland) Diploma thesis: “Evaluating time series to reveal successional patterns”, under the supervision of PD Dr. O. Wildi, WSL (Birmensdorf)

1999 – 2003

Assistant in the Mountain Forest Ecology Group (ETH)

1999 – 2003

Ph.D. thesis in the Mountain Forest Ecology Group, Department of Forest Sciences, ETH (Zurich): “Growth-dependent tree mortality: ecological processes and modeling approaches based on tree-ring data”, under the supervision of Prof. Dr. H. Bugmann (Mountain Forest Ecology, Zurich), Prof. Dr. F. H. Schweingruber (WSL, Birmensdorf), and Prof. Dr. B. S. Pedersen (Dickinson College, Pennsylvania USA)