Pathways of tree diversity effects on forest dynamics

Pathways of tree diversity effects on forest dynamics – combining empirical analysis and mechanistic modelling Der Fakultät für Biowissenschaften, Pharmazie und Psychologie der Universität Leipzig eingereichte DISSERTATION Vorgelegt von Frédéric Martin Holzwarth

Danksagung An dieser Stelle möchte ich mich bei allen Personen bedanken, die mich in den vergangenen Jahren in Bezug auf diese Arbeit unterstützt und vorangebracht haben. An erster Stelle Christian Wirth für die kontinuierliche intellektuelle Herausforderung und Befruchtung. Für den schnellen und freundlichen Einstieg in Deine Arbeitsgruppe, die spannenden Themen der Projekte, die wir zusammen entwickelt und durchdacht haben, die Ehrlichkeit im Umgang mit informativem Lob und konstruktiver Kritik und dass Du bei all Deiner Arbeit stets zuvorkommend, fröhlich und persönlich geblieben bist und noch Zeit für gelegentliche Gespräche über Literatur hattest. Ich bin gerne zu Dir nach Jena und dann nach Leipzig gekommen. Meinen KollegInnen in der Arbeitsgruppe für gegenseitige Hilfestellungen, Gespräch und eine insgesamt ausnehmend freundliche Art des Umgangs. Britta Kummer für die vielen kleinen und großen Gefallen. Meinen Zimmergenossen Katherina Pietsch, Mario Liebergesell und Daniel Marra für die vielen lustigen Momente, konspirativen Gespräche und den fachlichen Austausch über die Grenzen unserer doch recht verschiedenen Themengebiete hinweg. Es ist mir eine Freude, mit Euch zu sein. Alexandra Weigelt – mit Deinem klaren Geist in Fachgesprächen, mit Witz und Ehrlichkeit und unermüdlichem Engagement bist Du für mich die Seele der Arbeitsgruppe und eine bedeutende Gesprächspartnerin. Meinen Co-Autoren Nadja Rüger, Sophia Ratcliffe, Anja Kahl, Jürgen Bauhus, Karin Nadrowski, Shaun Levick und Christian Wirth für die jeweils intensive Zusammenarbeit, gegenseitige Unterstützung und den wertvollen Austausch. Andreas Huth und Friedrich Bohn für die Einladung zu zwei Vorträgen und den anschließenden informativen Austausch über unsere jeweiligen Vegetationsmodelle. Thomas Hickler und Veiko Lehsten für die Einführung in und Hilfe zum Vegetationsmodell LPJ–GUESS. Meinen Betreuern und Förderern im Studium: Branislav Sloboda, Heiner Flessa, Joachim Saborowski und Ursel Kües die mir mit Inspiration, fachlichem und persönlichen Austausch den Weg Richtung Ökosystemforschung gewiesen und geebnet haben. Für das gewissenhafte Korrekturlesen der Arbeit oder Teilen davon: Sophia Ratcliffe, Alexandra Weigelt, Katherina Pietsch und Michael Holzwarth.

Pathways of tree diversity effects on forest dynamics – combining empirical analysis and mechanistic modelling

Der Fakultät für Biowissenschaften, Pharmazie und Psychologie der Universität Leipzig eingereichte DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.)

Vorgelegt von Frédéric Martin Holzwarth, M.Sc. geboren am 10. Mai 1980 in Bad Homburg, Deutschland Leipzig, den 24. September 2015

Bibliographische Darstellung Frédéric Holzwarth Pathways of tree diversity effects on forest dynamics – combining empirical analysis and mechanistic modelling Fakultät für Biowissenschaften, Pharmazie und Psychologie, Universität Leipzig Dissertation 184 Seiten (exklusive Einleitungs- und Schlussteil: 170 Seiten), 783 Literaturangaben1 (davon 469 innerhalb der Originalarbeiten und Anhänge), 38 Abbildungen2 (davon 31 innerhalb der Originalarbeiten und Anhänge), 22 Tabellen (davon 21 innerhalb der Originalarbeiten und Anhänge) Die vorliegende Dissertationsschrift beschäftigt sich mit dem Zusammenhang zwischen Biodiversität und Walddynamik. Sie ist als kumulative Dissertation basierend auf drei wissenschaftlichen Veröffentlichungen konzipiert. In einer generellen Einleitung wird der Stand der Forschung kurz skizziert und die übergreifende Methodik der Arbeit erklärt. Der Zusammenhang der drei Veröffentlichungen und ihre jeweiligen Methoden werden knapp erläutert. Danach folgen die Veröffentlichungen in ihrer jeweiligen Druckfassung inklusive der zugehörigen Anhänge. In zwei empirischen Forschungsprojekten (Publikation 1 und Publikation 2) wurden zwei wichtige Aspekte der Walddynamik (Mortalität und Wachstum) unter dem Blickwinkel von Art-Identität und Diversität untersucht. Diese Studien haben auch die umfassendere Modellierungsstudie (Publikation 3) beeinflusst, in der Wirkungspfade der funktionellen Komposition auf Ökosystemfunktionen näher untersucht wurden. Hier wurden in einem Modellversuch Dynamiken und Teilprozesse der Walddynamik eingehend untersucht. In einer abschließenden Diskussion werden Potential und Einschränkungen der Arbeiten umrissen sowie mögliche Implikationen für die Forschung sowie potentielle Fortsetzungen der Arbeit angedeutet.

Dopplungen der Zitate zwischen den Originalarbeiten und zwischen Originalarbeiten und dem Text der Dissertation sind möglich 2 Dopplungen der Abbildungen innerhalb des Textes der Dissertation sind möglich 1

Diese Dissertation basiert auf folgenden Publikationen: Holzwarth F, Kahl A, Bauhus J, Wirth C (2013) Many ways to die—partitioning tree mortality dynamics in a near-natural mixed deciduous forest. Journal of Ecology, 101, 220–230. DOI: 10.1111/1365-2745.12015 Ratcliffe S, Holzwarth F, Nadrowski K, Levick S, Wirth C (2015) Tree neighbourhood matters – Tree species composition drives diversity-productivity patterns in a nearnatural beech forest. Forest Ecology and Management, 335, 225–234. DOI: 10.1016/j. foreco.2014.09.032 Holzwarth F, Rüger N, Wirth C (2015) Taking a closer look: disentangling effects of functional diversity on ecosystem functions with a trait-based model across hierarchy and time. Royal Society Open Science, 2, 140541. DOI: 10.1098/rsos.140541

„Die Ökologie als Erbin der Idee des Ganzen kann auf den Rechner zur Darstellung von unübersehbaren Zusammenhängen nicht verzichten. Die Netzwerk-Maschine ist hier bereits philosophisches Gerät.“ — Botho Strauß, aus: „Beginnlosigkeit“ „Der Mensch überlebt nicht als wohlangepaßter Öko-Insasse eines ‚komplexen Biotops‘, sondern er überlebt, indem er eine abstrakte Vorstellung gewinnt, ein präzises Wissen, schließlich eine Idee als modus operandi.“ — Botho Strauß, aus: „Beginnlosigkeit“ „Nachdem wir einen dichten Saum von Schlehdorn und Kornellen durchbrochen hatten, traten wir in den Hochwald ein, in dessen Gründen noch nie der Schlag der Axt erklungen war. Die alten Stämme […] standen im feuchten Glanz wie Säulen, deren Kapitelle der Dunst verbarg. Wir schritten unter ihnen wie durch weite Vestibüle, und gleich dem Zauberwerk auf einer Bühne hingen Efeuranken und Klematisblüten aus dem Unsichtbaren auf uns herab. Der Boden war hoch bedeckt mit Mulm und moderndem Geäst, auf dessen Rinde sich Pilze, brennend rote Becherlinge, angesiedelt hatten, so daß uns ein Gefühl von Tauchern, die durch Korallengärten wandeln, überschlich. Wo einer dieser Riesenstämme vom Alter oder durch den Blitz geworfen war, da traten wir auf kleine Lichtungen hinaus, auf denen der gelbe Fingerhut in dichten Büscheln stand. Auch wucherten Tollkirschensträucher auf dem morschen Grunde, an deren Zweigen die Blumenkelche in braunem Violett wie Totenglöckchen schaukelten.“ — Aus: „Auf den Marmorklippen“ von Ernst Jünger.

Table of Content / Inhaltsverzeichnis General Introduction

8

Paper 1

48

Paper 2

74

Paper 3

86

General Discussion

148

Abstract

164

Zusammenfassung

170

Nachweise über Anteile der Co-Autoren

179

Wissenschaftlicher Werdegang

182

Wissenschaftliche Veröffentlichungen

183

Selbstständigkeitserklärung

184

General Introduction Structure of the work The present work is structured as a cumulative dissertation thesis focusing on three peer-reviewed publications all within the context of ecosystem functioning, forest dynamics and diversity of tree species.

The rise of functional biodiversity research Ecology as a scientific discipline emerged in the 19th century, when scientists extended the idea of mechanistic organisms (going back to Descartes) onto the environment, in which they lived, and assumed that their mutual interactions are also governed by mechanistic principles. Thus nature could be seen upon as a system being composed of sub-systems: the physical matrix and the organisms populating it. As a mechanistic perspective on a system asks for balances of input, output and content, the analogy of a household (οΐκος / oíkos, ‘house’) was found, but in contrast to economy, where the rules of the household are not only to be studied, but also to be set (νέμειν / nemein, ‘to decide / distribute’), in ecology they are just to be observed and understood (λογία / logía, ‘study of’). Ecology may thus be seen upon as a node that formed at the crossroads between 1) rationalism (idea of reducible complexity) and empiricism (idea of gaining knowledge through observation by means of inductive reasoning) as philosophical backgrounds, 2) the stunning multitude of environments and organisms observed in nature in the wake of the exploration of the world starting from Europe (e.g. von Humboldt, Darwin, Wallace) and finally 3) the liberation from seeing this multitude as beautiful but created given to rather seeing it as a phenomenon with a past and future (theory of evolution); which can be partly understood and thus probably be perceived as even more beautiful (cf. Dawkins 2006: “The truths of evolution, along with many other scientific truths, are so engrossingly fascinating and beautiful.”) The core motivations in ecology are to understand species evolution, coexistence, interaction with and shaping by and of the environment. As such, biodiversity was an issue of ecological research right from the start, (e.g. the Hortus Gramineus Woburnensis, Darwin 1859, also cited in Hector & Hooper 2002 or The Park Grass Experiment in 1856, Lawes & Gilbert 1880, also cited in Tilman et al. 1994) and was mentioned in a few scientific publications related to ecosystem stability again in the 1950ies (‘diversity–stability hypotheses’, Odum 1953; MacArthur 1955; Elton 1958, cf. also: McCann 8

2000). It is rather astonishing that the research on biodiversity was dormant for so long and only re-emerged, though now with much more drive, when accelerated global species extinction became a publicly recognised fact in the 1980ies and public interest in conservation was at a peak in Western countries (e.g. Ehrlich & Ehrlich 1981, the 1st National Forum on BioDiversity, September 1986, Washington, D.C., USA, Wilson & Peter 1988; Wilson 1989). The term biodiversity was then popularised by the 1992 United Nations Conference on Environment and Development in Rio de Janeiro.

The 6th mass extinction and the advent of biodiversity research With the focus on accelerated species loss also the question arose, whether with each extinction of a species not only a peculiarity of evolution and beauty in nature was lost, but also whether functions of ecosystems would be negatively affected. Starting from there, the domain of functional biodiversity research (in contrast to evolution, seeing biodiversity mainly as an outcome) in ecology emerged and a wave of research in it was sparked with the SCOPE (Scientific Committee on Problems of the Environment) conference near Bayreuth, Germany, in 1991 on ‘Ecosystem Functioning of Biodiversity’. It was a “meeting [that] brought together ecologists and population biologists, both directed toward evaluating the consequences of human-driven disruption of natural systems.” (Mooney et al. 1996). This research began to look at biodiversity also as a driver, not just outcome, of ecosystem functions. This widened perspective of biodiversity being a hinge between separate organisms and ecosystem functions found recognition as an important topic of international politics through, e.g. the international DIVERSITAS programme on biodiversity science in 1991 (jointly established by the UNESCO, SCOPE and the International Union of Biological Science), the Convention on Biological Diversity signed by world leaders in 1992 on the UN Conference on Environment and Development in Rio de Janeiro (UNEP – United Nations Environment Programme 1994), the Global Biodiversity Assessment in 1995 (UNEP – United Nations Environment Programme 1995), the Millennium Ecosystem Assessment in 2005 (MEA – Millennium Ecosystem Assessment 2005) or the establishment of the Intergovernmental Platform on Biodiversity and Ecosystem Services (IPBES) in 2012. These efforts in monitoring biodiversity and assessing its function and value are motivated by the crisis of loss in diversity but seem to be mostly without significant effect – and the loss of diversity of life (species, genes and networks) due to human impact continues without losing momentum, having been dubbed the 6th mass extinction (Sala et al. 2000; Butchart et al. 2010; Pereira et al. 2010; Barnosky et al. 2011; Ceballos et 9

al. 2015). And with it, potential as well as actual detrimental effects on ecosystem functions and services accumulate (Hooper et al. 2012; Cardinale et al. 2012). From the perspective of committed science, there is but the option to deepen the understanding of and raise awareness for the role of biodiversity in the complex play of ecosystems and their mutual links to human society. On the side of describing and monitoring diversity, the ultimate key for its description is still the knowledge of the individual species. Biodiversity emerges from species forming a community and boils down to species again, as E. O. Wilson envisions the step ”that community ecology must take: analyse ecosystems in detail, from the bottom up. Biologists are returning to natural history with a new sense of mission. They cannot expect to learn much more from the top down, from the properties of whole ecosystems (energy flow, nutrient cycles, biomass) interpolated to the properties of communities and species. Only with a detailed knowledge of the life cycles and biology of large numbers of constituent species will it be possible to create principles and methods that can precisely chart the future of ecosystems in the face of the human onslaught. Then there might be an answer to the question I am asked most frequently about the diversity of life: if enough species are extinguished, will the ecosystems collapse, and will the extinction of most other species follow soon afterward? The only answer anyone can give is: possibly. By the time we find out, however, it might be too late. One planet, one experiment.” (Wilson 1992).

BEF – Biodiversity and Ecosystem Functioning Wilson also argued against a common viewpoint, where species are more or less interchangeable mediators of physical and chemical processes with their individuality being not much more than fashion. Plainly put: biodiversity is just a result, not a driver of ecosystem function. Modern functional biodiversity research, along his case, challenged this tenet: “Why has there been such controversy? The assertion that biodiversity could be one of the factors controlling ecosystem functioning represented a paradigm shift in ecology. Biodiversity, which had long been thought to be controlled by productivity and environmental variation, was now being suggested as controlling productivity and ecosystem variability. This reversal of long-held cause-and-effect relationships forced re-exploration of concepts and definitions, and demanded the development of new hypotheses. Indeed, much of the controversy was debate about what might be causing biodiversity to influence various ecosystem processes.” (Kinzig et al. 2001b), reiterating a leading question from the SCOPE meeting in 1991: Does 10

biodiversity matter for ecosystem integrity, functioning, and the ecosystem’s provision of goods and services to humanity? (Schulze & Mooney 1994). Consequently, some researchers put focus on this direction of influence by manipulating biodiversity experimentally – with three early papers supporting the emerging BEF hypotheses on stability and productivity: Tilman & Downing (1994) and Naeem et al. (1994; 1995).

Modern biodiversity field experiments From this time on, modern field experiments were set up and monitored to gather empirical evidence for BEF relationships. Because of the short life cycles and relative ease of manipulating and controlling species diversity, grassland experiments were among the first systems, where BEF theories were tested and revised on a broader scale. Such as the ‘Cedar Creek biodiversity experiments’, set up in 1994 (Tilman et al. 1996), eight experiments across Europe (BIODEPTH), set up in 1995 and 1996 (Hector et al. 1999), an experiment in California, set up in 1992 (Hooper & Vitousek 1997) and the ‘JenaExperiment’, set up in 2002 (Roscher et al. 2004). They all found significant positive influences of diversity of species or functional groups on ecosystem functions such as productivity, carbon storage or stability. However, these findings were also challenged: Huston (1997) suggested confounding factors (‘hidden treatments’) and nonrandom sampling of species pools would explain the results in the early papers mentioned above (Tilman & Downing 1994; Naeem et al. 1994, 1995). Huston (1997) also suggested that a statistical artefact, called the ‘selection probability effect’ (“increasing probability of selecting species with a specific property in samples of increasing number that are randomly selected from any group of species”), could lead to spurious results in the follow-up study of the Cedar Creek experiment with ‘diversity treatments’ using randomly selected sets of species (Tilman et al. 1996). This notion also found support with Aarssen (1997) and Grime’s ‘mass ratio hypothesis’ (Grime 1998). While the first two flaws mentioned could be coped with through stronger orthogonal and random experimental design (e.g. Tilman et al. 1996; Hector et al. 1999), the ‘selection probability effect’ proved to be difficult to exclude experimentally. Instead, a simple mathematical separation (‘additive partitioning’) into so-called ‘selection effects’ (dominance through selective processes by species with particular traits) and ‘complementarity effects’ (resource partitioning and facilitation) was devised (Hector 1998; Loreau 1998). It showed in a first application that the reported positive results of biodiversity on productivity in grasslands (Hector et al. 1999) held up and that the ‘selection effect’ was more than just a statistical artefact but emerges also through some real biological interactions (Loreau & Hector 2001). Further methods and levels of partitioning were proposed but did not enter the mainstream discourse (e.g. Fox 2006). 11

BEF – consensus and generality Two opposing views characterised the ‘Diversity Debate’ in the late 90ies and showed the disagreement around the ‘selection effect’ and its contribution to the observed responses to experimental manipulations of biodiversity – but also the genuine scientific effort in investigating BEF relationships (Wardle et al. 2000; Naeem 2000): 1) there are clear, causative relationships between diversity and ecosystem functioning (e.g. Naeem et al. 1994, 1995; Tilman 1996, 1999) and 2) ecosystem properties are not necessarily driven by species diversity per se, but rather the main drivers of ecosystem properties are the key functional attributes or traits of the dominant species present and the composition of functional types (e.g. Grime 1998; Hooper & Vitousek 1998; Huston et al. 2000). As a joint attempt in the first BEF consensus paper in 2001 (Loreau et al. 2001), a dozen researches with diverging views only consented on the tentative statement “that at least some minimum number of species is essential for ecosystem functioning under constant conditions and that a larger number of species is probably essential for maintaining the stability of ecosystem processes in changing environments.” The continued and accompanying theoretical scepticism helped strengthening theory and refine experiments. This debate over the validity of experimental designs and possible mechanisms of biodiversity effects promoted a flourishing research and publication process, where studies from the same and new experiments, in grasslands and many other ecosystems, piled up to confirm, challenge and specify the evidence from biodiversity effects on ecosystem functions, leading to more than 600 biodiversity experiments with results published in several hundred papers by 2009 (Cardinale et al. 2011). Still, in 2005 the second consensus paper (Hooper et al. 2005, with six authors from Loreau et al. 2001) mostly re-iterated the 2001 statements with scientists agreeing on the notion that biodiversity can stabilise ecosystem process rates but added that “Certain combinations of species are complementary in their patterns of resource use and can increase average rates of productivity and nutrient retention.” The first extensive quantitative meta-analysis of BEF experiments (Balvanera et al. 2006) cautiously confirmed positive BEF relationships at large, concluding that the “experimental evidence for a relationship between biodiversity and ecosystem process rates is compelling, but the issue remains contentious” and that “considerations of the way in which biodiversity is defined and manipulated, and disentangling the many separate effects and the interactions between them, as well as those with environmental heterogeneity, will be a major challenge for the next generation of experiments.” A concurrent meta-analysis published later that year (Cardinale et al. 2006) was less enthusiastic, reporting “that the standing stock of, and resource depletion by, the most species-rich polyculture tends to be no different from that of the single most productive species 12

used in an experiment” indicating that the ‘selection effect’ might be the main mechanism without strong proofs for ‘complementarity effects’ and the ‘Diversity Debate’ remained unconcluded. However, in another meta-analysis just one year later (Cardinale et al. 2007) some of the same authors conceded that in “12% of all experiments do diverse polycultures achieve greater biomass than their single most productive species” (a phenomenon called ‘transgressive overyielding’) and “that although productive species do indeed contribute to diversity effects, these contributions are equalled or exceeded by species complementarity” – refuting the doubt mentioned above, diversity effects may largely depend on selection but also result from biological processes involving multiple species. They show that “mixtures of species produce an average of 1.7 times more biomass than species monocultures” and finally suggest that “experiments to date have, if anything, underestimated the impacts of species extinction on the productivity of ecosystems”. From this time on, meta-analyses and reviews confirmed this general picture: “There is now unequivocal evidence that declining diversity of plants and algae in the world’s ecosystems will, on average, lead to decreases in the biomass of producers and limited evidence suggests that, on average, declining diversity of plants may reduce rates of decomposition and the efficiency by which biologically essential elements are recycled back into their inorganic forms.” (Cardinale et al. 2011). Yet, the underlying processes responsible for complementarity among species remained obscure and mechanistic explanations lacked (Cardinale et al. 2011). Two consecutive meta-analyses (both on the same data set) highlighted the importance of biodiversity loss for ecosystems (Cardinale et al. 2012; Hooper et al. 2012). Hooper et al. (2012) noted that its effects on productivity and decomposition are of comparable magnitude to the effects of many other global environmental changes, which was independently and very similarly observed also by Tilman et al. (2012). However, Cardinale et al. (2011) stressed the lack of deeper knowledge about the biological mechanisms that are responsible for complementarity among species and urged that “ecologists have yet to develop a mechanistic explanation for diversity effects.” While there seems to be an unchallenged consensus on the average positive effect of biodiversity on the efficiency by which ecological communities capture resources, produce biomass, decompose and recycle nutrients and mounting evidence that it increases the stability of ecosystem functions, it also became obvious that both the species dominating a community (‘identity’ of a community) next to differences 13

in functional traits among organisms (‘diversity’) have large influences on ecosystem functions: “Research and syntheses over the past 10 years have made it clear that both the identity and the diversity of organisms jointly control the functioning of ecosystems. Quantification of the variance explained by species identity versus diversity in >200 experiments found that, on average across many ecosystems, each contributes roughly 50% to the net biodiversity effect.” (Cardinale et al. 2012). These findings highlight the necessity to dig deeper into the mechanistic underpinnings of BEF and to source diversity effects to assembly and composition of species and their respective traits, as Kinzig et al. (2001a) have put it: “Understanding how communities assemble, how they disassemble, and how diversity–functioning relationships can emerge as the result of coexistence and assembly processes […] is at the heart of some of the most fundamental and compelling unanswered questions in ecology.” Answers to this seem to be in reach but are also a pressing need in the light of accelerating global change: “Ecology must be a discipline that can explain what structured the natural world in the era before human global dominance […] The major and simultaneous advances that have occurred during two intensive decades of investigating biodiversity are a model of the scientific efforts required if society is to gain the knowledge needed to wisely manage a world that humans now dominate through a myriad of often inadvertent actions.” (Tilman et al. 2014)

Causes and mechanisms of BEF – the functional approach While it is crucial to first find empirical evidence whether at all there are any effects of biodiversity on ecosystem functioning – even if theory does not predict them or predicts even negative effects (e.g. May 1973, who challenged the ‘diversity–stability hypothesis’ cf. Elton 1958 on mathematical grounds) – clearly theory and experiments should seek for explanations of these and extract the relevant mechanisms. Some possible mechanisms behind positive effects of diversity in plant communities identified in a review by Srivastava & Vellend (2005) were 1) niche complementarity, functional facilitation, dilution effect and selection effect (all being relevant for productivity) – analogous to the general mechanisms suggested by Fridley (2001): complementarity, facilitation, and selection effect – and 2) insurance effect, portfolio effect and compensator dynamic effect (all being relevant for stability). However, no matter which process is considered, any mechanistic explanation of diversity effects has to be based on differences of process-relevant characteristics between species (Grime 1998). These so-called ‘functional traits’ play a role in ecological processes and determine a species’ behaviour in them. Even the most simple biodiversity effect, the selection effect, relies on species being functionally different from each other. The use of species richness as a descriptor of 14

biodiversity in most early but also many current studies is implicitly based on the assumption that a species pool occupies the niche space either randomly or uniformly – such that the individual functional identity may be ignored (Díaz & Cabido 2001). This notion was soon found to be too simple: “Although species richness is easier to measure, a more predictive science might be achieved if appropriate functional classifications were devised.” (Loreau et al. 2001). A first step beyond species richness was to capture the variety of functions in a species pool in ‘functional groups’ – essentially a hierarchical classification assuming that between-group variation is bigger than the nested in-group variation. These functional groups aggregate species according to certain key functional features, e.g. nitrogen-fixers vs. non-fixers. Although classification of plants has been done for a long time, e.g. according to strategies like the CSRscheme by Grime (1977), the grouping into ‘functional groups’, being defined as nonphylogenetic groupings of species which perform similarly in an ecosystem based on a set of common biological attributes, life-history characteristics and resource allocation is more recent in BEF research (Gitay & Noble 1997). For example, the Jena-Experiment categorised 60 grassland species according to 17 attributes describing morphological, phenological and physiological traits into four ‘plant functional groups’: legumes, grasses, small herbs and tall herbs and used these as a basis to assemble species mixtures and in some studies for analysis (Roscher et al. 2004). As functional groups are based on sets of functional traits, the step towards looking at individual trait configurations and communities as trait assemblies was fairly short and depended mainly on the wider availability of species-level trait information (Kattge et al. 2011) and the development of indices of biodiversity that allowed the integration of these individual values (Petchey & Gaston 2002). According to the widely accepted definition of Violle et al. (2007) ‘functional traits’ are defined as “morphophysio-phenological traits, which impact fitness indirectly via their effects on growth, reproduction and survival, the three components of individual performance” and as such are measurable at the individual level. At this point, trait research began to blend in with community ecology and biodiversity research (e.g. Díaz & Cabido 2001; Naeem 2002). As modern trait research has one focus on uncovering leading dimensions of ecological variation among species and across biomes (e.g. Reich et al. 1998; Westoby 1998; Reich et al. 1999; Cornelissen 1999; Franks & Farquhar 1999; Westoby et al. 2002; Diaz et al. 2004; Iida et al. 2012), thus revealing underlying trade-offs (e.g. Tilman 1990; Walters & Reich 1996; MullerLandau 2010; Wright et al. 2010) or economic spectra (e.g. Wright et al. 2004; Shipley et al. 2006; Chave et al. 2009; Baraloto et al. 2010; Pietsch et al. 2014) that organisms tend 15

to conform, it suggests that species follow different strategies to survive and thrive. Further, it implies that these strategies developed from unavoidable compromises and that no single strategy alone guarantees success, essentially allowing co-existence of and complementarity between species – in effect, a major topic of BEF research. Consequently, current functional BEF research tries to link traits, trait distribution, species coexistence, community assembly and ecosystem functioning (e.g. Suding et al. 2003; Lavorel & Garnier 2002; Lavorel et al. 2007; Suding & Goldstein 2008; Roscher et al. 2012) by means of a number of schemes how traits scale up through the community level to ecosystems and thus drive ecosystem functioning: e.g. the ‘response-and-effect framework’ (Lavorel & Garnier 2002; Naeem & Wright 2003; Suding et al. 2008) or the ‘traits–states–rates scheme’ (Purves & Vanderwel 2014). These ‘functional’ or ‘trait based’ approaches focus on identifying mechanisms of biodiversity effects via the relationships among taxonomic diversity, functional diversity and community structure: “An understanding of how changes in species richness and composition, and biodiversity in general, influence ecosystem properties requires an understanding of the functional traits of the species involved.” (Hooper et al. 2005). In the recent ecological literature, trait based approaches have been strongly advanced and advocated (e.g. McGill et al. 2006; Ackerly & Cornwell 2007; Hillebrand & Matthiessen 2009). However, contrasting approaches have each their strengths and may complement the trait based one or blend into it (McGill et al. 2006), e.g. the ‘neutral theory of biodiversity and biogeography’, assuming that differences in traits between species have no effect on population dynamics at large (Hubbell 2001; Gaston & Chown 2005), the focus on pairwise species interactions (Canham et al. 2006; Engel & Weltzin 2008) or the ‘metabolic scaling theory’, which posits that the metabolic rate of organisms governs many patterns in ecology (West et al. 1997; Enquist et al. 1999). As an extension to taxonomic indicators of diversity, a plethora of indices of ‘functional diversity’ based on trait values and their abundance in a community were developed (Villéger et al. 2008; Laliberté & Legendre 2010), which may focus on different aspects of the total suite of functional traits in a community, such as only response traits or leaf traits, or on different components or ‘facets’ of the trait distribution (Petchey & Gaston 2002; Mason et al. 2005; Petchey & Gaston 2006; Mouchet et al. 2010, Schleuter et al. 2010; Ricotta & Moretti 2011). These indices represent various facets of the functional composition (e.g. richness, diversity, evenness, identity) of a community and thus may be tightly or loosely correlated or be roughly independent and statistically orthogonal and may partly relate to different underlying BEF hypotheses (cf. ‘Diversity Debate’). Such as the abundance weighted mean (community weighted mean, CWM) of a trait 16

as an indicator of the identity of a community (‘mass-ratio hypothesis’ Grime 1998), measures of abundance weighted trait dispersion (e.g. Rao’s quadratic entropy, functional dispersion, functional divergence, functional variance), measures of unweighted trait dispersion or multivariate range (functional richness, functional volume), both related to complementarity, and measures of regularity (functional evenness, functional regularity), related to efficiency of resource use (Villéger et al. 2008; Schleuter et al. 2010). In parallel to these developments in empirical research, similar concepts evolved in the realm of vegetation modelling. The ‘functional groups’ have their analogue in so-called ‘Plant Functional Types’ (PFT), a concept to simplify the representation of plants in a computer model, rather than including information at the species level, because information on the latter may be far too sparse on a global or even a regional scale, and to reduce computational complexity (e.g. Smith et al. 1993; Gitay & Noble 1997; Leemans 1997; Harrison et al. 2010). Other more regional models may use individual species (e.g. Hickler et al. 2012). Both PFTs and species are represented as a list of parameters and equations in vegetation models (Box 1996). And in both cases there is a strong indicator for the exclusive use of functional traits, since they may simply be equivalent or come close to the model parameters or processes. So coming from a conceptual and process-based perspective on ecosystems and plant communities as in ecological modelling, the need for functional trait information and integration arose as a necessity and, as one of the original motivations, led to collections of trait information up to global trait databases (Kattge et al. 2011).

Time scale and succession As BEF research got more refined over time, also the corresponding experiments got older and continued to generate valuable data. In a 2007 meta-analysis (Cardinale et al. 2007) this was highlighted: “Importantly, both the net effect of diversity and the probability of polycultures being more productive than their most productive species increases through time, because the magnitude of complementarity increases as experiments are run longer.” This finding of diversity effects of producer diversity on producer biomass growing stronger as experiments continued and ‘matured’ was confirmed by consecutive meta-analyses (Cardinale et al. 2011; Cardinale et al. 2012), adding that diversity effects are likely stronger for experiments that are performed at larger spatial scales. Compared to earlier publications, this suggested that, if anything, BEF experiments have under-estimated the functional role of producer diversity in ecosystems. Going even beyond that, Reich et al. (2012) found that the effects 17

of diversity on biomass productivity also became less saturating over time, suggesting that “effects of diversity-dependent ecosystem feedbacks and interspecific complementarity accumulate over time.” These notions strongly put forward the time dimension as an important aspect of BEF – and came from and referred to grasslands, those systems that were initially chosen as model systems because of the short life spans of species involved and their life-cycles fitting into research-grant schemes. For forest ecosystems, it is a trivial observation that the forest dynamics, species composition and hence the ecosystem processes change over time tremendously – and so should relationships to biodiversity (Barrufol et al. 2013). With the first promising results on BEF from grasslands and other model ecosystems, BEF research quickly expanded to the domain of forests with their peculiar and long-term succession. One exemplary step stone marking this was a LINKECOL (Linking Community and Ecosystem Ecology) workshop held in Weimar, Germany, in 2002: “The basic idea behind the workshop was to extend the ongoing debate about the relationship between biodiversity and ecosystem processes to the forest realm.” (Scherer-Lorenzen et al. 2005a)

Forest vs. grassland As I focused on forest ecosystems in this work, we should ask: What kind of biological differences between fast-growing grassland systems and forests are important when considering BEF relationships? Scherer-Lorenzen et al. (2005b) answer: “While herbaceous/grassland communities rebuild most of their interacting aboveground structures year by year from close to zero, trees may take a hundred or more years to fill a large three-dimensional volume, which permits very small differences among individuals to accumulate in a compound-interest fashion. In herbaceous species such interest effects also exist, but are mainly limited to reproductive output and belowground structures [...]. Individuals of herbaceous systems reach maximum height year by year, whereas trees persist at gradually increasing height. This is not just a scaling issue in space and time, but a substantial qualitative difference in how species and their individuals interact. One consequence of this difference is that far more co-dominants tend to coexist in long established and non-fertilised grassland systems, whereas mature temperate or boreal forests commonly exhibit a dominance of few, mostly one to three, species. Such mature forest ecosystems are thus much more dependent on the characteristics of a small set of species than are grassland systems.” It may be the slow adjustment of the vegetation structure and the composition as well as the soil but also the slow accumulation of compound-interest effects of small trait differences (Körner 18

2005) that set forests so distinctly apart from grasslands in BEF research. Obviously, the higher longevity and the greater height of trees expand the temporal and vertical scale of potential biodiversity effects (Pretzsch 2014). The time dimension may lead to negative as well as positive biodiversity effects and it may very well matter what point during succession is considered (Forrester 2014; Río et al. 2014). As Kinzig & Pacala (2001) suggest, a negative diversity–succession effect may result from lowachieving early successionals delaying the establishment of more productive late successionals. In contrast, positive diversity–succession effects on productivity and stability may emerge from, e.g. the temporally overlapping development of trees with differing shade tolerance and growth ability (Morin et al. 2011; Morin et al. 2014) or correlation of other functional traits with the successional aspect (Caspersen & Pacala 2001). Although intense research on the functional aspect of BEF in forests has just begun, the debate whether mixed forests exhibit different productivity than the respective monocultures is as old as forest science (e.g. Hartig 1791; Cotta 1817). The functional peculiarity of trees and the successional dynamics of forests suggest that forest biodiversity research will continue to differ significantly from grassland biodiversity research (Scherer-Lorenzen et al. 2005b).

Forests – important and diverse terrestrial ecosystems The importance of forests as ecosystems is underlined by a few figures: they cover over 30% of the earth’s land area (FAO 2010) and store almost 80% of the terrestrial biomass of the planet (Watson et al. 2000). They store a large fraction and act as sources and sinks of significant amounts of carbon and contribute to over two thirds of global terrestrial net primary production (Shvidenko et al. 2005; Heimann & Reichstein 2008). At the same time, the world’s forests host an estimated 100’000 tree species and provide habitat for half or more of the world’s known terrestrial plant and animal species – tree diversity is a key feature of many tropical and temperate forest ecosystems (Oldfield et al. 1998; Shvidenko et al. 2005). Globally, tree species richness is declining due to deforestations (Shvidenko et al. 2005; Hansen et al. 2013). With this dramatic loss of species diversity, it is important to know how and to what extent plant diversity matters for the functioning of forests, especially in terms of productivity, carbon storage and consumer diversity (Butchart et al. 2010; Cardinale et al. 2012).

BEF research in forests: inventories, experiments, models Basically, there are three methods examining BEF relationships in forests: observational studies using inventory data of existing forests, plantation experiments and 19

experiments with vegetation models (Naeem & Wright 2003). Forest inventory data cover long diversity gradients and different successional stages, where a spectrum of forest diversities exists as the result of forest management and natural succession (Körner 2005). However, in inventory data individual plots tend to be particularly small (< 0.05 ha) and so suffer from strong edge effects when defining neighbourhood diversity. They are confounded by environmental heterogeneity and are thus hardly comparable, they mostly stem from unknown or differing successional trajectories and their composition can be both a result as well as a driver of forest dynamics (Vilà et al. 2005; Baeten et al. 2013). Hence, they generally lack the orthogonality of diversity with identity and other variables, especially successional time and age, which would be necessary to disentangle diversity effects from age, size and environment and hence focus more on limited sets of species compositions (e.g. Vilà et al. 2007; Toïgo et al. 2015). Still, as large inventories may cover several predictor combinations, with the use of apt statistical methods, this can be partly coped with and thus make inventory-based BEF studies a valuable resource, especially when it comes to mature forests, comparison across biomes and natural disturbances (Caspersen & Pacala 2001; Paquette & Messier 2011; Zhang et al. 2012; Vilà et al. 2013; Ruiz-Benito et al. 2014; Ratcliffe et al. in print). In contrast, plantation experiments are the method of choice to separate drivers and asses BEF processes in importance and their underlying mechanisms. For forests, however, experiments are far fewer than for grasslands and most are still young, thus their results are restricted to the very early and transient stages of succession. There a some older classic forest yield experiments, which already showed under- and overyielding and complementarity for mixtures of mostly two or three species (e.g. Kelty 1992; Pretzsch 2005; Bauhus et al. 2004; Forrester 2014), but they mostly lack generality and a functional investigation and are restricted to short diversity gradients of a few commercially important species. Currently, there are 18 modern large forest BEF experiments globally on 36 different sites (cf. www.treedivnet.ugent.be/experiments.html, viewed August, 2015), which systematically explore BEF relationships in forests (Verheyen et al. 2015). The oldest ones having been set up in 1999 in Finland (‘Satakunta Tree Species Diversity Experiment’: Vehviläinen & Koricheva 2006) and from 2001 to 2003 in the tropics (‘Sardinilla Project’, Panama: Potvin et al. 2011), others have followed at a pace of about one per year. In total, they cover around 785 ha, with the largest of ca. 500 ha having been set up in 2010 (‘Sabah Biodiversity Experiment’, Borneo: Hector et al. 2011). These experiments have a sufficiently long diversity gradient and may allow separating between diversity and identity effects and account for confounding factors and also assess multiple ecosystem functions. However, being still very young compared to typical old-growth forest ages of more than 100 years, 20

they yet do not allow a comprehensive mechanistic analysis of the interplay of succession, biodiversity and forest biomass dynamics. Further, deviations of plantation experiments from natural forests, for example in the trophic structure or the tree age distribution, limit the spectrum of processes which can be analysed for biodiversity effects (Leuschner et al. 2009). As a third way, experiments can be conducted in vegetation models that represent vegetation structure and processes in a mathematical framework. Computer-aided forest modelling has a long history (e.g. Botkin et al. 1972), however, using vegetation models to examine BEF questions by creating virtual experiments is more recent (e.g. Kinzig & Pacala 2001; Falster et al. 2011; Morin et al. 2011; Morin et al. 2014; Pedro et al. 2014) and are typically limited to a few processes that may induce mixture effects, which are represented in a given model (Pretzsch et al. 2015). With the use of vegetation models, also the understanding of forest dynamics, community assembly and species co-existence – processes via which any diversity effect must be mediated – can be deepened (e.g. Pacala et al. 1996; Smith et al. 2001; Keane et al. 2001; Purves & Vanderwel 2014).

BEF research in forests: ongoing challenges The sheer notion of forest ecosystem functions depending on tree species and their mixture may be valid in itself, but also calls for an explanation of how this dependency is structured (Forrester & Pretzsch 2015). Both, ecosystem functions and community assembly in forests, are linked via the complex interplay of recruitment, growth and mortality, these three being the key processes in forest dynamics (Shugart 1984). A mechanistic theory of BEF in forests shall link any effects of biodiversity (diversity of individual organisms) on ecosystem functions to one of these processes. Forest dynamics can simplistically be seen upon as changes of the number of trees, being added through recruitment or subtracted through mortality, and changes of a trees dimension and proportion through growth and tissue turnover. These form the processes behind important ecosystem functions, such as productivity, and thus may mediate effects of species composition. These top-level processes are also mutually linked and related via sub-processes to the states of a tree: its dimensions, its proportions and that of its neighbours. Understanding and predicting the processes of forest dynamics is therefore indispensable to estimate and comprehend the relationship of species composition and successional dynamics and thus stand at the centre of BEF research in forests (Shugart 1984; Purves & Pacala 2008). Resolving the hierarchy of the processes of forest dynamics further to individual sub-processes (e.g. photosynthesis, respiration and turnover of tissues (wood, leaves, roots), mortality causes) and tree dimensions 21

(e.g. height, leaf area, tissue masses) finally allows linking to functional traits and assessing their respective influence (Falster et al. 2011). In a simplified equation of mass balance, growth represents the additive and mortality the subtractive term, so both are of equal importance and none should be omitted for the full picture. However, in contrast to their growth, tree mortality is less well understood and appears to be one of the greatest challenges of forest ecology (Watkinson 1992). Tree mortality may be caused by very different agents, it may be caused extrinsically or intrinsically or as a combination of both, it may be a gradual process or an instantaneous event and the relevance of each factor varies during a trees ontogeny (Franklin et al. 1987). In any case, mortality of trees – as of any kind of plant – depends on the individuals’ dimension (Mencuccini et al. 2005; Peñuelas 2005) and its neighbourhood (Das et al. 2008). These are both factors, which are much more defined in forests than grasslands and which are essential to characterise species composition on a small scale. A comprehensive mechanistic understanding of individual tree mortality needs to first disentangle and categorise the different causes or modes of mortality (Larson & Franklin 2010) and then to attribute responsible processes (Chao et al. 2009) in order to provide a mechanistic interpretation. This way, along a chain or network of subprocesses, the final event of mortality may be traced to individual characteristics, exogenous factors, tree neighbourhood, competition and also to the surrounding species composition, thus revealing responsible drivers (Franklin et al. 1987; Dobbertin 2005; Wunder et al. 2008; Hurst et al. 2011; de Toledo et al. 2012). These efforts typically require large, extensive and spatially referenced datasets (Lines et al. 2010). The study of the relationship between species composition and mortality in forests, a field yet in its beginning and up to now mostly a black box, may need even larger datasets (Lutz & Halpern 2006; Liang et al. 2007; Healy et al. 2008; Rüger et al. 2011) or depend on vegetation models (Morin et al. 2011). Tree growth as a continuous process is more accessible to observation and mainly depends on abiotic drivers and the local tree neighbourhood (Piotto 2008), which modulates the abiotic drivers as a result of facilitation, complementarity and competition (Paquette & Messier 2011). However, the underlying mechanisms of how complementarity, tree species diversity and species identity control individual tree growth and stand level production of biomass are less well understood (Vilà et al. 2003; Nadrowski et al. 2010). Their study is difficult, as they tend to be confounded by factors such as successional stage and climate (Vilà et al. 2005), whereas sheer diversity effects tend to 22

be significantly smaller than the effect of species identity (Jacob et al. 2010). Few forest studies have traced community level diversity effects to the individual tree level, which would be necessary to identify mechanisms (Liang et al. 2007; Potvin & Gotelli 2008). Tracing individual tree growth to proximity and relative abundances of neighbours, and thus relative contribution to competition, may help separate identity from diversity effects (Canham et al. 2004; Uriarte et al. 2004; Kirwan et al. 2007; Potvin & Dutilleul 2009; Thorpe et al. 2010). This leads to another challenge in forest BEF research: the disentanglement of effects from identity and diversity as facets of community composition (cf. ‘Diversity Debate’, above Cardinale et al. 2012), as well as setting diversity effects on a functional rather than a taxonomic basis (Violle et al. 2007). Species richness or identity can be only weakly informative and cannot be generalised; sets of functional traits characterise species with respect to certain ecological processes: how they react and feedback into them, such that trait based diversity measures would allow for a more functional and thus mechanistic understanding of diversity effects (Díaz & Cabido 2001). Finally, community composition and the processes of forest dynamics experience dramatic shifts during succession (Bazzaz 1996; Lichter 1998; Caspersen & Pacala 2001). With ongoing succession, functional composition, ecosystem functioning and hence BEF relationships are expected to change (Wirth & Lichstein 2009; Morin et al. 2011; Morin et al. 2014; Barrufol et al. 2013; Lasky et al. 2014) and the picture will only be complete, if not just snapshots, but longer phases of succession are studied. There are currently no experiments or datasets that would allow a comprehensive mechanistic analysis of the interplay of succession, biodiversity and forest dynamics, which acknowledge the various facets and the dynamic nature of trait influences. One of the alluring challenges of BEF research in forests lies in bringing traits, processes and functions together – in order to reveal underlying mechanisms (Cardinale et al. 2012).

Overarching Strategy As shown above, the relationship between ecosystem functions and functional composition of forests encompasses a multitude of processes that are mutually linked and that can be sorted along a natural hierarchy. They span from 1) aspects of individual performance (functional traits, e.g. rates of carbon uptake, tissue turnover, mortality 23

and fecundity) via 2) vegetation states (e.g. average height, leaf-area cover, density) and 3) community assembly through forest dynamics (recruitment, growth and mortality) to 4) ecosystem functions like productivity, nutrient cycling or biomass storage (Suding et al. 2008; Mouchet et al. 2010; Falster et al. 2011). To establish links from traits to functions, it is necessary to resolve the hierarchy of processes with their pertaining drivers and outcomes, their relevant traits and affected states. I use the ‘traits–states–rates scheme’ (TSR) (Purves & Vanderwel 2014) as a conceptual model with which to capture and describe the influence of biodiversity on ecosystem functions in forests along the aforementioned hierarchy (Fig. 1). It assumes that “[a] combination of the current states of the community, with the traits of individuals, implies a set of rates, which implies a new set of states, and so on.” The combination of traits and respective abundances (a state) may be reflected in abstract concepts such as functional composition. From this conceptual perspective, functional composition influences the rates. The feedback between rates and states is the domain of forest dynamics, where the structural composition of a forest changes over time. All of these are embedded in an environment, which influences all effect paths. I have endeavoured to tap on all components of this framework from different angles with different methodologies to reach a comprehensive as well as instructive application. In two research projects (Paper 1 and Paper 2) I focused on empirical data and application, in a third project (Paper 3), I went beyond the restrictions of empirical data availability and used a vegetation model to access and simulate any model concept of interest. I have approached the topic with a variety of methods: starting with field work and inventories, continuing with several statistical analyses, proceeding to trait collection and obtaining trait values from empirical data, to implementation of processes in a vegetation model and finally conducting and analysing model experiments. Observations and experiments, empirical and modelling studies have each their own limitations and advantages. In any epistemic process they are all required and intimately connected as part of the scientific method. Here, the first two studies are empirical and go from hypotheses via observations to predictions. The third study is not empirical but theoretical based on empirically derived model formulations. It goes from theory (predictions) via experiments to hypotheses. I thus have tried to work on all segments of the spiral of the scientific method in varying depth and with varying methods but on a common subject and immersed in the stream of the research community.

24

functional composition

Legend influence or component

functional traits

states (height, biomass, …)

environment

overarching relationship

rates (growth, mortality, recruitment)

feedback over time

forest dynamics

traits

ecosystem functions

states

(productivity)

rates

Figure 1. Conceptual model with which to capture and describe the influence of functional composition on ecosystem functions: the ‘traits–states–rates scheme’ (TSR) (Purves & Vanderwel 2014) – extended to include the concept of functional composition and its link to rates, the role of the environment and the domain of forest dynamics as encompassing the rates and their influence on states in the course of time. The rates influence some ecosystem functions, such as stand-level productivity, to which they sum up to.

Study system In the framework of an initiative to advance biodiversity and ecosystem research in Germany, three exemplary large-scale and long-term research sites were established. The ‘Biodiversity Exploratories’ (www.biodiversity-exploratories.de) are a German Science Foundation funded research project (DFG Priority Programme 1374) and serve as open research platform with a long-term perspective for all functional biodiversity and ecosystem research in Germany (Fischer et al. 2010). My thesis is embedded in and partly funded by this programme. One of the exploratories is situated in the HainichDün, one of the largest contiguous deciduous forests in Germany, populated by a fairly species-rich mixture of beech and other hardwoods and with a history of low intensity management. 25

European beech forest with a variable admixture is one of the most important forest types in Central Europe. Although tree species richness tends to not be very high in all Central European forests, these forest types are suitable for BEF research for two reasons: they often come close to the potential natural vegetation and span large areas, rather than being restricted to small scale edaphic or climatic conditions and at the same time they host a comparatively decent amount of different tree species, each in significant proportions. Inspired by these relatively rich systems, I conducted the studies of Paper 1 and Paper 2 in a 28.5 ha plot of mature deciduous forest (‘Weberstedter Holz’; trees aged 1 to >250 years), located in the ‘Hainich National Park’ (51°06’ N, 10°31’ E), Thuringia, Germany. The National Park is part of Germany’s largest contiguous deciduous forest (Hainich-Dün) and is listed as a UNESCO World Heritage site. The site has been permanently forested for over 200 years and has remained free of harvesting or thinning for over 40 years (Butler-Manning 2007). It is dominated by beech (Fagus sylvatica L.), with an admixture of ash (Fraxinus excelsior L.), hornbeam (Carpinus betulus L.), sycamore (Acer pseudoplatanus L.) and wych elm (Ulmus glabra Huds.) (Table 1).

Table 1. Inventory data of the plot (total area 28.5 ha) in 1999, in 2007 and of trees that died in this period: number of stems, basal area (BA) [m2 ha-1]. Respective percentages in parentheses. 1999 BA [m2 ha-1] Trees

Species Trees Ash 564 (4) Beech 13297 (90) Wych Elm 70 (0) Hornbeam 391 (3) Sycamore 322 (2) Other 82 (1) Total 14726 (100)

26

6.1 24.3

(17)

2007 BA [m2 ha-1] Trees

528

(4)

6.6

(68) 12197

(90)

25.5

(18)

Dead BA [m2 ha-1]

39

(2)

0.26

(14)

(69) 1535

(92)

1.02

(55)

0.6

(2)

39

(0)

0.3

(1)

35

(2)

0.33

(18)

1.6

(5)

361

(3)

1.6

(4)

30

(2)

0.10

(5)

2.6

(7)

345

(3)

2.7

(7)

14

(1)

0.08

(4)

0.6

(2)

82

(1)

0.6

(2)

10

(1)

0.06

(3)

35.9 (100) 13552 (100)

37.2 (100) 1663 (100)

1.85 (100)

Paper 1: Many ways to die—partitioning tree mortality dynamics in a near-natural mixed deciduous forest functional species identity composition functional traits

DBH states (height, biomass, …)

environment

growth rates (growth, mortality, mortality recruitment)

mortality processes forest dynamics

ecosystem functions (productivity)

Figure 2. Conceptual model with processes and drivers studied in Paper 1. Colour and line meanings as in Fig. 1, which is in pale underneath. In Paper 1 I scrutinised tree mortality as a key process of forest dynamics and an important driver of carbon cycling (Fig. 2), because tree longevity determines the residence time of biomass and as a result the size of the biomass pool (Wirth & Lichstein 2009). Understanding and predicting tree mortality is therefore indispensable for modelling the dynamics, diversity and functions of forest ecosystems (Purves & Pacala 2008). Although it is the main negative rate occurring in vegetation biomass balance, the complement of growth, it has received far less scientific attention than the latter. Partly because in commercial forests, when trees are harvested, natural death plays a smaller role and partly because it is a rare and stochastic process, harder to come by than growth. Hence, the question of when and why trees eventually die is largely unsolved. It appears to be context-dependent and species-specific and remains one of the greatest challenges of forest ecology (Watkinson 1992; Hurst et al. 2011). A comprehensive mechanistic analysis of individual tree mortality should unscramble and classify the various causes or modes of mortality (Chao et al. 2009). Partitioning tree mortality into different causes of death allows the tracing and mechanistic modelling of individual key processes of forest dynamics. 27

As old-tree mortality is usually modelled simplistically in forest dynamic models, its rate being derived from reported maximum ages without any mechanistic considerations (Hawkes 2000; Keane et al. 2001; Porté & Bartelink 2002; Lutz & Halpern 2006), I wanted to provide a mechanistic interpretation helping to improve and break down mortality algorithms in forest succession models. I thus addressed the following questions: (i) How do individual tree dimensions and their previous growth explain the mortality of the different modes, (ii) how and to what degree can overall mortality be partitioned into the different mortality modes, (iii) how do the mortality rates of the different species compare to each other and which specific demographic traits can be inferred from the patterns and (iv) can we derive estimates of longevity or any other practical measure from survival scenarios based on mortality models that could be useful for mechanistic vegetation models? In this paper I did not yet consider diversity effects. Instead, I focused on individual and species level predictors and the partitioning into processes. In a follow-up study, Paper 3, I implemented the gained insight on mortality processes as depending on various causes and individual properties in a vegetation model to achieve an approximation to diversity–mortality relationships. Only this way, I suppose, the potentially complex relationship may be properly addressed (Morin et al. 2011). However, I acknowledge that in future studies we will need to analyse the direct effect of diversity on mortality. For this, I needed another inventory interval, data which were only gathered recently and could not enter this thesis.

Paper 2: Tree neighbourhood matters – Tree species composition drives diversity–productivity patterns in a near-natural beech forest This paper’s first author is Sophia Ratcliffe and I contributed significantly to its conception, analysis and writing. In Paper 2, we focussed on the positive side of the vegetation carbon balance, tree growth. As growth is a continuous process, as compared to the rare and discrete events of mortality, it is easier to trace back to possible predictors. Not only at the level of the individual, but also of the neighbouring community. The extent to which complementarity and species identity control tree growth in natural and near-natural forests is a current contentious issue (Zhang et al. 2012; Ruiz-Benito et al. 2014), and helping to resolve it is the focus of this study. Here we tested whether tree diversity affected tree growth at the tree and stand level, while accounting for size, vitality and local topography and assessed the influence of species identity of the focus as well as the neighbouring trees (Fig. 3). 28

functional species identity + diversity composition functional traits

DBH states (height, biomass, …)

environment topography

growth rates

neighbourhood influence

(growth, mortality, recruitment)

forest dynamics

ecosystem functions (productivity)

Figure 3. Conceptual model with processes and drivers studied in Paper 2. Colour and line meanings as in Fig. 1, which is in pale underneath. Competition, a key mechanism underlying diversity–growth relationships, occurs between individuals (Scherer-Lorenzen et al. 2007; Potvin & Dutilleul 2009). Hence a neighbourhood approach may be used to quantify local interactions and infer whether any observed individual tree growth enhancement is driven by altered interactions due to local changes in relative abundance of neighbours (Canham et al. 2004; Uriarte et al. 2004; Kirwan et al. 2007; Potvin & Dutilleul 2009; Thorpe et al. 2010). Doing so allows us to understand how tree species respond to increased diversity and how this is reflected at the community level. The aim of this study was to test whether (i) a greater diversity of neighbourhood tree species enhances individual tree growth, (ii) any observed diversity effect is driven by differences in competitive interaction strengths, and (iii) determine how individual tree level diversity–growth relationships are reflected at the stand level.

29

Paper 3: Taking a closer look: disentangling effects of functional diversity on ecosystem functions with a trait-based model across hierarchy and time functional composition functional traits

states (height, biomass, …)

controlled environment environment

rates (growth, mortality, recruitment)

forest dynamics

ecosystem functions (productivity)

Figure 4. Conceptual model with processes and drivers studied in Paper 3. Colour and line meanings as in Fig. 1, which is in pale underneath. In Paper 3, I provided a synthesis of empirical data, partly from the previous two studies, and ecosystem modelling to render insights into mechanisms of biodiversity effects on ecosystem functions. I started from the perspective that the ecosystem model may be considered a surrogate of nature, whose internal design is complete enough to encompass key mechanisms that may play a role in BEF (Pretzsch et al. 2015) and complex enough to render more than trivial results or circular logics. The model allows us to control the environment, extract any information on modelled processes and parameters, the functional composition and the states and rates of the analysis scheme (Fig. 4) and to model a number of experimental situations for a number of years – only computing time is limiting here. For the model experiment, I chose a trait based approach, where biodiversity is described by the distribution of plant functional traits in a community. Functional traits typically translate into measurable quantities of a number of attributes. While this may 30

be a very encompassing way to describe the composition of an ecosystem in a functional way, it also entails complexity in terms of the trait space being multi-dimensional and each trait having a distribution, rather than just a single value. These are friendly challenges, though, as the dimensionality issue may be easily resolved with ordination methods that also help to focus on general plant strategies as well as with statistical descriptors representing mean, range and spread of the trait distribution. These descriptors represent what is called functional composition and I refer to these metrics as facets of functional composition. Still, I wanted to tackle two other challenges that are often ignored in BEF research in forests. The first is more obvious: that trait influence may change over time and the second is just nasty, from the viewpoint of a fieldworker: that traits may influence processes at different levels of the natural hierarchy of organisation. The large time spans, in which forest dynamics and thus community assembly take place is nearly prohibitive for real-world experiments – and thus pose a strong demand for forest modelling, having sparked model developments as early as the 70ies (‘Jabowa’, Botkin et al. 1972) and also mark a focus of this study. The hierarchy of trait-influence is known but hardly considered in the design or analysis of BEF experiments – probably because the general assessment of the size and prevalence of biodiversity effects at large were first to be established before digging deeper. Though now, it is high time to do so. It might be “a welcome advancement in a field that has become grossly oversimplified by graphing every conceivable process against species richness in an attempt to show that ‘biodiversity is good’.” (David U. Hooper in the review of this paper). The model allows tapping into various processes and states of different hierarchy and assembly level, which further may be used to disentangle process pathways, their importance, interactions, drivers and changes over successional time. This Paper 3 provides not only a synthesis of empirical work from different sources, such as the previous Papers 1 and 2, literature on traits and processes and extraction of traits from large inventories. It also is a fusion of empirical research on traits and processes in BEF with the modelling of ecosystems, which stems from generic principles of plant physiology, forest dynamics and macroecology. This way, we reach a comprehensiveness that is hardly achievable in observational studies.

31

Introduction to Methods For the studies, I have drawn from a variety of methodical approaches: inventories in the field, statistical analyses (for, e.g. error identification and estimation, imputation of missing values, error propagation, correction for spatial autocorrelation, regression analysis), as well as working with trait databases, trait calibration from empirical data, programming in a vegetation model and a combination of modelling with statistical path analysis.

Study system In the forest site ‘Weberstedter Holz’ on an area of 28.5 ha, all trees with a diameter at breast height (dbh) of 1 cm or more, summing up to more than 15’000 stems, were surveyed in the summers of 1999 and 2007. Coordinates of the trunk base, species, dbh, a dominance rating, vitality information and status (live or dead) were recorded (cf. Table 1). A subset of the dead trees was sampled with an increment puncher in order to retrieve information of previous growth. A major challenge lay in harmonising and merging the two periods and the two methods of growth measurement for live and dead trees. Additionally, several field trips were undertaken to re-measure trees with unlikely measurements or re-asses trees with unclear status or species. High resolution LiDAR data was available for the whole study area from which a digital terrain model (DTM) at 0.5 m spatial resolution was constructed to derive topographic variables.

Paper 1 In this paper, I needed a method, which could trace the observed mortality events, which fell into six different modes of death, to the predictors tree size and growth for three tree species. This is a typical case for logistic regression, where discrete events are approximated by probabilities that can also be scaled to arbitrary time periods, such as a single year. The two main challenges here were to design an estimation procedure that would incorporate all mortality modes simultaneously (essentially a multinomial problem) plus trees of unknown fate, deal with non-monotonous effects and allow propagating all uncertainties from the predictor level into the prediction uncertainty. As the first and the third are issues that standard solutions cannot deal with, I chose to revert to a Markov Chain Monte Carlo (MCMC) estimation method, where all relationships in the statistical model can be individually programmed, and a simultaneous, hierarchical estimation allows for seamless integration of the error propagation. I used the program WinBUGS (Gilks et al. 1994). 32

The predictors tree size and growth both had their respective measurement errors. For growth, these were relatively large, making it mandatory to account for them. Additionally, growth relied on different measurement methods for live and dead trees and of the dead trees only ca. one third was measured. Hence, I imputed the growth of non-sampled dead trees with auxiliary data. To make these values commensurable and to incorporate the respective uncertainties, it was also necessary to develop a predictive model for growth. This, in turn, was achieved by developing a method that predicts individual tree growth with the information on growth of surrounding similar trees and competition. This part might seem meticulous, especially because it entailed more work than the main method, though I here want to stress the need for error propagation as part of any statistical method. In this study, I also wanted to bridge from empirical results to vegetation models by informing them on the level of processes and parameters. I used the mortality model and linked it simultaneously to a regression model that estimated age from tree size, using a separate data set of tree discs. I ran survival scenarios with different combinations of mortality modes and thus derived estimations of tree longevity under various circumstances. I contrasted my results for beech with mortality processes in the model of Wirth & Lichstein (2009), as well as with whole-patch mortality in the vegetation model LPJ–GUESS (Smith et al. 2001; Hickler et al. 2012). This way I could inform the study of Paper 3 on the level of mortality processes and related species specific traits.

Paper 2 In this paper, we used two modelling approaches to quantify the effect of local neighbourhood diversity on individual tree and plot level growth using the same data as in Paper 1 (cf. Table 1). At the individual tree level, our objectives were to quantify the effect of diversity and competitive interactions on individual tree growth. At the stand level, our objectives were to quantify the effects of stand diversity on the joint performance of different species. As indicators of species admixture, we used Shannon’s index of diversity and a con- vs. heterospecific, or species specific competition index to also account for identity effects. We further controlled for other influential co-variables, such as tree size, previous damages and topographic variables derived from a digital terrain model (elevation and wetness). As we found a significant spatial autocorrelation of tree growth, we investigated it by estimating ‘Moran’s I’ statistic and quantified it with semivariograms. We chose to fit the models using Generalised Least Squares (GLS). The appeal of GLS models is that 33

an error function can be used that accounts for spatial autocorrelation and, with the addition of a ‘nugget’ term, measurement error within the data. For the individual approach, we used zones of influence with varying extension, for the plot level approach, the dataset was split into several non-overlapping plots with a common size derived from the individual approach. The use of a diversity index as well as a species specific competition index allowed to assess how much of a diversity effect is mediated via attenuated neighbourhood competition. The plot level approach allows for estimating the effects of diversity, independent of species specific reactions, and the identity effects occurring at the community level. Complementing each other, both feed into a more mechanistic understanding of diversity and identity effects in forests as well as giving examples of effect ranges and sizes, which also served as a reference and support for approaches and findings in Paper 3.

Paper 3 In this study I went beyond empirical approaches but relying on them. I set out with the notion that any observed or assumed BEF effect calls for a more detailed resolution to unravel its mechanisms. I deem this especially important in forests with their vertical structure and temporal dynamics. For obvious reasons, long-term experiments and observations in forests are prohibitively laborious. There it is, where model experiments come in. Vegetation models try to mimic natural systems in various ways by combining knowledge about system behaviour in a framework of mathematical equations. I here chose to use the trait-calibrated, process-based dynamic vegetation/ecosystem model LPJ–GUESS (Smith et al. 2001; Hickler et al. 2012) to gain a mechanistic understanding of the effects of functional composition on ecosystem productivity by tracing the processes from traits over individual performance, community assembly to stand-level ecosystem state and rate variables over long successional time scales. LPJ–GUESS has been used successfully in ca. 100 studies (cf. www.nateko.lu.se/LPJ– GUESS, viewed August, 2015) addressing e.g. regional forest dynamics (Hickler et al. 2004) and continental tree species distribution (Hickler et al. 2012), but not yet for BEF studies. The latter indicates that it was not designed to reproduce BEF theories, but rather allows an unbiased approach towards testing BEF hypotheses. LPJ–GUESS combines the details in energy and matter balances from DGVMs (Dynamic Global Vegetation Models) (Sitch et al. 2003) and the demographic processes of forest dynamics from forest gap models (Bugmann 2001). It simulates vegetation structure and composition in response to spatial and temporal variation in temperature, 34

precipitation, incoming radiation and soil physical properties (Fig. 5). Physiological processes and associated fluxes of carbon and water are simulated on a daily time step, whereas forest dynamics are simulated annually (Sitch et al. 2003; Hickler et al. 2004). Spatial heterogeneity of forest structure is accounted for by simulating a number of replicate patches (0.1 ha) that all have the same climate and soil type but differ in their disturbance history and stochastic processes such as tree recruitment and mortality. The vegetation in each patch is represented by tree cohorts, where trees of the same age and species are represented by an ‘average’ individual (Lagergren et al. 2012). Species are characterised by different static parameters, equivalent to functional traits. A complete description of model equations is given in Smith et al. (2001) and Gerten et al. (2004).

temperature, precipitation, radiation, CO2 vegetation structure & species composition

Daily processes soil hydrology

soil water content

stomatal conductance

Annual processes biomassallocation allocation biomass & growth

photosynthesis

net primary production

recruitment establishment & mortality mortality &

autotrophic respiration heterotrophic respiration

ecosystem atmosphere C exchange

leaf & root phenology

wildfire disturbance

tissue turnover

soil organic matter Figure 5. Conceptual representation of LPJ–GUESS showing the main processes, time steps, state variables and input environmental data. 35

All these features qualify LPJ–GUESS for our intended use. However, other vegetation models of equivalent value could have been used (cf. ecobas.org/www-server/rem/ models.html, viewed August, 2015, for a wide range of ecological models and Pretzsch et al. 2015 for a review on species mixing in forest growth models). Vegetation models may be classified according to their approach for modelling forest dynamics: processbased, empirical and a hybrid thereof (Pretzsch et al. 2015). Many traditional ‘Forest yield models’ tend to be parameterised locally and based on empirical relationships, which excludes them for a mechanistic analysis of BEF relationships. Further, the principles governing mixed-species behaviour may be either modelled with empirical factors (no interaction, via species-specific competition indices or using multipliers affecting growth rates and stand density) or in a process-based representation by incorporating within-stand environmental conditions, species-specific structures and resource uptake and availability (Pretzsch et al. 2015). Again, only the latter qualified for this study. Finally, the spatial representation of the vegetation can be on stand, patch or explicit level and the ontogeny can be grouped into species only (no population structure), same-age cohorts or individuals. I deem that both the first cases were not appropriate to capture enough detail to represent relevant processes of forest dynamics and species interaction, excluding some global DGVMs, e.g. LPJ (Sitch et al. 2003) or ORCHIDEE (Krinner et al. 2005). Individual-based and spatially explicit models offer the greatest level of ecological realism and detail, perfectly qualifying for our purpose in principle, but they are also computationally intensive, which can make running large numbers of model experiments difficult, e.g. SORTIE (Pacala et al. 1993; Pacala et al. 1996; Coates et al. 2003), FORMIND (Köhler & Huth 1998; Bohn et al. 2014), BALANCE (Grote & Pretzsch 2002) or SORTIE-ND (Canham et al. 2004; Canham et al. 2006). I chose to work with the intermediately complex class of gap-models, representing vegetation in age-cohorts on the spatial scale of patches (with the size of gaps created by large trees falling – hence the name). Several models would still not be suitable because of strong foci on single regions or certain processes. I found that, among other candidate gap-models (e.g. ForClim Bugmann 1996; Didion et al. 2009), LPJ–GUESS met a reasonable compromise between generality (global application and simulation of long time intervals), accuracy of processes representation (forest dynamics), realism (detail in energy, carbon and water balance, a heritage from the LPJ–DGVM ancestor) and computational speed (Levins 1966; Levin et al. 1997).

36

I had to adapt and extend the model in order to use it for a BEF study. First, the extraction of the empirically useful output measures (e.g. various mortality processes, various biomass fluxes) needed to be programmed, and second, a different and more detailed input, in terms of species parameters and environmental drivers (climate and soil), had to be fed in. New processes were implemented based on Paper 1 (storm related and crushing mortality), other processes were adapted and added to allow influence of species specific trait information (allometry and maximum tree height). I collected a vast number of species trait information that would translate into model parameters. For originally 38 woody species that commonly occur in central European forests, I gathered information on 31 functional traits. I derived them from our own forest inventory data and obtained them from the scientific literature and trait databases (via the TRY-database, Kattge et al. 2011). For many trait and species combinations I found several values, for many others none, such that some were averaged based on the quality of the sources and others were extrapolated from higher taxonomic levels. The model was then validated with the trait and environmental data against the inventory data from the ‘Weberstedter Holz’. This was done not on the exact species level but on the level of ecosystem behaviour, since models, however detailed they might be, should not be mistaken as perfect representations of reality. Accordingly, they need to match reality in a few relevant aspects but are not expected to replace real experiments and natural systems. In this process, also programming errors or inaccuracies were detected and corrected. Using the model for a biodiversity experiment but not working on the detail level of real species poses a particular challenge. I dealt with it through a heuristic strategy that retained the diversity of species trait information but decoupled it from the real species by constructing pseudo-species from the correlation structure in the species– trait matrix. Typically, vegetation models use plant functional types, which are very broad generalisations of growth strategies found in the realm of plants, such as ’temperate broadleaved summer green tree’. Unlike them, the pseudo-species were rigidly created from empirical trait values of species and also reflected the diversity along a major functional gradient. They thus allow communicating from the empirical work to the model frame. From the sampled trait information, I ordinated 22 traits, equivalent to model parameters, from 31 broadleaved tree species in a principal component analysis (PCA) to retrieve empirical trade-offs. From this manifold, I chose to use only the first axis, because it was most strongly related to the key processes in our study system, a temperate forest. The first axis distinguished early- vs. late-successional species. Then, I created 16 pseudo-species that I arranged evenly spaced along the empirical 37

trade-off represented by the first axis (cf. Fig. 1 in Paper 3). So, from a large number of trait values and species, I systematically deduced a set of pseudo-species arranged along a multi-trait gradient, which reflects a trade-off observed in the pool of extant woody species. I assert that biodiversity as concept may be represented not only in various indicators but also that it is multi-dimensional, thus also requiring more than one indicator. I here chose three measures of functional composition that represent roughly independent ‘facets’ of the functional trait distribution: range (functional richness), spread (functional dissimilarity) and location (functional identity). While dissimilarity and identity represent diversity and identity, richness may be important to reflect the potential to where the composition can shift during succession. I developed experiments with an orthogonal design, where the different facets of functional composition were as little correlated as possible, such that their influences may be separated. All model experiments were run on a single site with its parameters derived from the study site ‘Weberstedter Holz’. Adding to the complexity of three indicators for functional diversity, I considered the dynamic nature of trait influence, the changing roles that traits play during succession and the hierarchy of trait influence from more basic to more aggregated ecosystem properties and functions, because relating functional traits directly to ecosystem functions would jump over several levels of the organismic hierarchy. I suggest that tracing trait effects across hierarchical levels in specific phases of forest succession is necessary to pinpoint mechanisms of BEF relationships. The multi-dimensionality and relatedness of the retrieved data from the model output required an apt method to analyse them. Parallel univariate analyses would miss the interrelatedness of the data and not allow propagation of effects along hierarchies. I found that path analysis, a method of the structural equation modelling (SEM) toolbox, allows representing complex pathways, the intrinsic process hierarchy and nestedness of variables. I designed the path analysis to mirror the vegetation model in key aspects applying the concepts of the ‘traits–states–rates scheme’ (TSR) of Purves & Vanderwel (2014). I thus could trace the path of biomass change via ecosystem rates and states finally to the different facets of functional composition. This way, I could pinpoint specific mechanisms underlying BEF relationships in forests – over long time-scales and across the entire hierarchy.

38

Conclusions I have set out to approach the field of forest dynamics and the effect of tree-species and their diversity on these dynamics from two angles: empirical research on inventory data and simulation of model experiments. For this, I tapped into large forest inventory data, published data from the literature and trait-databases. I worked with a range of statistical tools, programming and analysis methods. I allowed myself to be guided by the idea of reducible complexity in forest dynamics, a mechanistic perspective on ecosystem processes and a functional approach to biodiversity to generate new insights. Still, I have kept in mind that all these may at best be just new hypotheses and models of an ever-changing and never wholly understandable nature in all its beauty and complexity.

References Aarssen LW (1997) High productivity in grassland ecosystems: effected by species diversity or productive species? Oikos, 80, 183–184. Ackerly DD, Cornwell WK (2007) A trait-based approach to community assembly: partitioning of species trait values into within-and among-community components. Ecology Letters, 10, 135–145. Baeten L, Verheyen K, Wirth C et al. (2013) A novel comparative research platform designed to determine the functional significance of tree species diversity in European forests. Perspectives in Plant Ecology, Evolution and Systematics, 15, 281–291. Balvanera P, Pfisterer AB, Buchmann N, He J, Nakashizuka T, Raffaelli D, Schmid B (2006) Quantifying the evidence for biodiversity effects on ecosystem functioning and services. Ecology Letters, 9, 1146–1156. Baraloto C, Timothy Paine CE, Poorter L et al. (2010) Decoupled leaf and stem economics in rain forest trees. Ecology Letters, 13, 1338–1347. Barnosky AD, Matzke N, Tomiya S et al. (2011) Has the Earth’s sixth mass extinction already arrived? Nature, 471, 51–57. Barrufol M, Schmid B, Bruelheide H et al. (2013) Biodiversity promotes tree growth during succession in subtropical forest. Bauhus J, van Winden AP, Nicotra AB (2004) Aboveground interactions and productivity in mixedspecies plantations of Acacia mearnsii and Eucalyptus globulus. Canadian journal of forest research, 34, 686–694. Bazzaz FA (1996) Plants in changing environments: linking physiological, population, and community ecology. Cambridge University Press. Bohn FJ, Frank K, Huth A (2014) Of climate and its resulting tree growth: Simulating the productivity of temperate forests. Ecological Modelling, 278, 9–17. Botkin DB, Janak JF, Wallis JR (1972) Some ecological consequences of a computer model of forest growth. The Journal of Ecology, 849–872. Box EO (1996) Plant functional types and climate at the global scale. Journal of Vegetation Science, 309–320. Bugmann HK (1996) A simplified forest model to study species composition along climate gradients. Ecology, 77, 2055–2074. Bugmann HK (2001) A review of forest gap models. Climatic Change, 51, 259–305.

39

Butchart SH, Walpole M, Collen B et al. (2010) Global biodiversity: indicators of recent declines. Science, 328, 1164–1168. Butler-Manning D (2007) Stand structure, gap dynamics and regeneration of a semi-natural mixed beech forest on limestone in central Europe - a case study. PhD-Thesis, Freiburg im Breisgau, Germany, 265 pp. Canham CD, LePage PT, Coates KD (2004) A neighborhood analysis of canopy tree competition: effects of shading versus crowding. Canadian journal of forest research, 34, 778–787. Canham CD, Papaik MJ, Uriarte M, McWilliams WH, Jenkins JC, Twery MJ (2006) Neighborhood analyses of canopy tree competition along environmental gradients in New England forests. Ecological Applications, 16, 540–554. Cardinale BJ, Duffy, J. Emmett, Gonzalez A et al. (2012) Biodiversity loss and its impact on humanity. Nature, 486, 59–67. Cardinale BJ, Matulich KL, Hooper DU et al. (2011) The functional role of producer diversity in ecosystems. American Journal of Botany, 98, 572–592. Cardinale BJ, Srivastava DS, Duffy, J. Emmett, Wright JP, Downing AL, Sankaran M, Jouseau C (2006) Effects of biodiversity on the functioning of trophic groups and ecosystems. Nature, 443, 989–992. Cardinale BJ, Wright JP, Cadotte MW, Carroll IT, Hector A, Srivastava DS, Loreau M, Weis JJ (2007) Impacts of plant diversity on biomass production increase through time because of species complementarity. Proceedings of the National Academy of Sciences, 104, 18123–18128. Caspersen JP, Pacala SW (2001) Successional diversity and forest ecosystem function. Ecological Research, 16, 895–903. Ceballos G, Ehrlich PR, Barnosky AD, García A, Pringle RM, Palmer TM (2015) Accelerated modern human–induced species losses: Entering the sixth mass extinction. Science Advances, 1, e1400253. Chao K, Phillips OL, Monteagudo A, Torres-Lezama A, Vásquez Martínez R (2009) How do trees die? Mode of death in northern Amazonia. Journal of Vegetation Science, 20, 260–268. Chave J, Coomes DA, Jansen S, Lewis SL, Swenson NG, Zanne AE (2009) Towards a worldwide wood economics spectrum. Ecology Letters, 12, 351–366. Coates KD, Canham CD, Beaudet M, Sachs DL, Messier C (2003) Use of a spatially explicit individualtree model (SORTIE/BC) to explore the implications of patchiness in structurally complex forests. Forest Ecology and Management, 186, 297–310. Cornelissen JH (1999) A triangular relationship between leaf size and seed size among woody species: allometry, ontogeny, ecology and taxonomy. Oecologia, 118, 248–255. Cotta H (1817) Anweisung zum Waldbau. Arnoldische Buchhandlung, Dresden und Leipzig. Darwin C (1859) The Origin of Species by Means of Natural Selection. Or the Preservation of Favoured Races in the Struggle for Life. John Murray, Albemarle Street, London. Das A, Battles J, van Mantgem PJ, Stephenson NL (2008) Spatial elements of mortality risk in oldgrowth forests. Ecology, 89, 1744–1756. Dawkins R (2006) The God delusion. Houghton Mifflin Co., Boston. de Toledo JJ, Magnusson WE, Castilho CV, Nascimento HE (2012) Tree mode of death in Central Amazonia: Effects of soil and topography on tree mortality associated with storm disturbances. Forest Ecology and Management, 263, 253–261. Diaz S, Hodgson JG, Thompson K et al. (2004) The plant traits that drive ecosystems: evidence from three continents. Journal of Vegetation Science, 15, 295–304. Díaz S, Cabido M (2001) Vive la difference: plant functional diversity matters to ecosystem processes. Trends in Ecology and Evolution, 16, 646–655. Didion M, Kupferschmid AD, Zingg A, Fahse L, Bugmann HK (2009) Gaining local accuracy while not losing generality-extending the range of gap model applications. Canadian journal of forest research, 39, 1092–1107. Dobbertin M (2005) Tree growth as indicator of tree vitality and of tree reaction to environmental stress: a review. European Journal of Forest Research, 124, 319–333.

40

Ehrlich PR, Ehrlich A (1981) Extinction: the causes and consequences of the disappearance of species. Elton CS (1958) The ecology of invasions by plants and animals. Mathuen & Co., London. Engel EC, Weltzin JF (2008) Can community composition be predicted from pairwise species interactions? Plant Ecology, 195, 77–85. Enquist BJ, West GB, Charnov EL, Brown JH (1999) Allometric scaling of production and life-history variation in vascular plants. Nature, 401, 907–911. Falster DS, Brännström Å, Dieckmann U, Westoby M (2011) Influence of four major plant traits on average height, leaf-area cover, net primary productivity, and biomass density in single-species forests: a theoretical investigation. Journal of Ecology, 99, 148–164. FAO (2010) Global Forest Resources Assessment 2010 Main Report. FAO. Fischer M, Bossdorf O, Gockel S et al. (2010) Implementing large-scale and long-term functional biodiversity research: The Biodiversity Exploratories. Basic and Applied Ecology, 11, 473–485. Forrester DI (2014) The spatial and temporal dynamics of species interactions in mixed-species forests: from pattern to process. Forest Ecology and Management, 312, 282–292. Forrester DI, Pretzsch H (2015) Tamm Review: On the strength of evidence when comparing ecosystem functions of mixtures with monocultures. Forest Ecology and Management. Fox JW (2006) Using the Price Equation to partition the effects of biodiversity loss on ecosystem function. Ecology, 87, 2687–2696. Franklin JF, Shugart HH, Harmon ME (1987) Tree death as an ecological process. BioScience, 550–556. Franks PJ, Farquhar GD (1999) A relationship between humidity response, growth form and photosynthetic operating point in C3 plants. Plant, Cell & Environment, 22, 1337–1349. Fridley JD (2001) The influence of species diversity on ecosystem productivity: how, where, and why? Oikos, 93, 514–526. Gaston KJ, Chown SL (2005) Neutrality and the niche. Functional Ecology, 19, 1–6. Gerten D, Schaphoff S, Haberlandt U, Lucht W, Sitch S (2004) Terrestrial vegetation and water balance—hydrological evaluation of a dynamic global vegetation model. Journal of Hydrology, 286, 249–270. Gilks WR, Thomas A, Spiegelhalter DJ (1994) A language and program for complex Bayesian modelling. The Statistician, 169–177. Gitay H, Noble IR (1997) O What are functional types and how should we seek them. Plant functional types: their relevance to ecosystem properties and global change, 1. Grime JP (1977) Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory. American naturalist, 1169–1194. Grime JP (1998) Benefits of plant diversity to ecosystems: immediate, filter and founder effects. Journal of Ecology, 86, 902–910. Grote R, Pretzsch H (2002) A model for individual tree development based on physiological processes. Plant Biology, 4, 167–180. Hansen MC, Potapov PV, Moore R et al. (2013) High-resolution global maps of 21st-century forest cover change. Science, 342, 850–853. Harrison SP, Prentice IC, Barboni D, Kohfeld KE, Ni J, Sutra J (2010) Ecophysiological and bioclimatic foundations for a global plant functional classification. Journal of Vegetation Science, 21, 300–317. Hartig GL (1791) Anweisung zur Holzzucht für Förster. Neue Akademische Buchhandlung, Marburg. Hawkes C (2000) Woody plant mortality algorithms: description, problems and progress. Ecological Modelling, 126, 225–248. Healy C, Gotelli NJ, Potvin C (2008) Partitioning the effects of biodiversity and environmental heterogeneity for productivity and mortality in a tropical tree plantation. Journal of Ecology, 96, 903–913. Hector A (1998) The effect of diversity on productivity: detecting the role of species complementarity. Oikos, 597–599. Hector A, Hooper R (2002) Darwin and the First Ecological Experiment. Science, 295, 639–640.

41

Hector A, Philipson C, Saner P et al. (2011) The Sabah Biodiversity Experiment: a long-term test of the role of tree diversity in restoring tropical forest structure and functioning. Philosophical Transactions of the Royal Society B: Biological Sciences, 366, 3303–3315. Hector A, Schmid B, Beierkuhnlein C et al. (1999) Plant diversity and productivity experiments in European grasslands. Science, 286, 1123–1127. Heimann M, Reichstein M (2008) Terrestrial ecosystem carbon dynamics and climate feedbacks. Nature, 451, 289–292. Hickler T, Smith B, Sykes MT, Davis MB, Sugita S, Walker K (2004) Using a generalized vegetation model to simulate vegetation dynamics in northeastern USA. Ecology, 85, 519–530. Hickler T, Vohland K, Feehan J et al. (2012) Projecting the future distribution of European potential natural vegetation zones with a generalized, tree species-based dynamic vegetation model. Global Ecology and Biogeography, 21, 50–63. Hillebrand H, Matthiessen B (2009) Biodiversity in a complex world: consolidation and progress in functional biodiversity research. Ecology Letters, 12, 1405–1419. Hooper DU, Adair, E. Carol, Cardinale BJ et al. (2012) A global synthesis reveals biodiversity loss as a major driver of ecosystem change. Nature, 486, 105–108. Hooper DU, Chapin FS, Ewel JJ et al. (2005) Effects of biodiversity on ecosystem functioning: a consensus of current knowledge. Ecological Monographs, 75, 3–35. Hooper DU, Vitousek PM (1997) The effects of plant composition and diversity on ecosystem processes. Science, 277, 1302–1305. Hooper DU, Vitousek PM (1998) Effects of plant composition and diversity on nutrient cycling. Ecological Monographs, 68, 121–149. Hubbell SP (2001) The unified neutral theory of biodiversity and biogeography (MPB-32). Princeton University Press. Hurst JM, Allen RB, Coomes DA, Duncan RP (2011) Size-specific tree mortality varies with neighbourhood crowding and disturbance in a montane Nothofagus forest. PloS ONE, 6, e26670-e26670. Huston MA (1997) Hidden treatments in ecological experiments: re-evaluating the ecosystem function of biodiversity. Oecologia, 110, 449–460. Huston MA, Aarssen LW, Austin MP et al. (2000) No consistent effect of plant diversity on productivity. Science, 289, 1255. Iida Y, Poorter L, Sterck FJ, Kassim AR, Kubo T, Potts MD, Kohyama TS (2012) Wood density explains architectural differentiation across 145 co-occurring tropical tree species. Functional Ecology, 26, 274–282. Jacob M, Leuschner C, Thomas FM (2010) Productivity of temperate broad-leaved forest stands differing in tree species diversity. Annals of Forest Science, 67, 503. Kattge J, Díaz S, Lavorel S et al. (2011) TRY–a global database of plant traits. Global Change Biology, 17, 2905–2935. Keane RE, Austin M, Field C, Huth A, Lexer MJ, Peters D, Solomon AM, Wyckoff P (2001) Tree mortality in gap models: application to climate change. Climatic Change, 51, 509–540. Kelty MJ (1992) Comparative productivity of monocultures and mixed-species stands. In: The ecology and silviculture of mixed-species forests: a festschrift for David M. Smith (eds Kelty MJ, Larson BC, Oliver CD), pp 125–141. Springer Science & Business Media. Kinzig AP, Pacala SW (2001) Successional Biodiversity and Ecosystem Functioning. Chapter 9. In: The functional consequences of biodiversity: empirical progress and theoretical extensions (eds Kinzig AP, Pacala SW, Tilman D), pp 175–212. Princeton University Press. Kinzig AP, Pacala SW, Tilman D (2001a) Looking Back and Peering Forward. Chapter 14. In: The functional consequences of biodiversity: empirical progress and theoretical extensions (eds Kinzig AP, Pacala SW, Tilman D), pp 314–329. Princeton University Press. Kinzig, AP, Pacala, SW, Tilman, D (Eds.) (2001b) The functional consequences of biodiversity: empirical progress and theoretical extensions. Princeton University Press. Kirwan L, Lüscher A, Sebastia MT et al. (2007) Evenness drives consistent diversity effects in intensive grassland systems across 28 European sites. Journal of Ecology, 95, 530–539.

42

Köhler P, Huth A (1998) The effects of tree species grouping in tropical rainforest modelling: Simulations with the individual-based model FORMIND. Ecological Modelling, 109, 301–321. Körner C (2005) An introduction to the functional diversity of temperate forest trees. In: Forest diversity and function: temperate and boreal systems (eds Scherer-Lorenzen M, Körner C, Schulze E), pp 13–37. Springer. Krinner G, Viovy N, Noblet-Ducoudré N de et al. (2005) A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system. Global Biogeochemical Cycles, 19. Lagergren F, Jönsson AM, Blennow K, Smith B (2012) Implementing storm damage in a dynamic vegetation model for regional applications in Sweden. Ecological Modelling, 247, 71–82. Laliberté E, Legendre P (2010) A distance-based framework for measuring functional diversity from multiple traits. Ecology, 91, 299–305. Larson AJ, Franklin JF (2010) The tree mortality regime in temperate old-growth coniferous forests: the role of physical damage. Canadian journal of forest research, 40, 2091–2103. Lasky JR, Uriarte M, Boukili VK, Erickson DL, John Kress W, Chazdon RL (2014) The relationship between tree biodiversity and biomass dynamics changes with tropical forest succession. Ecology Letters, 17, 1158–1167. Lavorel S, Díaz S, Cornelissen, J Hans C et al. (2007) Plant functional types: are we getting any closer to the Holy Grail? In: Terrestrial ecosystems in a changing world (eds Canadell JG, Pataki DE, Pitelka LF), pp 149–164. Springer Science & Business Media. Lavorel S, Garnier E (2002) Predicting changes in community composition and ecosystem functioning from plant traits: revisiting the Holy Grail. Functional Ecology, 16, 545–556. Lawes JB, Gilbert JH (1880) Agricultural, botanical, and chemical results of experiments on the mixed herbage of permanent meadow, conducted for more than twenty years in succession on the same land. Part I. Philosophical Transactions of the Royal Society of London, 171, 289–416. Leemans R (1997) The use of plant functional type classifications to model global land cover and simulate the interactions between the terrestrial biosphere and the atmosphere. Plant functional types: their relevance to ecosystem properties and global change, 1, 289. Leuschner C, Jungkunst H, Fleck S (2009) Functional role of forest diversity: pros and cons of synthetic stands and across-site comparisons in established forests. Basic and Applied Ecology, 10, 1–9. Levin SA, Grenfell B, Hastings A, Perelson AS (1997) Mathematical and computational challenges in population biology and ecosystems science. Science, 275, 334–343. Levins R (1966) The strategy of model building in population biology. American scientist, 421–431. Liang J, Buongiorno J, Monserud RA, Kruger EL, Zhou M (2007) Effects of diversity of tree species and size on forest basal area growth, recruitment, and mortality. Forest Ecology and Management, 243, 116–127. Lichter J (1998) Primary succession and forest development oncoastal Lake Michigan sand dunes. Ecological Monographs, 68, 487–510. Lines ER, Coomes DA, Purves DW (2010) Influences of forest structure, climate and species composition on tree mortality across the eastern US. PloS ONE, 5, e13212. Loreau M (1998) Separating sampling and other effects in biodiversity experiments. Oikos, 600–602. Loreau M, Hector A (2001) Partitioning selection and complementarity in biodiversity experiments. Nature, 412, 72–76. Loreau M, Naeem S, Inchausti P et al. (2001) Biodiversity and ecosystem functioning: current knowledge and future challenges. Science, 294, 804–808. Lutz JA, Halpern CB (2006) Tree mortality during early forest development: a long-term study of rates, causes, and consequences. Ecological Monographs, 76, 257–275. MacArthur R (1955) Fluctuations of animal populations and a measure of community stability. Ecology, 36, 533–536. Mason NW, Mouillot D, Lee WG, Wilson JB (2005) Functional richness, functional evenness and functional divergence: the primary components of functional diversity. Oikos, 111, 112–118. May RM (1973) Stability and complexity in model ecosystems. Princeton University Press.

43

McCann KS (2000) The diversity–stability debate. Nature, 405, 228–233. McGill BJ, Enquist BJ, Weiher E, Westoby M (2006) Rebuilding community ecology from functional traits. Trends in Ecology and Evolution, 21, 178–185. MEA – Millennium Ecosystem Assessment (Ed.) (2005) Ecosystems and human well-being. Island Press Washington, DC. Mencuccini M, Martínez-Vilalta J, Vanderklein D, Hamid HA, Korakaki E, Lee S, Michiels B (2005) Size-mediated ageing reduces vigour in trees. Ecology Letters, 8, 1183–1190. Mooney HA, Cushman JH, Medina E, Sala OE, Schulze E (1996) The Scope Ecosystem Functioning of Biodiversity Program. SCOPE–Scientific Committee on Problems of the Environment International Council of Scientific Unions, 55, 1–6. Morin X, Fahse L, Mazancourt C, Scherer-Lorenzen M, Bugmann HK (2014) Temporal stability in forest productivity increases with tree diversity due to asynchrony in species dynamics. Ecology Letters, 17, 1526–1535. Morin X, Fahse L, Scherer-Lorenzen M, Bugmann HK (2011) Tree species richness promotes productivity in temperate forests through strong complementarity between species. Ecology Letters, 14, 1211–1219. Mouchet MA, Villeger S, Mason NW, Mouillot D (2010) Functional diversity measures: an overview of their redundancy and their ability to discriminate community assembly rules. Functional Ecology, 24, 867–876. Muller-Landau HC (2010) The tolerance–fecundity trade-off and the maintenance of diversity in seed size. Proceedings of the National Academy of Sciences, 107, 4242–4247. Nadrowski K, Wirth C, Scherer-Lorenzen M (2010) Is forest diversity driving ecosystem function and service? Current Opinion in Environmental Sustainability, 2, 75–79. Naeem S (2000) Reply to Wardle et al. Bulletin of the Ecological Society of America, 241–246. Naeem S (2002) Disentangling the impacts of diversity on ecosystem functioning in combinatorial experiments. Ecology, 83, 2925–2935. Naeem S, Thompson LJ, Lawler SP, Lawton JH, Woodfin RM (1994) Declining biodiversity can alter the performance of ecosystems. Nature, 368, 734–737. Naeem S, Thompson LJ, Lawler SP, Lawton JH, Woodfin RM (1995) Empirical evidence that declining species diversity may alter the performance of terrestrial ecosystems. Philosophical Transactions of the Royal Society B: Biological Sciences, 347, 249–262. Naeem S, Wright JP (2003) Disentangling biodiversity effects on ecosystem functioning: deriving solutions to a seemingly insurmountable problem. Ecology Letters, 6, 567–579. Odum B (1953) Fundamentals of ecology. Saunders, Philadelphia. Oldfield S, Lusty C, MacKinven A (1998) The world list of threatened trees. World Conservation Press. Pacala SW, Canham CD, Saponara J, Silander Jr, John A, Kobe RK, Ribbens E (1996) Forest models defined by field measurements: estimation, error analysis and dynamics. Ecological Monographs, 66, 1–43. Pacala SW, Canham CD, Silander Jr, John A (1993) Forest models defined by field measurements: I. The design of a northeastern forest simulator. Canadian journal of forest research, 23, 1980–1988. Paquette A, Messier C (2011) The effect of biodiversity on tree productivity: from temperate to boreal forests. Global Ecology and Biogeography, 20, 170–180. Pedro MS, Rammer W, Seidl R (2014) Tree species diversity mitigates disturbance impacts on the forest carbon cycle. Oecologia, 177, 619–630. Peñuelas J (2005) Plant physiology: a big issue for trees. Nature, 437, 965–966. Pereira HM, Leadley PW, Proença V et al. (2010) Scenarios for global biodiversity in the 21st century. Science, 330, 1496–1501. Petchey OL, Gaston KJ (2002) Functional diversity (FD), species richness and community composition. Ecology Letters, 5, 402–411. Petchey OL, Gaston KJ (2006) Functional diversity: back to basics and looking forward. Ecology Letters, 9, 741–758.

44

Pietsch KA, Ogle K, Cornelissen JH et al. (2014) Global relationship of wood and leaf litter decomposability: the role of functional traits within and across plant organs. Global Ecology and Biogeography, 23, 1046–1057. Piotto D (2008) A meta-analysis comparing tree growth in monocultures and mixed plantations. Forest Ecology and Management, 255, 781–786. Porté A, Bartelink HH (2002) Modelling mixed forest growth: a review of models for forest management. Ecological Modelling, 150, 141–188. Potvin C, Dutilleul P (2009) Neighborhood effects and size-asymmetric competition in a tree plantation varying in diversity. Ecology, 90, 321–327. Potvin C, Gotelli NJ (2008) Biodiversity enhances individual performance but does not affect survivorship in tropical trees. Ecology Letters, 11, 217–223. Potvin C, Mancilla, Buchmann N et al. (2011) An ecosystem approach to biodiversity effects: Carbon pools in a tropical tree plantation. Forest Ecology and Management, 261, 1614–1624. Pretzsch H (2005) Diversity and productivity in forests: evidence from long-term experimental plots. In: Forest diversity and function: temperate and boreal systems (eds Scherer-Lorenzen M, Körner C, Schulze E), pp 41–64. Springer. Pretzsch H (2014) Canopy space filling and tree crown morphology in mixed-species stands compared with monocultures. Forest Ecology and Management, 327, 251–264. Pretzsch H, Forrester DI, Rötzer T (2015) Representation of species mixing in forest growth models. A review and perspective. Ecological Modelling, 313, 276–292. Purves DW, Pacala SW (2008) Predictive models of forest dynamics. Science, 320, 1452–1453. Purves DW, Vanderwel MC (2014) Traits, states and rates: understanding coexistence in forests. In: Forests and Global Change (eds Coomes DA, Burslem DF, Simonson WD), pp 161–194. Cambridge University Press. Ratcliffe S, Liebergesell M, Ruiz-Benito P et al. (in print) Modes of functional biodiversity control on tree productivity across the European continent. Global Ecology and Biogeography. Reich PB, Ellsworth DS, Walters MB, Vose JM, Gresham C, Volin JC, Bowman WD (1999) Generality of leaf trait relationships: a test across six biomes. Ecology, 80, 1955–1969. Reich PB, Tilman D, Isbell F, Mueller K, Hobbie SE, Flynn DF, Eisenhauer N (2012) Impacts of biodiversity loss escalate through time as redundancy fades. Science, 336, 589–592. Reich PB, Walters MB, Ellsworth DS, Vose JM, Volin JC, Gresham C, Bowman WD (1998) Relationships of leaf dark respiration to leaf nitrogen, specific leaf area and leaf life-span: a test across biomes and functional groups. Oecologia, 114, 471–482. Ricotta C, Moretti M (2011) CWM and Rao’s quadratic diversity: a unified framework for functional ecology. Oecologia, 167, 181–188. Río M del, Schütze G, Pretzsch H (2014) Temporal variation of competition and facilitation in mixed species forests in Central Europe. Plant Biology, 16, 166–176. Roscher C, Schumacher J, Baade J, Wilcke W, Gleixner G, Weisser WW, Schmid B, Schulze E (2004) The role of biodiversity for element cycling and trophic interactions: an experimental approach in a grassland community. Basic and Applied Ecology, 5, 107–121. Roscher C, Schumacher J, Gubsch M, Lipowsky A, Weigelt A, Buchmann N, Schmid B, Schulze E (2012) Using plant functional traits to explain diversity–productivity relationships. PloS ONE, 7, e36760. Rüger N, Huth A, Hubbell SP, Condit R (2011) Determinants of mortality across a tropical lowland rainforest community. Oikos, 120, 1047–1056. Ruiz-Benito P, Gómez-Aparicio L, Paquette A, Messier C, Kattge J, Zavala MA (2014) Diversity increases carbon storage and tree productivity in Spanish forests. Global Ecology and Biogeography, 23, 311–322. Sala OE, Chapin FS, Armesto JJ et al. (2000) Global Biodiversity Scenarios for the Year 2100. Science, 287, 1770–1774. Scherer-Lorenzen, M, Körner, C, Schulze, E (Eds.) (2005a) Forest diversity and function: temperate and boreal systems. Springer.

45

Scherer-Lorenzen M, Körner C, Schulze E (2005b) The functional significance of forest diversity: a synthesis. In: Forest diversity and function: temperate and boreal systems (eds Scherer-Lorenzen M, Körner C, Schulze E), pp 377–389. Springer. Scherer-Lorenzen M, Schulze E, Don A, Schumacher J, Weller E (2007) Exploring the functional significance of forest diversity: a new long-term experiment with temperate tree species (BIOTREE). Perspectives in Plant Ecology, Evolution and Systematics, 9, 53–70. Schleuter D, Daufresne M, Massol F, Argillier C (2010) A user’s guide to functional diversity indices. Ecological Monographs, 80, 469–484. Schulze E, Mooney HA (1994) Biodiversity and Ecosystem Function. Springer, Berlin. Shipley B, Lechowicz MJ, Wright I, Reich PB (2006) Fundamental trade-offs generating the worldwide leaf economics spectrum. Ecology, 87, 535–541. Shugart H (1984) A theory of forest dynamics: the ecological implications of forest succession models. Shvidenko A, Barber CV, Persson R (2005) Forests and woodland systems. In: Ecosystems and human well-being (ed MEA – Millennium Ecosystem Assessment). Island Press Washington, DC. Sitch S, Smith B, Prentice IC et al. (2003) Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biology, 9, 161–185. Smith B, Prentice IC, Sykes MT (2001) Representation of vegetation dynamics in the modelling of terrestrial ecosystems: comparing two contrasting approaches within European climate space. Global Ecology and Biogeography, 10, 621–637. Smith TM, Shugart HH, Woodward FI, Burton PJ (1993) Plant Functional Types. In: Vegetation Dynamics & Global Change (eds Solomon AM, Shugart HH), pp 272-292. Springer US. Srivastava DS, Vellend M (2005) Biodiversity-ecosystem function research: is it relevant to conservation? Annual Review of Ecology, Evolution, and Systematics, 267–294. Suding KN, Goldberg DE, Hartman KM (2003) Relationships among species traits: separating levels of response and identifying linkages to abundance. Ecology, 84, 1–16. Suding KN, Goldstein LJ (2008) Testing the Holy Grail framework: using functional traits to predict ecosystem change. New Phytologist, 180, 559–562. Suding KN, Lavorel S, Chapin FS et al. (2008) Scaling environmental change through the community-level: a trait-based response-and-effect framework for plants. Global Change Biology, 14, 1125–1140. Thorpe HC, Astrup R, Trowbridge A, Coates KD (2010) Competition and tree crowns: a neighborhood analysis of three boreal tree species. Forest Ecology and Management, 259, 1586–1596. Tilman D (1990) Constraints and tradeoffs: toward a predictive theory of competition and succession. Oikos, 3–15. Tilman D (1996) Biodiversity: population versus ecosystem stability. Ecology, 77, 350–363. Tilman D (1999) The ecological consequences of changes in biodiversity: A search for general principles. Ecology, 80, 1455–1474. Tilman D, Dodd ME, Silvertown J, Poulton PR, Johnston AE, Crawley MJ (1994) The park grass experiment-insights from the most long-term ecological study. Tilman D, Downing JA (1994) Biodiversity and stability in grasslands. Nature, 367, 363–365. Tilman D, Isbell F, Cowles JM (2014) Biodiversity and Ecosystem Functioning. Annual Review of Ecology, Evolution, and Systematics, 45, 471. Tilman D, Reich PB, Isbell F (2012) Biodiversity impacts ecosystem productivity as much as resources, disturbance, or herbivory. Proceedings of the National Academy of Sciences, 109, 10394–10397. Tilman D, Wedin D, Knops J (1996) Productivity and sustainability influenced by biodiversity in grassland ecosystems. Nature, 379, 718–720. Toïgo M, Vallet P, Perot T, Bontemps J, Piedallu C, Courbaud B (2015) Overyielding in mixed forests decreases with site productivity. Journal of Ecology, 103, 502–512. UNEP – United Nations Environment Programme Conference of the parties to the Convention on biological diversity.

46

UNEP – United Nations Environment Programme Global Biodiversity Assessment, Cambridge. Uriarte M, Condit R, Canham CD, Hubbell SP (2004) A spatially explicit model of sapling growth in a tropical forest: does the identity of neighbours matter? Journal of Ecology, 92, 348–360. Vehviläinen H, Koricheva J (2006) Moose and vole browsing patterns in experimentally assembled pure and mixed forest stands. Ecography, 29, 497–506. Verheyen K, Vanhellemont M, Auge H et al. (2015) Contributions of a global network of tree diversity experiments to sustainable forest plantations. Ambio, 1–13. Vilà M, Carrillo-Gavilán A, Vayreda J et al. (2013) Disentangling biodiversity and climatic determinants of wood production. PloS ONE, 8, e53530. Vilà M, Inchausti P, Vayreda J, Barrantes O, Gracia C, Ibáñez JJ, Mata T (2005) Confounding factors in the observational productivity-diversity relationship in forests. In: Forest diversity and function: temperate and boreal systems (eds Scherer-Lorenzen M, Körner C, Schulze E), pp 65–86. Springer. Vilà M, Vayreda J, Comas L, Ibáñez JJ, Mata T, Obón B (2007) Species richness and wood production: a positive association in Mediterranean forests. Ecology Letters, 10, 241–250. Vilà M, Vayreda J, Gracia C, Ibáñez JJ (2003) Does tree diversity increase wood production in pine forests? Oecologia, 135, 299–303. Villéger S, Mason NW, Mouillot D (2008) New multidimensional functional diversity indices for a multifaceted framework in functional ecology. Ecology, 89, 2290–2301. Violle C, Navas M, Vile D, Kazakou E, Fortunel C, Hummel I, Garnier E (2007) Let the concept of trait be functional! Oikos, 116, 882–892. Walters MB, Reich PB (1996) Are shade tolerance, survival, and growth linked? Low light and nitrogen effects on hardwood seedlings. Ecology, 77, 841–853. Wardle DA, Huston MA, Grime JP, Berendse F, Garnier E, Lauenroth WK, Setälä H, Wilson SD (2000) Biodiversity and ecosystem function: an issue in ecology. Bulletin of the Ecological Society of America, 235–239. Watkinson A (1992) Plant senescence. Trends in Ecology and Evolution, 7, 417–420. Watson RT, Noble IR, Bolin B, Ravindranath NH, Verardo DJ, Dokken DJ (2000) Land use, land-use change and forestry: a special report of the Intergovernmental Panel on Climate Change. Cambridge University Press. West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science, 276, 122–126. Westoby M (1998) A leaf-height-seed (LHS) plant ecology strategy scheme. Plant and soil, 199, 213–227. Westoby M, Falster DS, Moles AT, Vesk PA, Wright IJ (2002) Plant ecological strategies: some leading dimensions of variation between species. Annual review of ecology and systematics, 125–159. Wilson EO (1989) Threats to Biodiversity. Scientific American, 108–116. Wilson EO (1992) The Diversity of Life. Harvard University Press, Cambridge, USA. Wilson, EO, Peter, FM (Eds.) (1988) Biodiversity. Papers from the National Forum on BioDiversity, held September 21-25, 1986, in Washington. National Academy Press. Wirth C, Lichstein JW (2009) The Imprint of Species Turnover on Old-Growth Forest Carbon BalancesInsights From a Trait-Based Model of Forest Dynamics. In: Old-Growth Forests. Function, Fate and Value (eds Wirth C, Gleixner G, Heimann M), pp 81–113. Springer. Wright IJ, Reich PB, Westoby M et al. (2004) The worldwide leaf economics spectrum. Nature, 428, 821–827. Wright SJ, Kitajima K, Kraft NJ et al. (2010) Functional traits and the growth-mortality trade-off in tropical trees. Ecology, 91, 3664–3674. Wunder J, Brzeziecki B, Żybura H, Reineking B, Bigler C, Bugmann HK (2008) Growth–mortality relationships as indicators of life-history strategies: a comparison of nine tree species in unmanaged European forests. Oikos, 117, 815–828. Zhang Y, Chen HY, Reich PB (2012) Forest productivity increases with evenness, species richness and trait variation: a global meta-analysis. Journal of Ecology, 100, 742–749.

47

Paper 1 Title:

Many ways to die—partitioning tree mortality dynamics in a near-natural mixed deciduous forest

Journal: Journal of Ecology Authors: Holzwarth F, Kahl A, Bauhus J, Wirth C

48

Journal of Ecology

doi: 10.1111/1365-2745.12015

Many ways to die – partitioning tree mortality dynamics in a near-natural mixed deciduous forest Frederic Holzwarth1*, Anja Kahl1, Jürgen Bauhus2 and Christian Wirth1 1

AG Spezielle Botanik und Funktionelle Biodiversität Institut für Biologie Universität Leipzig, Johannisallee 21, 04103, Leipzig, Germany; and 2Waldbau-Institut Albert-Ludwigs Universität, Tennenbacherstr. 4, 79085, Freiburg im Breisgau, Germany

Summary 1. Partitioning of tree mortality into different modes of death allows the tracing and mechanistic modelling of individual key processes of forest dynamics each varying depending on site, species and individual risk factors. This, in turn, may improve long-term predictions of the development of old-growth forests. 2. Six different individual tree mortality modes (uprooted and snapped (both with or without rot as a predisposing factor), standing dead and crushed by other trees) were analysed, and statistical models were derived for three tree species (European beech Fagus sylvatica, hornbeam Carpinus betulus and common ash Fraxinus excelsior) based on a repeated inventory of more than 13 000 trees in a 28 ha near-natural deciduous forest in Central Germany. 3. The frequently described U-shaped curve of size-dependent mortality was observed in beech and hornbeam (but not ash) and could be explained by the joint operation of processes related to the six distinct mortality modes. The results for beech, the most abundant species, suggest that each mortality mode is prevalent in different life-history stages: small trees died mostly standing or being crushed, medium-sized trees had the highest chance of survival, and very large trees experienced increased rates of mortality, mainly by uprooting or snapping. Reduced growth as a predictor also played a role but only for standing dead, all other mortality modes showed no relationship to tree growth. 4. Synthesis. Tree mortality can be partitioned into distinct processes, and species tend to differ in their susceptibility to one or more of them. This forms a fundamental basis for the understanding of forest dynamics in natural forests, and any mechanistic modelling of mortality in vegetation models could be improved by correctly addressing and formulating the various mortality processes. Key-words: beech, demographic trait, growth estimation, growth-related mortality, longevity, mortality mode, mortality model, plant population and community dynamics, size-related mortality

Introduction Tree mortality is one of the key processes in forest dynamics (Franklin, Shugart & Harmon 1987; Runkle 2000; Chao et al. 2009). In unmanaged forests, it influences successional pathways and the composition of forest communities (Shugart 1987), creates gaps, the precondition for regeneration (Franklin, Shugart & Harmon 1987; Canham, Papaik & Latty 2001) and is an important driver of carbon cycling. This is because tree longevity determines the residence time of carbon and as a result the size of the carbon pool in forest biomass (Wirth & Lichstein 2009). Understanding and pre-

*Correspondence author. E-mail: [email protected]

dicting tree mortality are therefore indispensable for modelling the dynamics, diversity and biogeochemistry of forest ecosystems (Purves & Pacala 2008). However, in contrast to tree growth, it is less well understood. There are a multitude of processes operating simultaneously that cause tree death, a fact that is reflected by the diversity of formulations in forest dynamic models (Hawkes 2000; Keane et al. 2001; Porté & Bartelink 2002; Hickler et al. 2012). The question of when and why trees eventually die is largely unsolved. Tree mortality appears to be context dependent and species specific, it is highly stochastic and one of the greatest challenges of forest ecology (Watkinson 1992; Hurst et al. 2011). Processes leading to a tree’s death comprise of lethal damage through disturbances or infestations and gradual decline in vigour by accumulated stress (Franklin, Shugart & Harmon 1987).

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society

49

2 F. Holzwarth et al. Understanding and quantifying these various processes are important to attribute correctly causes of tree mortality and are expected to improve vegetation models significantly (Keane et al. 2001). Old-tree mortality is usually modelled simplistically in forest dynamic models, its rate being derived from reported maximum ages without any mechanistic considerations (Hawkes 2000; Keane et al. 2001; Porté & Bartelink 2002; Lutz & Halpern 2006). A comprehensive mechanistic understanding of individual tree mortality needs to first disentangle and categorize the different causes or modes of mortality (Larson & Franklin 2010). Among exogenous causes are wind-throw (Canham, Papaik & Latty 2001), crushing by other trees (Larson & Franklin 2010), fire (Franklin, Shugart & Harmon 1987) and biotic attacks on trees (Cherubini et al. 2002). Many studies address stress due to competition or water deficiency, which reduces tree vitality and thus results in a critical lack of resources (Peet & Christensen 1987; Wunder et al. 2007; Allen et al. 2010). It is debated whether trees lose vitality with age (Franklin, Shugart & Harmon 1987; Watkinson 1992; Lanner 2002; reviews: Petit & Hampe 2006; Kutsch et al. 2009). Whilst the concept of senescence (understood as an endogenously controlled process, sensu Watkinson 1992) does not apply to the longest-living tree species (Pinus longaeva D. K. Bailey, Lanner & Connor 2001), it is not clear whether, and to what degree, it applies to other shorter-lived tree species (Schweingruber & Wirth 2009). Researchers generally agree that the age of a tree is not a good predictor of mortality, because the meristem remains young (Franklin, Shugart & Harmon 1987; Mencuccini et al. 2005) and deleterious mutation rates are very low in trees (Peñuelas 2005; Petit & Hampe 2006). Instead, with increasing tree size, transport problems through the increasing complexity of the vascular transport system may arise (hydraulic limitation hypothesis) (Ryan, Phillips & Bond 2006), and the risk of wind-related damages rapidly increases as does the chance of infection by destabilizing or potentially lethal pathogens through the breakage of large, long branches and hence the accumulation of wounds (Franklin, Shugart & Harmon 1987; Canham, Papaik & Latty 2001; Dhôte 2005; Schulze et al. 2009; Larson & Franklin 2010). Recent studies that have modelled the general patterns of mortality for different temperate tree species in different regions and sites confirmed the general assumptions that survival rates are higher with increased growth, reduced competition and increased size (e.g. Fridman & Ståhl 2001; Bigler & Bugmann 2003; Wunder et al. 2007; Das et al. 2008; Lines, Coomes & Purves 2010). However, survival rates have been shown to decline again in very large trees (Monserud & Sterba 1999; Yao, Titus & MacDonald 2001; Lines, Coomes & Purves 2010), which hints at different underlying mortality causes for larger trees when compared with smaller trees. To explicitly model the process of old-tree mortality, very large inventories are needed that include larger trees and also a sufficient number of mortality events in this size class. Moreover, it is necessary to record the circumstances of death for each tree, even though determining the cause might entail a

50

great degree of uncertainty (Fridman & Ståhl 2001; de Toledo et al. 2012). Because of this, as an observable surrogate the mode of mortality, which can ‘indicate the most probable agent of mortality’ (de Toledo et al. 2012), is frequently used to get a hold on the different mortality processes (Chao et al. 2009; Larson & Franklin 2010). In contrast, a precise attribution of a proximate cause needs thorough observations and short inventory periods, which are rarely achieved (Lutz & Halpern 2006; van Mantgem & Stephenson 2007). In this study, we analysed a large data set of deciduous trees (90% beech) in a near-natural stand, covering a large range of sizes and including several very large trees with a diameter at breast height (d.b.h.) of up to 126 cm. Mortality modes were assessed, and we used this information to (i) model different modes of tree mortality embracing the whole life history of trees from sapling to gapmaker, (ii) provide a mechanistic interpretation helping to improve mortality algorithms in forest succession models and (iii) compare species survival rates across gradients of tree size to infer aspects of life-history strategies. Moreover, we present a solution for dealing with different measurement methods for live and dead trees, and with negative growth measurements, which present a notorious problem in all inventory-based studies. Unlike other studies that either kept (Yao, Titus & MacDonald 2001) or even omitted negative values from the data set (Wunder et al. 2007, 2008), we estimated and included measurement errors in the model framework. The objective of this study was to partition mortality patterns of three deciduous tree species into different proximate (observable) processes and to assess the implications of this on mechanistic modelling efforts. We thus addressed the following questions: (i) How do individual tree characteristics explain the mortality of the different modes? (ii) how and to what degree can overall mortality be partitioned into by the different mortality modes? (iii) how do the mortality rates of the different species compare to each other and what specific demographic traits can be inferred from the patterns? and (iv) can we derive estimates of longevity or any other practical measure from survival scenarios based on mortality models that could be useful for mechanistic models of forest dynamics?

Materials and methods STUDY SITE AND INVENTORY DATA

The study was conducted in a 28.5 ha plot of mature deciduous forest (‘Weberstedter Holz’; trees aged 1–> 250 years), located in the Hainich National Park (51°06′ N, 10°31′ E), Thuringia, Germany. The National Park is part of Germany’s largest continuous deciduous forest (Hainich) and is listed as a UNESCO World Heritage site. The climate is suboceanic/subcontinental, long-term annual means are as follows: 7.5–8 °C air temperature and 750–800 mm precipitation (Knohl et al. 2003). Altitude is approximately 350 m a.s.l. with a gentle north facing slope (inclination 2–3°). The soil type at the study plot is a Luvisol developed from loess over limestone. The stand was managed as coppice-with-standards until about 1900, after which it was gradually transformed into a beech selection forest. Harvesting

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

Partitioning tree mortality 3 was reduced again in 1965, when it became part of a military training ground and ceased completely in 1997, when it was included in the core zone of the National Park (Mund 2004; Butler-Manning 2007). The main tree species in the plot were beech (Fagus sylvatica L.), ash (Fraxinus excelsior L.), hornbeam (Carpinus betulus L.), sycamore (Acer pseudoplatanus L.) and wych elm (Ulmus glabra Huds.) (Table 1). All trees on the plot with a diameter at breast height (d.b.h.)  1 cm were recorded in the summer of 1999. The tree parameters measured were as follows: coordinates of the trunk base, species, d.b.h. and status (live or dead) (Table 1). Trees were resampled in the summer 2007. Later inspection of the inventory data revealed that 27 trees were missing without any idea of their status. We assumed them to be missing at random with respect to mortality. Dead trees were defined as being physiologically dead or likely to die within a few months because of being uprooted completely or because the crown had been completely destroyed (Table S2-1,S2-2 in Supporting Information). Mortality modes were recorded (Table S1), as either: standing dead and fallen dead further distinguished into: uprooted, snapped and crushed by other trees. Where for uprooting and snapping, wood or root rot as predisposing factor (Larson & Franklin 2010) was also recorded, when the wood at the breaking point was degraded and the break was not in splinters but rather an even brittle fracture and also fruiting bodies [typically tinder fungus, Fomes fomentarius (L.) Kickx, red banded polypore, Fomitopsis pinicola (Sw.) P. Karst.] were present. The differentiation and respective identification followed Kahl (2008). Trees that disappeared were identified as dead but with an unknown mode of mortality. Clear evidence of insect attacks could not be obtained, and therefore, the importance of insects as a proximate cause of mortality remains unknown. Also, for a random subsample of dead trees (n = 620, 37% of all dead trees), wood cores (sample dimensions ca. 4 9 5–25 mm) were taken during the inventory of 2007 with an increment puncher (Table S3). To estimate the longevity of beech and the relationship between d.b.h. and tree age, we used 90 stem discs (d.b.h.: 0.6–107 cm, age: 5–285 years; D. Hessenmöller and E.-D. Schulze, unpubl. data; Mund 2004; contributing 45 stem discs each). These trees came from stands in the vicinity of the plot that were managed as selection forests or not managed at all.

MORTALITY MODEL

We modelled annual mortality probabilities (pannual) for each mortality mode (i), except unknown mortality, using logistic regression (eqn 1):

pannuali ¼ logitðXi bi Þ

eqn 1

where X is the design matrix of the linear predictors and b the respective parameter vector. The annual probability was scaled to the inventory interval of 8 years (eqn 2). pi ¼ 1  ð1  pannuali Þ8

eqn 2

The scaled probability (p) was used as predictor for the observations (eqn 3). deadi  Binomial ðpi Þ

eqn 3

The different mortality modes are mutually exclusive, and hence, the modelled respective probabilities should add up to a total mortality probability. Accordingly, we also modelled total mortality with the summed probabilities (eqn 4) Xn eqn 4 dead total  Binomialð i¼1 pi Þ where i = 1…n indicates the different mortality modes. This ensures coherence and acts as a surrogate to a multinomial distribution, which we could not use because of missing values contained in the data (known mortality but unknown mode). We fitted the logistic regression models combined in one model frame and independently for each of the three most abundant species. As explanatory variables, we used d.b.h. as proxy for tree size. As a proxy for tree growth, we estimated diameter increment (dincest, see below) and relative diameter increment (reldincest). Also, log-transformations (with varying additive constants to allow for different curvatures) of the variables and interactions between the explanatory variables were tested. We did not use basal area increment or relative basal area increment (such as Wunder et al. 2008), because the first would be strongly correlated to d.b.h. and the latter to reldincest, both for purely mathematical reasons. Only one growth variable (either dinc or reldinc) was used in the models. If the relationship between mortality and d.b.h. indicated a U-shape, we split eqn 1 into two models (labelled ‘early’ if decreasing with d.b.h. and ‘late’ if increasing with size) and added the resulting probabilities. To plot mortality estimates against d.b.h., where growth was also a predictor, we applied a simple model to estimate dincest with d.b.h. (see eqn S12 in Appendix S1). We estimated total mortality by combining all the models representing the separate modes. We used plots of observed mortality versus the predictors to set up candidate models and then the Deviance Information Criterion (DIC) as selection criterion. We simultaneously modelled the uncertainty of the measurements (d.b.h. and dincobs), imputed the missing values and estimated dincest with a sub model (eqns 5 and 6, see below). As goodness of fit, we calculated the area under the curve of the receiver operating characteristic

Table 1. Inventory data of the plot (total area 28.5 ha) in 1999, in 2007 and of trees that died in this period: number of stems, basal area per hectare (BA). Respective percentages in parentheses 1999 Species

Trees

Ash Beech Wych Elm Hornbeam Sycamore Other Total

564 13297 70 391 322 82 14726

2007

(4) (90) (0) (3) (2) (1) (100)

BA (m2 ha1)

Trees

6.1 24.3 0.6 1.6 2.6 0.6 35.9

528 12197 39 361 345 82 13552

(17) (68) (2) (5) (7) (2) (100)

Dead

(4) (90) (0) (3) (3) (1) (100)

BA (m2 ha1)

Trees

6.6 25.5 0.3 1.6 2.7 0.6 37.2

39 1535 35 30 14 10 1663

(18) (69) (1) (4) (7) (2) (100)

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

BA (m2 ha1) (2) (92) (2) (2) (1) (1) (100)

0.26 1.02 0.33 0.10 0.08 0.06 1.85

(14)) (55) (18) (5) (4) (3) (100)

51

4 F. Holzwarth et al. (AUC). Values of 0.6–0.7 are commonly regarded as average, between 0.7 and 0.8 as good and above 0.8 as excellent (Hurst et al. 2011). To assess the influence of modelling different mortality modes on the estimate of total mortality, we contrasted our approach with a simple ‘no-modes’ model that allowed for a similar curvature and used the same predictors (d.b.h. (transformed or untransformed) and growth).

ESTIMATION AND ERRORS OF TREE GROWTH

Tree growth measurements in this study came from two different sources: repeated d.b.h. measurements for live trees and sampling of dead trees with an increment puncher. Additionally, growth of nonsampled dead trees was imputed with auxiliary data. To make these values commensurable and to incorporate the respective uncertainties, we estimated growth (dincest) independently for each species with eqns 5 and 6: dincobs  Normalðdincest ; r2N Þ

eqn 5

dincest  Log-Normal ðdincpred ; r2pred Þ þ a

eqn 6

where dincobs is the observed diameter increment (dinc) in both live and dead trees, dincest is the estimated true dinc and the measurement error is rN, which could either be the measurement error of live or dead trees, or zero for trees with missing increment measurements. In eqn 6, the mean (dincpred) and variance (r2pred ) were derived from predictive models, which, together with the respective errors (rN), are further explained in Appendix S1. An additive constant (a) was introduced to set a threshold at half the minimum observed growth of wood cores from this study (0.05 mm a1). To assess the usefulness of this approach, we also tested a simplified mortality model for beech, here referred to as the ‘simple-growth model’. In this model, we used the original growth values (dincobs) without considering the measurement errors and missing values were imputed with an ordinary linear model (see Appendix S1).

LONGEVITY AND LIFETIME MORTALITY OF BEECH

To derive general estimates of beech longevity, we needed to relate mortality rates to tree age. To estimate tree age from the d.b.h. values for beech, we modelled the relationship between d.b.h. and age with eqn 7 using the free parameters a1–a4 (data points, fitted curve, parameter estimates and additional information in Fig. S1) d:b:h:  a1 þa2 logð1 þ a3 agea4 Þ

eqn 7

Equation 7 was chosen to find a form that fitted the data well and that could also be extrapolated to ages greater than those observed with reasonable estimates. We used the estimates (including the uncertainties) of d.b.h. and the simultaneously available annual growth estimations (dinc) per age as input for the mortality model of beech. We then ran survival scenarios (as cumulative products of the annual survival rates) with different combinations of mortality modes and thus derived estimations of tree longevity under various circumstances, starting with trees with a d.b.h. of 0 (height = 1.30 m). We contrasted our results for beech with mortality processes in the model of Wirth & Lichstein (2009), referred to as ‘W&L’, as well as with whole-patch mortality in the vegetation model LPJ–GUESS (Smith, Prentice & Sykes 2001; Hickler et al. 2012). In W&L, self-thinning is related to biomass production and whole-patch mortality to longevity and remains constant over the lifetime, whilst whole-patch mortal-

52

ity in LPJ–GUESS is also derived from longevity but increases with age. For the first approach, we modelled a height to age relationship using data from Mund (2004). However, to make it comparable with our study, we allowed mortality to start at an age of 15 years, at which age we assume that saplings have reached a height of 1.30 m. Longevity is defined in both approaches as the age at which 1% of the initial population survived and we followed this definition here. In both approaches, we fixed longevity at 300 years (Felbermeier & Mosandl 2002; this study). We used WinBUGS (Gilks, Thomas & Spiegelhalter 1994), the R-Program (R Development Core Team 2011) and the R packages ‘R2WinBUGS’ (Sturtz, Ligges & Gelman 2005) and ‘ROCR’ (Sing et al. 2009) for Bayesian and conventional analysis. Simulations in WinBUGS were run with two chains until convergence, which we assumed when the Gelman–Rubin statistic was below 1.1 for all estimated nodes. To speed up convergence and reduce correlations of parameter estimates, variables used as predictors in the Bayesian analysis were rescaled to a mean of 0 and a variance of 1, where possible. For all stochastic nodes, we used uninformative (flat) priors if not stated otherwise. When additive constants for a log-transformation needed to be estimated, they were set to a fixed value in the final model, so as not to add to the uncertainty of the parameter estimates.

Results In the period of 8 years between the two inventories, at least 1663 trees died, with 27 trees of unknown status (Table 1). This translates into an annualized mortality rate of 1.5% in absolute numbers and 0.66% of the basal area. The majority of trees died standing (61% of all trees), they were generally small but also included larger trees up to a d.b.h. of 90 cm. Uprooting and snapping, with and without rot, affected only few and mainly large and very large trees. Crushing was a common cause of mortality for smaller trees (165 trees), but also a few large trees were crushed. Unknown mortality, that is, trees that had disappeared, was most common in smaller trees. In terms of the basal area, standing dead accounted for 36% of the dead trees basal area, uprooting with rot and without rot for 8% and 23%, respectively, snapping with rot and without rot for 17% and 7%, respectively (Table S2-1 and Fig. S2). With respect to growth, trees that died standing grew somewhat slower than trees that survived and no obvious difference was found between crushed and surviving trees. Growth of trees that were uprooted or snapped, irrespective of predisposing rot, was generally higher than that of surviving trees, which was mainly a size effect. The different distributions of the predictors (Fig. S2) corroborate the usage of separate models for each mortality mode. MODELLING OF MORTALITY

According to the lowest DIC (summed up for all mortality submodels) and parameter significance, we chose the models in Table 2 for further consideration and reported the respective parameter estimates and model fits (AUC). Details of all candidate models are reported in Table S4.

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

Partitioning tree mortality 5 Table 2. AUC, deviance information criterion (DIC) and mean parameter estimates (standard error, SE) from posterior distributions for best mortality models and, as a contrast, for ‘no-modes’ models. Parameter estimates refer to predictors on the original scale (no normalization); int. = intercept; additive constants c1 to c5 were assigned constant values: 1, 8, 16, 20 and 40 (cm), respectively Model Early Late

AUC

DIC

Explanatory variables

Parameter estimates: median (95% CI)

0.72

8581.8

int., log(d.b.h. + c2), dincest int., d.b.h.

1.8 (1.2, 2.5) 2.1 (2.4, 1.9) 1.4 (2.4, 0.45) 8.9 (10.0, 7.8) 0.052 (0.035, 0.072)

int., int., int., int., int., int., int., – –

Beech ‘no-modes’

Total

Beech

Standing Early Late Uprooted Uprooted and rot Snapped Snapped and rot Crushed Unknown Total

0.72

6227.1

0.89 0.68 0.81 0.75 0.69 – 0.73

450.0 161.0 168.0 208.7 1665.9 1097.3 8576.0

Ash

Total

0.71

241.2

int., log(d.b.h.)

1.3 (0.20, 2.8) 1.6 (2.0, 1.2)

Ash

Standing Uprooted Uprooted and rot Snapped Snapped and rot Crushed Unknown Total

0.84 – – – – – – 0.71

92.7 58.8 77.2 39.3 49.5 16.3 6.7 236.9

int., log(d.b.h.) int. int. int. int. int. – –

3.1 (1.7, 4.5) 2.4 (3.0, 2.0) 6.8 (7.7, 6.1)  6.5 (7.3, 5.8) 7.3 (8.7, 6.4) 7.0 (8.2, 6.2) 8.6 (11, 7.1) – –

Hornbeam

Total

0.66

208.4

int., d.b.h.

0.083 (3.3, 2.9) 1.2 (1.9, 0.37)

Hornbeam

Standing Uprooted Uprooted and rot Snapped Snapped and rot Crushed Unknown Total

0.82 0.77 – – – – – 0.68

119.6 52.4 15.5 15.5 37.0 37.2 4.3 205.7

int., d.b.h. int., log(d.b.h.) int. int. int. int. – –

4.0 (0.71, 7.0) 2.4 (3.3, 1.5) 11 (16, 6.7) 0.10 (0.0081, 0.21) 8.3 (11, 6.8) 8.3 (11, 6.7) 7.1 (8.5, 6.1) 7.0 (8.8, 6.1) –

log(d.b.h. log(d.b.h. log(d.b.h. d.b.h. d.b.h. d.b.h. log(d.b.h.

BEECH

For all mortality modes, d.b.h. proved to be a valid predictor, whilst standing dead trees were also affected by growth rates. For uprooting and snapping, we predicted a strong increase in susceptibility with tree size, whilst uprooting remained constantly important and snapping with rot became the most important mode at d.b.h. > 80 cm (Fig. 1, Table 2). The risk of being crushed by other trees decreased considerably with increasing size. Standing dead was estimated to be the most prevalent mode in small trees and to rapidly decrease with size but also to increase again for very large trees (Fig. 1). Standing dead trees showed, as the only mode, a relationship with reduced growth (Fig. 2). Absolute growth (dincest) proved to be a slightly better predictor than relative growth (reldincest). No significant interaction between size and growth was found (Fig. 2, Table S4). The contrasting ‘simple-growth’ model, which did not estimate dincest but used the unaltered values and did not account for measurement errors, had an equally good fit (Table S4). The effect size for dincobs, however, was slightly smaller and less certain than for dincest (parameter means: 1.8 versus 1.4, Table S4).

+ c3), dincest + c5) + c4)

+ c1 )

5.9 (5.1, 6.7) 3.2 (3.5, 2.9) 1.8 (2.7, 1.0) 42 (57, 21) 7.3 (2.9, 11) 17 (20, 14) 2.4 (1.7, 3.1) 9.9 (11, 9.0) 0.029 (0.0044, 0.051) 10 (11, 9.2) 0.039 (0.018, 0.059) 11 (12, 10) 0.062 (0.047, 0.079) 3.7 (4.1, 3.2) 1.2 (1.4, 1.0) – –

Total mortality assumed the form of the well-known U-shaped curve (Fig. 1): very small trees had a high risk of mortality, which would also be increased by lesser growth (Fig. 2). Trees of intermediate size (d.b.h. 30–50 cm) had the least risk of dying, whilst very large trees with a d.b.h. > 60 cm had an increased mortality risk, with all mortality modes except crushing being relevant here. The simple ‘no-modes’ model, that lumped together all mortality modes and allowed for a flexible curvature, rendered a similar curve, with a slightly worse model fit (AUC 0.72 versus 0.73, Table 2). However, it had a higher prediction uncertainty across the whole range of d.b.h., especially for very large trees (Fig. S3), and a weaker and less certain parameter estimate for growth (Table 2). OTHER SPECIES

The small sample size of ash and hornbeam restricted model complexity. Only d.b.h. was found to be a significant predictor of standing and total mortality (Table 2 and Fig. 3). Growth did not show any sign of having an effect on the mortality risk (Table 2). For hornbeam, a significant influence

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

53

0.2 0.1 0.05

Dincest (cm a–1)

í6 í7 0.04

20

0.5

0.01

0.1

50

100

Fig. 2. Modelled annual standing dead probabilities [iso-lines, (%)] overlaying modelled annual growth (dincest) (cm a1) over d.b.h. (cm), both axes on log-scale. Symbols mark individual trees with black open triangles: dead (standing mortality) and grey dots: live or other mortality modes. Light grey dashed line: simple fit of dincest over d.b.h. (eqn S12).

0.02

0.03

10

d.b.h (cm)

0.00

0.01

Probability

0.1

0.5

5

1

1.5

3

2

2.5

1

3.5

Total Standing Uprooted Uprooted/rot Snapped Snapped/rot Crushed

4

0.05 í10

0.02

í9

í8

Logit

í5

0.5

í4

05 0.

í3

6 F. Holzwarth et al.

100 –1

80

LONGEVITY AND LIFETIME MORTALITY OF BEECH

The age to d.b.h. relationship and the respective model are displayed in Fig. S1. The extrapolation appears reasonable and was thus considered usable for further analysis. Although, because we did not have additional data of comparable stands to support the extrapolation beyond the maximum observed age of 285 years, any inference should be treated with caution. Depending on the mortality mode, different survival curves (Fig. 4) and thus different estimates of longevity were obtained from the survival scenarios. The early occurring tree deaths (crushing and early part of standing dead) would not suffice to kill a population (no estimated longevity). The later occurring mortality (uprooting, snapping and the later part of

54

–2

Logit

–5 –6 0.10

Ash Beech

Probability

0.08

Hornbeam

0.02

of d.b.h. on uprooting was found. The standing mortality rates of ash and hornbeam were estimated to be relatively high, even at the intermediate d.b.h. range (30–50 cm). Only above this range, they were as low as or lower than beech. Other than that, uprooting and snapping only played minor roles and crushing was nearly irrelevant (Table 2). The picture changed slightly for total mortality rates. Here, ash maintained low mortality rates at larger d.b.h. ranges (> 60 cm), whilst for beech and hornbeam, a significant rise with increasing d.b.h. was found.

0.00

Fig. 1. Modelled annual mortality logits and probabilities over d.b.h. (cm) for beech. Thick lines: median estimates, thin lines and shaded area: 95% credible interval. For standing and total mortality, a modelled growth for the respective d.b.h. was assumed (dincest ~ d.b.h., cf. eqn S12).

–3

60

d.b.h. (cm)

–4

40

0.06

20

0.04

0

0

20

40

60

80

100

d.b.h. (cm) Fig. 3. Modelled annual total mortality logits and probabilities over d.b.h. (cm) for three species. For beech, a modelled growth for the respective d.b.h. was assumed (cf. eqn S12). Thick lines: median estimates, thin lines and shaded area: 95% credible interval.

standing dead) resulted in an estimated longevity of 405 (95% CI: 337–500) years. For total mortality, a longevity of 379 (319–464) years was estimated. Longevities derived from the modelling approaches were much lower (Fig. 4).

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

0.04

0.16

0.36

0.64

Late Early Total W&L whole-patch W&L self-thinning W&L total LPJíGUESS whole-patch

0

Surviving proportion

1

Partitioning tree mortality 7

0

100

200

300

400

500

Age Fig. 4. Survival proportions with different scenarios for beech. Assumed 100% at a height of 1.30 m, which is equivalent to a d.b.h. of 0 cm. The scenarios referring to results from this study are as follows: late (uprooting, snapping and the later part of standing dead), early (crushing and early part of standing dead) and total. Proportion of the population surviving at a given age when applying different or all mortality modes (scenarios) and for three approaches: data-driven models of this study and two mechanistic models (see text). Thick lines: median estimates, thin lines and shaded area: 95% credible interval. The y-axis is root transformed. The 1% level, which serves as a threshold to define longevity, is marked with a horizontal line. Bold ticks at the bottom mark median estimates of longevity, thin lines the respective 95% credible interval.

However, this is rather trivial because of the predefined input parameter (longevity = 300 years). With regard to the form of the survival curves, applying the self-thinning mortality of Wirth & Lichstein (2009) lead to a similar curve as the early mortality in our model. Whole-patch mortality as compared to late mortality of our model showed a quicker and stronger onset, whilst it was weaker in later stages. LPJ–GUESS whole-patch mortality closely mimicked the modelled curvature of late mortality (Fig. 4).

Discussion In our study, we were able to disentangle the frequently described U-form of the size (and also age) dependency of mortality, often just taken for granted (Rüger et al. 2011), as the joint product of different mechanisms related to six distinct mortality modes. As our results for beech indicated, the modes occurred at different life-history stages of the trees. Standing mortality and crushing were important mainly in young and small trees, whereas uprooting and snapping, and to some degree also standing mortality, occurred in late and very late stages. We have demonstrated clearly that mechanistic modelling of mortality across all life stages of a tree very much relies on knowledge of the mode of each mortality event, to which the proximate cause is closely linked (van Mantgem & Stephenson 2007; Larson & Franklin 2010), and that the assumption of constant mortality rates, which is often applied in forest dynamic models (Keane et al. 2001), is too simplistic. Nonetheless, the absolute rates of mortality and the relative importance of the modes are highly species and site

specific and may also be shifted by singular events (such as the heat wave in 2003). We found that tree size (diameter at breast height, d.b.h.) explained a large part of the mortality patterns observed. Growth was a significant predictor of standing dead in beech trees, which suggests that mortality in these trees was caused, inter alia, by stress, be it induced by competition or pathogens, which are hard to disentangle because of the strong interdependence (van Mantgem & Stephenson 2007; Larson & Franklin 2010). We assume that growth was also important for the other species, but the data were too sparse and the uncertainty of the growth estimates too large, to detect an effect. Lowest growth rates were observed in small and presumably shaded trees that may struggle to maintain a positive carbon balance. This contributes to the high mortality observed in small trees. Major sources of uncertainty relating to the influence of growth on mortality were the measuring methods and the estimation of a large proportion of data, as explained in the Materials and Methods section, and the averaging of growth over 8 years. This period might be too long and dilute any signal of stress as it may take < 8 years for a tree to die from stress (Bigler & Bugmann 2003). The effect size of growth on standing mortality was to some extent larger and also less uncertain when compared to the ‘simplegrowth’ model, which is less informative because of not accounting for the different methods of measurement and for errors. However, we admit a more refined and less uncertain information on growth could be hoped for. PARTITIONING TOTAL MORTALITY

In the case of beech and hornbeam, the total mortality rate assumed a U-shaped curve against d.b.h. and we could trace back this emergent pattern to six distinct and presumably differently caused mortality modes. This shape was already found by Monserud & Sterba (1999, for Norway spruce) and others (Yao, Titus & MacDonald 2001; Smith, Rizzo & North 2005; Temesgen & Mitchell 2005; Lines, Coomes & Purves 2010; Hurst et al. 2011) and hypothesized by Franklin, Shugart & Harmon (1987). However, these studies could not relate the shape of the curve to different mortality causes or modes, and in some species, mortality rates may level off with increasing size (Petit & Hampe 2006). The use of mortality causes or modes in detailed and mechanistic approaches has been extensively discussed (e.g. Franklin, Shugart & Harmon 1987; Fridman & Ståhl 2001) and more recently been applied (e.g. van Mantgem & Stephenson 2007; Chao et al. 2009; Larson & Franklin 2010). However, there is an apparent lack of ascribing the lifetime mortality regime (the U-shape) to various underlying processes, which we attempted with this study. Although the mortality modes used here are rather descriptive, they certainly point to different proximate causes (Larson & Franklin 2010). Total mortality dynamics could be modelled with the ‘nomodes’ model without strongly reducing the model fit, this being just a matter of curve fitting. However, we got less certain parameter estimates, mainly for the influence of growth,

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

55

8 F. Holzwarth et al. which was relevant only for one mortality mode in the full model. We also acknowledge potential errors in the attribution of the mortality modes. Of all variables, this is arguably the most subjective and relies on the experience and diligence of the surveyors. In this study, we could not quantify or incorporate the degree of uncertainty of this parameter but recommend that it be considered during the inventory and analysis of future studies and that census intervals be as short as possible to better identify modes or proximate causes of death. Possible underlying processes of the modes could be an interrelated network of competition, lethal and nonlethal pathogens for standing dead, mainly wind for uprooting and snapping without signs of rot, lethal pathogens (rot fungi) in combination with wind, for uprooting and snapping with rot, whilst the incidence of lethal pathogens can be preceded by competition and other pathogenic stress. Crushing by other trees can be seen as mode and proximate cause at the same time. HOW DO SPECIES COMPARE

Considering tree size as a proxy for tree age, we compare total and standing mortality rates across the life history of the three modelled species. Total mortality rates were similar at the lower d.b.h. ranges for ash and hornbeam and higher than that of beech. This pattern changed in large and very large trees: mortality rates increased in beech and hornbeam, whilst it remained low with no apparent increase in ash. We expect that, at some point, the mortality rates for ash would increase with size, as their susceptibility to pathogens and wind-throw naturally increases. However, with the available data, we could not identify an increase and conclude that it is small in the observed range of d.b.h. and only is significant at larger d.b.h.. Susceptibility to wind-throw depends a great deal on tree size (height, crown exposed area), tree species, site characteristics (rooting depth, exposition) and canopy roughness (Canham, Papaik & Latty 2001; Dhôte 2005; Albrecht et al. 2012). In the stand, beech and ash were the tallest trees with maximum heights of 40 m and above and hornbeam the shortest, reaching around 33 m (ButlerManning 2007). In winter, beech has a denser crown compared to ash (they have larger leaves; Corner’s rule). Its wood is less flexible, and its rooting patterns may be shallower than ash (Felbermeier & Mosandl 2002; Roloff & Pietzarka 1997). Yet, these facts do not wholly explain that only beech and hornbeam had increasing mortality rates with increasing size. Of all the tree species, mortality with predisposing rot was only relevant in beech. Fuentes Perivancich (2010) found that fungal fruiting bodies were more common in larger beech trees (d.b.h. > 40 cm) and of infected trees about three quarters died in a period of 10 years. Although fungal pathogens, which are potentially lethal for all the three species, were present in the stand, beech suffered the most. Tinder fungus (F. fomentarius), an important mortality agent, commonly prefers beech over the other species as a host (Kreisel, Dörfelt & Benkert 1980). The sheer density of beech and thus tinder fungi may help facilitate infections, whilst the

56

lower densities of other species might impair infection of host-specific pathogens. At smaller d.b.h., ash and hornbeam exhibited substantially higher mortality rates than beech (Fig. 3). This suggests that these species have a problem establishing in the stand. Beech is known to cast a lot of shade and to be very shade tolerant. Of the other species, ash is the least tolerant and hornbeam is intermediately tolerant (Niinemets & Valladares 2006). Comparing the aforementioned species with beech, Collet et al. (2008) observed reduced growth and Petritan, von Lüpke & Petritan (2007) higher mortality rates of saplings at low-light conditions. If, as we assume, the observed species differences are not just ephemeral phenomena and the differing mortality rates reflect fundamental demographic traits of these species, the differences in life-history mortality rates may help to explain abundance patterns. The actual species composition is a combined result of the historical coppice-with-standards management, which fostered the nonbeech species, a gradual change into a beech selection forest and natural regeneration. Whilst the lower mortality rates in small and young beech trees may have led to a general dominance of beech, the low mortality rates of larger ash trees, due to less susceptibility to lethal pathogens and wind damage, may have allowed these species to coexist and develop large and fecund old trees. Hornbeam, with its high mortality rate as a small tree and also higher mortality rate than the other species as a large tree, appears to be decreasing in abundance. With the complete lack of saplings surviving to heights of 1.30 m in the study period, it appears to be a relic species in the stand without any potential to persist. Another important factor for the regeneration pattern is roe deer browsing, which selectively disadvantages the nonbeech species (Kenderes, Mihók & Standovár 2008; Boulanger et al. 2009; Guse 2009). ESTIMATES OF LONGEVITY

Longevity, as defined by many forest dynamic models (review: Bugmann 2001), of beech could be estimated from demographic processes alone in a survival scenario. This estimate, however, is uncertain, because of extrapolating the data to ages higher than observed and no strict relationship between age and d.b.h. (Trotsiuk, Hobi & Commarmot 2012; this study). It corresponds only roughly to previous estimates. Piovesan et al. (2003) reported on beech trees aged more than 500 years old on a high-elevation site and estimated the maximum life span for beech to be more than 700 years. However, longevity as a parameter required by models might be very different from sheer age records (such as a reported 900 years, Felbermeier & Mosandl 2002). Because data on this parameter are rare, it remains a relevant source of uncertainty in the models. In our study, the beech population suffers from mortality in two phases: up to the age of c. 50 years, crushing and standing dead are the prevailing modes of death, then, after a calm phase, starting from c. 150 years and speeding up with age, the other modes, including standing dead, quickly reduce the

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

Partitioning tree mortality 9 population. This pattern could be summarized in the sequence self-thinning, stability and decline, which Hurst et al. (2011) attribute to ‘asymmetric competition’ killing small trees and ‘exogenous disturbance’ killing large trees. This underlines the importance of having a good understanding of mortality in the late stages of tree life for modelling long-term forest dynamics. The common assumption of constant lifetime mortality rates for the random component of mortality applied by Wirth & Lichstein (2009, there called ‘whole-patch mortality’) and many other forest dynamic models (e.g. Pacala et al. 1996; reviews: Hawkes 2000; Keane et al. 2001; there called ‘intrinsic mortality’) leads to an exponential decrease in population size and misses the phase of relatively low mortality. A similar dynamic may be reached if growth dependent mortality not only acts on young trees but increases again in larger and old trees (e.g. Botkin, Janak & Wallis 1972). However, it is by no means clear that very large trees necessarily grow slower. There are many examples where annual diameter increment does not strongly decrease in large trees (e.g. Mountford et al. 1999; Jaworski & Paluch 2002; Piovesan et al. 2005; Mund et al. 2010; this study) and decreased growth might in fact be a subsequent effect of pathogens. In contrast, modelling of mortality rates that increase with age, as in LPJ–GUESS, is in accordance with the pattern that we found. Again, our study hints that mortality in large trees is by no means intrinsic but rather a complex of exogenous mortality events partly mechanical (uprooting and snapping without the influence of pathogens) and partly stress-related or biotic.

Conclusions Mortality dynamics, especially of large and old trees, are an important field of study. First, in the context of carbon sequestration because they contain a lot of biomass and continue to grow up to late ages (Wirth 2009) and also in the context of biodiversity research because large trees that die function as gapmakers for regeneration (McCarthy 2001; Hurst et al. 2011). Mechanistic and predictive models of forest dynamics have to account for the mechanisms of individual tree mortality and need the appropriate mechanical understanding, as well as empirical parameter estimates, preferably on a species level (Purves & Pacala 2008). We conclude that knowledge of the various mortality modes or proximate causes and their respective dynamics is an essential component for a better understanding of old-growth forest dynamics and mechanistic modelling approaches.

Acknowledgements We thank Jürgen Huss for establishing the large-scale inventory site ‘Weberstedter Holz’ in 1999 in the course of the European Nat-Man project and David Butler-Manning, Osama Mustafa, Susann Willnecker and Ulrich Zählsdorf for their help during the second inventory in 2007. We are grateful to Manfred Grossmann for the permission to work in the core area of the National Park and for substantial support during the 2007 inventory. Ernst-Detlef Schulze, Dominik Hessenmöller and Martina Mund for kindly provided valuable data. Nadja Rüger gave helpful comments on the statistical modelling and Peter Otto insight into fungal tree pathogens. We thank Sophia Ratcliffe for proofreading.

The work has been funded by the Max-Planck-Society and the DFG Priority Program 1374 ‘Infrastructure-Biodiversity-Exploratories’ (WI 2045/7-1). Fieldwork permits were issued by the responsible state environmental office of Thüringen (according to § 72 BbgNatSchG). C.W. acknowledges the MaxPlanck-Society for funding the second inventory. We thank four anonymous referees for highly useful comments and suggestions on the manuscript.

References Albrecht, A., Hanewinkel, M., Bauhus, J. & Kohnle, U. (2012) How does silviculture affect storm damage in forests of south-western Germany? Results from empirical modeling based on long-term observations. European Journal of Forest Research, 131, 229–247. Allen, C.D., Macalady, A.K., Chenchouni, H., Bachelet, D., McDowell, N., Vennetier, M. et al. (2010) A global overview of drought and heat-induced tree mortality reveals emerging climate change risks for forests. Forest Ecology and Management, 259, 660–684. Bigler, C. & Bugmann, H. (2003) Growth-dependent tree mortality models based on tree rings. Canadian Journal of Forest Research, 33, 210–221. Botkin, D.B., Janak, J.F. & Wallis, J.R. (1972) Some ecological consequences of a computer model of forest growth. Journal of Ecology, 60, 849–872. Boulanger, V., Baltzinger, C., Saïd, S., Ballon, P., Picard, J.-F. & Dupouey, J.-L. (2009) Ranking temperate woody species along a gradient of browsing by deer. Forest Ecology and Management, 258, 1397–1406. Bugmann, H. (2001) A review of forest gap models. Climatic Change, 51, 259–305. Butler-Manning, D. (2007) Stand structure, gap dynamics and regeneration of a semi-natural mixed beech forest on limestone in central Europe – a case study. PhD Thesis, Albert-Ludwigs-Universität, Freiburg im Breisgau, Germany. Canham, C.D., Papaik, M.J. & Latty, E.F. (2001) Interspecific variation in susceptibility to windthrow as a function of tree size and storm severity for northern temperate tree species. Canadian Journal of Forest Research, 31, 1–10. Chao, K.-J., Phillips, O.L., Monteagudo, A., Torres-Lezama, A. & Vásquez Martínez, R. (2009) How do trees die? Mode of death in northern Amazonia. Journal of Vegetation Science, 20, 260–268. Cherubini, P., Fontana, G., Rigling, D., Dobbertin, M., Brang, P. & Innes, J.L. (2002) Tree-life history prior to death: two fungal root pathogens affect treering growth differently. Journal of Ecology, 90, 839–850. Collet, C., Piboule, A., Leroy, O. & Frochot, H. (2008) Advance Fagus sylvatica and Acer pseudoplatanus seedlings dominate tree regeneration in a mixed broadleaved former coppice-with-standards forest. Forestry, 81, 135–150. Das, A.J., Battles, J.J., van Mantgem, P.J. & Stephenson, N.L. (2008) Spatial elements of mortality risk in old-growth forests. Ecology, 89, 1744–1756. Dhôte, J.-F. (2005) Implication of forest diversity in resistance to strong winds. Forest Diversity and Function. Temperate and Boreal Systems (eds M. Scherer-Lorenzen et al.), pp. 291–307. Springer, Berlin, Heidelberg, New York. Felbermeier, B., Mosandl, R. (2002) Fagus sylvatica. Enzyklopädie der Holzgewächse. Handbuch und Atlas der Dendrologie (eds A. Roloff et al.), pp. 1–20. Wiley-VCH, Weinheim. Franklin, J.F., Shugart, H.H. & Harmon, M.E. (1987) Tree death as an ecological process. BioScience, 37, 550–556. Fridman, J. & Ståhl, G. (2001) A three-step approach for modelling tree mortality in Swedish forests. Scandinavian Journal of Forest Research, 16, 455– 466. Fuentes Perivancich, M.I. (2010) Mortality dynamics in an old-growth stand of beech (Fagus sylvatica) in Southern Sweden. Master’s Thesis, Swedish University of Agricultural Sciences, Alnarp. Gilks, W.R., Thomas, A. & Spiegelhalter, D.J. (1994) A language and program for complex Bayesian modeling. Statistician, 43, 169–177. Guse, T. (2009) Regeneration und Etablierung von sechs mitteleuropäischen Laubbaumarten in einem “naturnahen” Kalkbuchenwald des Nationalparks Hainich/Thüringen. Master’s Thesis, Friedrich-Schiller-Universität, Jena. Hawkes, C. (2000) Woody plant mortality algorithms: description, problems and progress. Ecological Modelling, 126, 225–248. Hickler, T., Vohland, K., Feehan, J., Miller, P.A., Smith, B., Costa, L. et al. (2012) Projecting the future distribution of European potential natural vegetation zones with a generalized, tree species-based dynamic vegetation model. Global Ecology and Biogeography, 21, 50–63. Hurst, J.M., Allen, R.B., Coomes, D.A. & Duncan, R.P. (2011) Size-specific tree mortality varies with neighbourhood crowding and disturbance in a Montane Nothofagus forest. PLoS ONE, 6, e26670.

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

57

10 F. Holzwarth et al. Jaworski, A. & Paluch, J. (2002) Factors affecting the basal area increment of the primeval forests in the Babia Gora National Park, southern Poland. Forstwissenschaftliches Centralblatt, 121, 97–108. Kahl, T. (2008) Kohlenstofftransport aus dem Totholz in den Boden. PhD Thesis, Albert-Ludwigs-Universität, Freiburg im Breisgau, Germany. Keane, R., Austin, M., Field, C., Huth, A., Lexer, M., Peters, D. et al. (2001) Tree mortality in gap models: application to climate change. Climatic Change, 51, 509–540. Kenderes, K., Mihók, B. & Standovár, T. (2008) Thirty years of gap dynamics in a Central European beech forest reserve. Forestry, 81, 111–123. Knohl, A., Schulze, E.-D., Kolle, O. & Buchmann, N. (2003) Large carbon uptake by an unmanaged 250-year-old deciduous forest in Central Germany. Agricultural and Forest Meteorology, 118, 151–167. Kreisel, H., Dörfelt, H. & Benkert, D. (1980) Karten zur Pflanzenverbreitung in der DDR. 3. Serie. Ausgewählte Makromyzeten. Akademische Verlagsgesellschaft Geest & Portig, Leipzig. Kutsch, W.L., Wirth, C., Kattge, J., Nöllert, S., Herbst, M., Kappen, L. (2009) Ecophysiological characteristics of mature trees and stands – consequences for old-growth forest productivity. Old-Growth Forests: Function, Fate and Value (eds C. Wirth et al. ), pp. 57–79. Springer, Berlin, Heidelberg, New York. Lanner, R.M. (2002) Why do trees live so long? Ageing Research Reviews, 1, 653–671. Lanner, R.M. & Connor, K.F. (2001) Does bristlecone pine senesce? Experimental Gerontology, 36, 675–685. Larson, A.J. & Franklin, J.F. (2010) The tree mortality regime in temperate old-growth coniferous forests: the role of physical damage. Canadian Journal of Forest Research, 40, 2091–2103. Lines, E.R., Coomes, D.A. & Purves, D.W. (2010) Influences of forest structure, climate and species composition on tree mortality across the eastern US. PLoS ONE, 5, e13212. Lutz, J.A. & Halpern, C.B. (2006) Tree mortality during early forest development: a long-term study of rates, causes, and consequences. Ecological Monographs, 76, 257–275. van Mantgem, P.J. & Stephenson, N.L. (2007) Apparent climatically induced increase of tree mortality rates in a temperate forest. Ecology Letters, 10, 909–916. McCarthy, J. (2001) Gap dynamics of forest trees: a review with particular attention to boreal forests. Environmental Review, 9, 1–59. Mencuccini, M., Martinez-Vilalta, J., Vanderklein, D., Hamid, H.A., Korakaki, E., Lee, S. et al. (2005) Size-mediated ageing reduces vigour in trees. Ecology Letters, 8, 1183–1190. Monserud, R.A. & Sterba, H. (1999) Modeling individual tree mortality for Austrian forest species. Forest Ecology and Management, 113, 109–123. Mountford, E.P., Peterken, G.F., Edwards, P.J. & Manners, J.G. (1999) Longterm change in growth, mortality and regeneration of trees in Denny Wood, an old-growth wood-pasture in the New Forest (UK). Perspectives in Plant Ecology, Evolution and Systematics, 2, 223–272. Mund, M. (2004) Carbon pools of European beech forests (Fagus sylvatica) under different silvicultural management. PhD Thesis, Georg-August-Universität , Göttingen. Mund, M., Kutsch, W.L., Wirth, C., Kahl, T., Knohl, A., Skomarkova, M.V. et al. (2010) The influence of climate and fructification on the inter-annual variability of stem growth and net primary productivity in an old-growth, mixed beech forest. Tree Physiology, 30, 689–704. Niinemets, Ü. & Valladares, F. (2006) Tolerance to shade, drought, and waterlogging of temperate Northern Hemisphere trees and shrubs. Ecological Monographs, 76, 521–547. Pacala, S.W., Canham, C.D., Saponara, J., Silander, J.A., Kobe, R.K. & Ribbens, E. (1996) Forest models defined by field measurements: estimation, error analysis and dynamics. Ecological Monographs, 66, 1–43. Peet, R.K. & Christensen, N.L. (1987) Competition and tree death. BioScience, 37, 586–595. Peñuelas, J. (2005) Plant physiology – a big issue for trees. Nature, 437, 965–966. Petit, R.J. & Hampe, A. (2006) Some evolutionary consequences of being a tree. Annual Review of Ecology, Evolution, and Systematics, 37, 187–214. Petritan, A.M., von Lüpke, B. & Petritan, I.C. (2007) Effects of shade on growth and mortality of maple (Acer pseudoplatanus), ash (Fraxinus excelsior) and beech (Fagus sylvatica) saplings. Forestry, 80, 397–412. Piovesan, G., Bernabei, M., Di Filippo, A., Romagnoli, M. & Schirone, B. (2003) A long-term tree ring beech chronology from a high-elevation oldgrowth forest of Central Italy. Dendrochronologia, 21, 13–22. Piovesan, G., Di Filippo, A., Alessandrini, A., Biondi, F., Schirone, B. & White, P.S. (2005) Structure, dynamics and dendroecology of an old-growth Fagus forest in the Apennines. Journal of Vegetation Science, 16, 13–28.

58

Porté, A. & Bartelink, H.H. (2002) Modelling mixed forest growth: a review of models for forest management. Ecological Modelling, 150, 141–188. Purves, D.W. & Pacala, S.W. (2008) Predictive models of forest dynamics. Science, 320, 1452–1453. R Development Core Team (2011) R: A Language and Environment for Statistical Computing. R Development Core Team, Wien, Austriza. http://www. R-project.org. Roloff, A., Pietzarka, U. (1997) Fraxinus excelsior. Enzyklopädie der Holzgewächse. Handbuch und Atlas der Dendrologie (eds A. Roloff et al.), pp. 1 –15. Wiley-VCH, Weinheim. Roloff, A., Weisgerber, H., Lang, U., Stimm, B. & Schütt, P. (1994) Enzyklopädie der Holzgewächse. Handbuch und Atlas der Dendrologie. Wiley-VCH, Weinheim. Rüger, N., Huth, A., Hubbell, S.P. & Condit, R. (2011) Determinants of mortality across a tropical lowland rainforest community. Oikos, 120, 1047– 1056. Runkle, J.R. (2000) Canopy tree turnover in old-growth mesic forests of eastern North America. Ecology, 81, 554–567. Ryan, M.G., Phillips, N. & Bond, B.J. (2006) The hydraulic limitation hypothesis revisited. Plant, Cell and Environment, 29, 367–381. Scherer-Lorenzen, M., Körner, C. & Schulze, E.-D. (2005) Forest Diversity and Function. Temperate and Boreal Systems. Ecological Studies, 176. Springer, Berlin, Heidelberg, New York. Schulze, E.-D., Hessenmöller, D., Knohl, A., Luyssaert, S., Boerner, A., Grace, J. (2009) Temperate and boreal old-growth forests: how do their growth dynamics and biodiversity differ from young stands and managed forests? Old-Growth Forests: Function, Fate and Value (eds C. Wirth et al.), pp. 343 –366. Springer, Berlin, Heidelberg, New York. Schweingruber, F.H., Wirth, C. (2009) Old trees and the meaning of “old”. Old-Growth Forests: Function, Fate and Value (eds C. Wirth et al.), pp. 35– 54. Springer, Berlin, Heidelberg, New York. Shugart, H.H. (1987) Dynamic ecosystem consequences of tree birth and death patterns. BioScience, 37, 596–602. Sing, T., Sander, O., Beerenwinkel, N. & Lengauer, T. (2009) ROCR: Visualizing the performance of scoring classifiers. R package version 1.0-4. http:// CRAN.R-project.org/package=ROCR. Smith, B., Prentice, I.C. & Sykes, M.T. (2001) Representation of vegetation dynamics in the modelling of terrestrial ecosystems: comparing two contrasting approaches within European climate space. Global Ecology and Biogeography, 10, 621–637. Smith, T.F., Rizzo, D.M. & North, M. (2005) Patterns of mortality in an oldgrowth mixed-conifer forest of the southern Sierra Nevada, California. Forest Science, 51, 266–275. Sturtz, S., Ligges, U. & Gelman, A. (2005) R2WinBUGS: a package for running WinBUGS from R. Journal of Statistical Software, 12, 1–16. Temesgen, H. & Mitchell, S.J. (2005) An individual-tree mortality model for complex stands of southeastern British Columbia. Western Journal of Applied Forestry, 20, 101–109. de Toledo, J.J., Magnusson, W.E., Castilho, C.V. & Nascimento, H.E.M. (2012) Tree mode of death in Central Amazonia: effects of soil and topography on tree mortality associated with storm disturbances. Forest Ecology and Management, 263, 253–261. Trotsiuk, V., Hobi, M.L. & Commarmot, B. (2012) Age structure and disturbance dynamics of the relic virgin beech forest Uholka (Ukrainian Carpathians). Forest Ecology and Management, 265, 181–190. Watkinson, A. (1992) Plant senescence. Trends in Ecology & Evolution, 7, 417–420. Wirth, C. & Gleixner, G. & Heimann, M. (2009) Old-Growth Forests: Function, Fate and Value. Ecological Studies, 207. Springer, Berlin, Heidelberg, New York. Wirth, C. & Lichstein, J.W. (2009) The imprint of succession on old-growth forest carbon balances insights from a trait-based model of forest dynamics. Old-Growth Forests: Function, Fate and Value (eds C. Wirth et al. ), pp. 81– 113. Springer, Berlin, Heidelberg, New York. Wirth, C. (2009) Old-growth forest: function, fate and value: a synthesis. OldGrowth Forests: Function, Fate and Value (eds C. Wirth et al. ), pp. 465– 491. Springer, Berlin, Heidelberg, New York. Wunder, J., Reineking, B., Matter, J.-F., Bigler, C. & Bugmann, H. (2007) Predicting tree death for Fagus sylvatica and Abies alba using permanent plot data. Journal of Vegetation Science, 18, 525–534. Wunder, J., Brzeziecki, B., Żybura, H., Reineking, B., Bigler, C. & Bugmann, H. (2008) Growth–mortality relationships as indicators of life-history strategies: a comparison of nine tree species in unmanaged European forests. Oikos, 117, 815–828.

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

Partitioning tree mortality 11 Yao, X., Titus, S.J. & MacDonald, S.E. (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.

Figure S3. Total mortality over d.b.h. for two models.

Received 23 May 2012; accepted 9 October 2012 Handling Editor: Pieter Zuidema

Tables S2. Inventory of mortality modes.

Table S1. Modes of death and criteria for identification.

Table S3. Sampled treerings of dead trees.

Supporting Information Additional Supporting Information may be found in the online version of this article:

Table S4. AUC, DIC and parameter estimates of candidate models.

Appendix S1. Estimation and errors of tree growth. Figure S1. Age estimation from stem discs for beech. Figure S2. Distribution of predictors d.b.h. and dincest for mortality modes.

© 2012 The Authors. Journal of Ecology © 2012 British Ecological Society, Journal of Ecology

59

Appendix S1 - Estimation and errors of tree growth Estimation of tree growth Wemodelleddincestwithequations5&6.Tothisend,itwasnecessarytodevelopapredictivemodͲ elofdiameterincrement.ThelinearmodelfortheestimationofdincpredisdetailedinequationS1. dincpred~comp+dincsim

eqnS1

Aspredictorsfordincpredweusedcomp,acompetitionindex,cf.equationS3andthegrowthofsimiͲ larsurroundingtrees(dincsim,cf.equationsS4to6)asanintegratingmeasureoftreesize,competiͲ tive pressure and spatial heterogeneity of site conditions. We applied the model S1 independently foreachspecies.Toassesstheusefulnessofdincsim,wecontrastedthisapproachwithjusttheother availablepredictors(comp,dbh),seebelow.

Modelling of variance Wefoundthevarianceofdinctobeheteroscedasticinthatitincreasedwithincreasingdinc.ToalͲ lowforunbiasedestimates,wethusmodelledthevarianceinequation6(ɐpred)withequationS2 logit(ɐpred/Ƚɐ)~log(dincsim)

eqnS2

whereɐpredisdividedbyȽɐ,setto1.2,sothatɐpredcanbegreaterthan1.WesetoutwithoutimplyͲ ingafunctionalrelationshipofɐpredandinapreliminarymodeljustmodelledfivedifferentvaluesof ɐpred(withincreasingvaluesofindependentlyestimatedstepsizeshavingeachaflatpriorbetween 0.05 and 0.7 cm aͲ1) assigned to each observation with equal (uniformative) sampling probability. PostͲhocvisualizationshowedarelationshipoftheestimatedɐpredtothevaluesofdincsim,whichled ustoformulateequationS2,whichinturnreducedmodelcomplexityagain.

Competition Index (comp) Wequantifiedthestrengthofcompetitionexertedbyneighboursoneachfocustree,independentof thetreespecies,withacompetitionindex(comp): ஑

మ

ܿ‫݌݉݋‬௝ ൌ σ௡௜ୀଵ Ƚଵ ሺο‫ܿ݁݌ݏ‬௜௝ ሻ ή ܾ݄݀௜ మ ή ݁ ି஑య ήௗ௜௦௧೔ೕ ή ݁ ି஑ర ήௗ௜௦௧೎೐೙೟ೝ೚೔೏ 

eqnS3

withcompjbeingthecompetitionindexofafocustreej,οspecijabinaryvariableforthespeciesdifͲ ference(1ifsameandȽͳifdifferentspecies),dbhithediameterofanyothertreeinthestand[cm], distijthedistance[m] betweenthefocustreeandatreeianddistcentroidthedistance betweenthe focustreeandthecentroidofallcompetitorsweightedbytheirinfluence(firstthreefactorsofthe

60

formula).WeappliedabordercorrectionbyassumingtheconditionacrosstheborderofthesamͲ pled plot would be as the observed average around the focus tree. Contrary to most distanceͲ dependentindicesfoundintheliterature(e.g.,Biging&Dobbertin1992,Stadtetal.2007),thisindex doesnotincludethefocustree’sdbhandisthusanindependentmeasureofthetreescompetitive environment and only weakly correlated to the focus tree’s dbh (Spearman’s ɏ = Ͳ0.33). It also inͲ cludes a term, which accounts for asymmetric conditions, e.g. clearings. The parameters Ƚͳ to ȽͶ werefittomaximizeSpearmanͲcorrelationofdincobswithcompbysystematicallyexploringthepaͲ rameterspace,(estimatedvalues:0.9,0.85,0.25and0.07).Forthisfitweusedonlybeechandonly treesthathadameasurementofdincand,iflive,onlythosethatdidnotexhibitanyunusualfeature, suchasbeingbroken,leaning,beingresprouts,etc.(n=11’875).TheparameterȽͳbeinglowerthan1 impliesasomewhatlesscompetitiveinfluenceofnonͲbeechtreesascomparedtoconspecifics.

Average growth of similar trees in the neighbourhood (dincsim) Itisobvious,thatnotonlycompetitionbutalsoenvironmentalconditions,whichmayvaryonasmall scale,aswellas,mostimportant,individualcharacteristicsofatreeinfluenceitsgrowth.Welacked spatialinformationonedaphicconditions,whichindicatee.g.nutrientavailability,waterloggingor wateravailability.Wethususedthegrowthofcomparableneighbourstocalculateasinglevariable dincsim(averagedincinneighbouringsimilartrees)asproxyforlocalsitequality,which,byvirtueof comparingonlytreeswithsimilarsizeandcompetitionstatusalsoincludedtheintrinsicsizecharacͲ teristic.Weusedsimilaritywithrespecttospecies(spec),size(dbh),competitionstatus(comp)and distance(dist)asaweighttocalculateaweightedmeanoftheobservedgrowth(dincobs)ofthesurͲ roundingtrees(equationS4) ௖௢௥௥Ǥ௘௫௣௢௡௘௡௧ೕ

݀݅݊ܿ௦௜௠ೕ ൌ σ௡௜ୀଵ ݀݅݊ܿ௢௕௦೔ ή ‫ݕݐ݅ݎ݈ܽ݅݉݅ݏ‬௜௝



eqnS4

wheresimilaritywascalculatedwithequationS5andthecorr.exponentwithequationS6 ‫ݕݐ݅ݎ݈ܽ݅݉݅ݏ‬௜௝ ൌ Ⱦଵ ሺο‫ܿ݁݌ݏ‬௜௝ ሻ ή ݁ ܿ‫ݎݎ݋‬Ǥ ݁‫ݐ݊݁݊݋݌ݔ‬௝ ൌ

మ మ మ ିቀοௗ௕௛೔ೕ Ȁሺஒమ ାஒయ ήௗ௕௛೔మ ሻାஒర ήο௖௢௠௣೔ೕ ାஒఱ ήοௗ௜௦௧೔ೕ ቁ

୪୭୥ሺଵାஒల ሻ ୪୭୥ቆ

భ భషౣ౗౮ቀೞ೔೘೔೗ೌೝ೔೟೤ೕ ቁ





eqnS5 eqnS6

ାஒల ቇ

InequationS5οspecijisabinaryvariableforthespeciesdifference(1ifsameandȾͳifdifferentspeͲ cies).Further,weusedGausskernels(secondfactorofequationS5)toweightthedistance(dist)and thedissimilarityofthesurroundingtreesi=1…nwithrespecttodbhandcompofthefocustreej (σdistij,σdbhijandσcompij).Wenormalizedsimilarity,sothatitsumsto1,correcteditwithanexͲ ponent(corr.exponent,equationS6)andthennormalizeditagain.Thiswasdonetopreventasingle neighbouringtreefromdominatingtheestimateofdincsim.Theparameters(ȾͳtoȾ͸)inequationsS5 andS6werefittomaximizeSpearmanͲcorrelationofdincobswithdincsimusingthesamedataasfor comp(seeabove)bysystematicallyexploringtheparameterspace.TheestimatesforȾͳtoȾ͸were: 0.005,11,0.0625,0.00167,0.00833and1.

61

Linearmodelsthatestimateddincobs(bothliveanddeadtrees)generallyperformedbetterwhenthe proxy for local site quality, dincsim, was included. We tested models that used log(dbh + c1), log(comp), log(dincsim +c2) and combinations thereof as predictors for dincobs (for beech only). The additive constants c1 and c2 were estimated to render a maximum model fit (here: 23 and 0.9). Goodnessoffitforthedifferentmodelswere: Model

Predictors

R2

(a)

log(comp)

0.15

(b)

log(dbh+c1)

0.40

(c)

log(dincsim+c2)

0.60

(d)

log(comp)+log(dbh+c1)

0.44

(e)

log(comp)+log(dincsim+c2)

0.61

 Amongthesimplemodels(atoc)thecompetitionindexhadanR2of0.15,dbhexplained40%and dincsimprovedtosignificantlyenhancetheexplanatorypowerwithanR2of0.6.Whenweusedthe models(d)and(e)tocalculatedincpredintheBayesianframe(equations5and6),theimprovement waslessstriking:model(d)hadapseudoǦR2of0.82,whilstmodel(e)had0.84.

Errors of tree growth Live trees Measurementerrorsofthedbh(ɐdbh)duringthetwoinventoriesresultedinanerrorofdincobsinlive trees(ɐlive).Sincewedidnothavereplicatemeasurementsofthesametrees,weestimatedtheerror withequationsS7andS8(Bolker2008)withallspeciespooled: dincobs~Normal(dincest,ɐʹlive)

eqnS7

dincest~LogǦNormal(ɊLN,ɐʹLN)+a

eqnS8

Estimatedtruegrowth(dincest)wasassumedtobelogͲnormallydistributed,withtheparameters(ɊLN andɐʹLN)beingestimatedindependentlyforsevendbhclassesofequalsamplesize.AnadditiveconͲ stant(a)wasintroducedtosetaminimumathalftheminimumobservedgrowthofwoodcoresfrom thisstudy(0.05mmaͲ1).Further,weassumedthemeasurementerrorofdbh(ɐdbh)tobeidenticalfor bothinventoriesandthusthevarianceswouldaddup(equationS9). ɐʹliveαʹɐʹdbh

eqnS9

First,weletɐʹdbhvaryindependentlyinseveraldbhͲclasses.Basedonvisualinspectionofthesefirst results,wesimultaneouslymodelledɐʹdbhasalinearfunctionofdbh(equationS10). ɐʹdbh~dbh

62

eqnS10

Dead trees For dead trees sampled with the increment puncher, we measured ring widths of the outermost growthrings(upto8ringsreflectingthe8Ͳyrinventoryinterval)andrecordedthemeanringwidth (Lintab™ 6, TSAPWin Professional 4.64, RINNTECH). We estimated the errors due to measurement and eccentricity of rings with repeated measurements (cores taken from different positions) on a subsampleof11trees.Thiserrorwasmodifiediflessthantheyoungest8ringscouldberetrieved andcounted.Formathematicalsimplicity,weassumedthattheringswereindependentsamples,so thattheerrorwouldincreasewithlessringsmeasured(n)bythefactor8/n. Further,weidentifiedtreesthathadhighchancesofnothavingformedavisibleringduringagrowth seasonbetweenthecensuses.Sincetherewasnowayofverifyingthisbymeansofe.g.crossͲdating (tooshortchronologies),wereliedonexpertjudgement:onegroupwasassignedachanceof50%of nothavingformedonering(n=54),anothergroupof50%ofnothavingformedaringinoneortwo years(withequalprobability)(n=23).Forthesetrees,weadjustedthemeasuredgrowthbyusingthe mean estimation considering the chance of unͲformed rings. The resulting increase of uncertainty (variance)wasaddedtotheestimatedvariancesofmeasurementuncertaintyandeccentricity.These threesourcesoferrorjointlymadeuptheerrorofdeadtreediameterincrement(ɐʹdead).Weonly used unflawed samples, where the outermost ring of the sample was the last ring the tree had grown,rendering536usablesamples,ofwhich74hadlessthan8rings(cf.TableS4).

“Simple-growth” model Asanexemplarycontrast(referredtoas“simpleͲgrowth”model),wealsousedtheunalteredgrowth measurementsasinputvaluesforthebeechmortalitymodelandimputedthemissinggrowthvalues withanordinarylinearmodel(equationS11) dincobs~dincsim+comp

eqnS11

withthepredictorsfromequationsS3andS4andahomogenousvariance,whichwasestimatedasa freeparameter.

Relation of growth to dbh Toplotmortalityestimatesagainstdbh,wheregrowthwasalsoapredictor,weappliedasimple model(equationS12,formderivedfromvisualinspection,withthefreeparametersɀͳtoɀͶ)toestiͲ matedincestwithdbh.Thisestimatewasthenusedasinputforthemortalitymodel,inadditionto dbh. ಋ

Ž‘‰ሺ݀݅݊ܿ௘௦௧ ሻ̱ɀଵ ൅ ɀଶ ൫ͳ െ ݁ ିஓయ ௗ௕௛ ర ൯ 

eqnS12



63

Withparameterestimates: Parameter ɀͳ ɀʹ ɀ͵ ɀͶ

Mean(SE) -3.4(.010) 2.1(.020) -0.00035(.000077) 2.5(.072)

References Biging,G.S.&Dobbertin,M.(1992)AComparisonofDistanceͲDependentCompetitionMeasuresfor HeightandBasalAreaGrowthofIndividualConiferTrees.ForestSci.,38,695–720. Bolker,B.M.(2008)EcologicalmodelsanddatainR.PrincetonUniversityPress,Princeton,N.J. Stadt,K.,Huston,C.,Coates,K.,Feng,Z.,Dale,M.&Lieffers,V.(2007)Evaluationofcompetitionand lightestimationindicesforpredictingdiametergrowthinmatureborealmixedforests.Ann.ForͲ estSci.,64,477–490. 

64



Fig.S1.Beechstemdiscsusedforageestimation:dbhoverage,fittedcurve(equation7)(black)and derivedfromthisfit,theageͲrelatedgrowththattreesproceedingonthemodelledtrajectorywould exhibit:dinc(green).Thicklines:medianestimates,thinlinesandshadedarea:95%credibleinterval. Extrapolatedbeyondthedata.Forthemodel,weusedpriorinformationatwhatagebeechtrees wouldgrowpastaheightof1.30m(beforethatagedbhismodelledtobenegative;dataderived fromfiguresinColletetal.(2001)andNageletal.(2006)renderingafitforalogͲnormalpriordistriͲ butionoftheparameterȽͳ(equation7)withtheparametersʅandʍ:2.7and0.35).Theresidual errorwasmodelledtoincreaselinearlywithage,aswasvisiblefromthedata.

Fig.S1 Parameterestimatesandstandarderrors(if“Ͳ“,thentheparameterwasfixedbecauseofstrong correlationtootherparameters)forequation7were: Parameter Mean(SE) -1.6(1.1) Ƚ ͳ 35.2(5.8) Ƚʹ 0.00061(.00021) Ƚ͵ 1.8(-) ȽͶ 

References Collet,C.,Lanter,O.&Pardos,M.(2001)Effectsofcanopyopeningonheightanddiametergrowthin naturallyregeneratedbeechseedlings.Ann.ForestSci.,58,127̽134. Nagel,T.A.,Svoboda,M.&Diaci,J.(2006)RegenerationpatternsafterintermediatewinddisturbͲ anceinanoldͲgrowthFagusͲAbiesforestinsoutheasternSlovenia.ForestEcol.Manag.,226, 268̽278. 



65

Fig.S2.Distributionoftreesaccordingtotheirstatusandmortalitymode(allspeciespooled)over logͲscaledgradientsofdbh[cm]andestimatedtrueannualgrowth(dincest)[cmaͲ1].Boxwidthsare proportionaltothelogarithmicofthesamplesize(cf.TableS3Ͳ1).

Fig.S2  

66



Fig. S3 Modelled total annual mortality probabilities over dbh [cm] for beech. “Total with modes” referstototalmortalityfromthemodel,whichincludesdifferentmortalitymodes,“TotalnoͲmodes” referstothe“noͲmodes”Ͳmodelwithoutdifferentiationbetweenmortalitymodes.Thicklines:mediͲ anestimates,thinlinesandshadedarea:95%credibleinterval.Amodelledgrowthfortherespective dbhwasassumed(dincest~dbh,cf.equationS12). 

Fig.S3 

67

68 Snapped Snapped Snapped &rot Crushed Ͳ

Ͳ

Ͳ

woodrot

woodrot

Ͳ

Ͳ

Stembreakage

Crownbreakage

Stembreakage

Crownbreakage

Crushed

Elmdisease







Uprooted&rot

rootrot

Uprooted

Unknown

Uprooted

Ͳ

Uprooted

Snapped &rot

Standingdeadwithoutanyofthefollowingcriteriaapplicable

Standing

Ͳ

Standingdead

treecouldnotbefoundagainatorarounditsknownposition

deadleaves,feedinggalleriesbelowbark

Crushedorpinnedbyothertreeoruprootedwiththerootcollarofalargertree

Splinterbreakageofthecrown

Splinterbreakageofthestem

Smoothbrittlebreakageofthecrownwithfruitingbodiesvisible

Smoothbrittlebreakageofthestemwithfruitingbodiesvisible

Breakageoftherootsatstembasiswithsignsofrottenwood(brittlebreakage)

Uprootedwithoutanysignsofrootrot

Criteria

Predisposingfactor GroupedMode

Mode

TableS1.Modesofdeathandcriteriaforidentification



69

Uprooted

Uprooted&rot

Snapped

Snapped

Snapped &rot

Crushed

Ͳ

Ͳ

Rootrot

Ͳ

Ͳ

Woodrot

Woodrot

Ͳ

Ͳ

Uprooted

Uprooted

Stembreakage

Crownbreakage

Stembreakage

Crownbreakage

Crushed

Elmdisease

Total



Total

Missing





Unknown

Unknown



Standing

Ͳ

Standingdead

Snapped &rot

Mode

Predisposing Grouped

factor

Mode

(21.5)

(0.4)

(9.9)

(0.1)

(1.6)

(0.3)

(0.7)

(1.3)

(3.2)

(60.9)

27

1663 (100.0)

358

7

165

1

27

5

12

21

54

1013

(2.9)

(3.8)

(5.5)

(0.3)

(16.4)

(2.4)

(4.2)

(7.7)

(22.3)

(34.5)

0.3

52.8 (100.0)

1.5

2.0

2.9

0.2

8.7

1.3

2.2

4.1

11.8

18.2

Allcount(%) AllBA(%)

theses.Forallspecies,percentageinparentheses

0

39 (7.4)

3 (0.3)

-

1 (0.1)

0 (-)

4 (1.1)

1 (0.4)

2 (0.4)

7 (1.8)

5 (1.5)

16 (1.7)

Ash

(1.1)

(2.0)

(-)

(6.3)

(0.7)

(1.7)

(1.6)

(7.3)

(8.3)

26

(0.2)

1535 (29.1)

353

-

159

0

17

3

8

10

36

949

Beech

0

30 (2.8)

1 (0.1)

-

3 (0.5)

0 (-)

3 (0.3)

0 (-)

1 (0.1)

1 (0.1)

5 (0.9)

16 (1.0)

1 (0.1)

14 (2.2)

0 (-)

-

1 (0.1)

1 (0.2)

2 (0.7)

0 (-)

1 (0.0)

1 (0.1)

3 (0.7)

5 (0.4)

Hornbeam Sycamore

0

35 (9.5)

1 (0.0)

7

0 (-)

0 (-)

0 (-)

1 (0.1)

0 (-)

2 (0.5)

1 (0.4)

23 (6.5)

Elm

Wych

0

10 (1.8)

0 (-)

-

1 (0.2)

0 (-)

1 (0.3)

0 (-)

0 (-)

0 (-)

4 (0.9)

4 (0.3)

Other

TableS2Ͳ1.Mappedmortalitymodesoftreesthatdiedintheperiod1999to2007withrespectivenumberoftreesandbasalarea(BA)[m2haͲ1]inparenͲ



70

Uprooted &rot

Snapped

Snapped &rot

Crushed

Rootrot

Ͳ

Woodrot

Ͳ

Uprooted

Stembreakage

Stembreakage

Crushed 33

18

1

2

1

11

All

3

1 (0.1)

2 (0.7)

Ash

25

15 (0.7)

2 (0.5)

1 (0.0)

7 (1.5)

Beech

2

1 (0.1)

1 (0.3)

1

1 (0.4)

2



Ash Beech Hornbeam Sycamore WychElm Total

Species



2 13 84

620

0

18

23

55

543

12

14



missing/incompleteouterring



24

sampledtrees



536

10

10

18

488

10

useablesamples



74

7

3

6

53

5

lessthan8ringsinsample



54

0

0

0

54

0

23

0

0

0

23

0

oneortwoyears

50%chanceofnoringin oneyear

1 (0.2)

1 (0.3)

Hornbeam Sycamore Other

TableS3.Sampledtreeringsofdeadtrees.Columnstotherightof“useablesamples”onlycontainuseablesamples.





Total

Uprooted

Ͳ

Uprooted

Total

Mode

Predisposing Grouped

factor

Mode

inventory

TableS2Ͳ2.TreesthatwerenotphysiologicallydeadbutestimatedtobeboundtodieorsurviveonlyasareͲsproutwithinthevegetationperiodofthe



71



Totalearly late Totalearly late Standingearly late Uprooted Uprooted&rot Snapped Snapped&rot Crushed Unknown Total DICSum Standingearly late Uprooted Uprooted&rot Snapped Snapped&rot Crushed Unknown Total DICSum

Standingearly

late Uprooted Uprooted&rot Snapped Snapped&rot Crushed Unknown Total DICSum

Model

Beech“noͲmodes” dincest Beech“noͲmodes” reldincest Beech dincest         Beech reldincest        

Beech

dincest log(dbh+c2)*dincest       

        



                       



6227.1 450.0 161.0 168.0 208.7 1665.9 1097.3 8576.0 18553.7 6230.2 450.5 160.9 167.9 208.7 1668.5 1095.3 8575.0 18556.9

0.72 0.89 0.68 0.81 0.75 0.69 0.73

0.72 0.89 0.68 0.81 0.76 0.68 0.73

0.89 0.68 0.81 0.76 0.68 0.73

449.9 161.1 168.0 209.0 1665.9 1100.7 8576.1 18551.5

6221.0

8583.5

0.73

0.72

8581.8

0.73

AUC DIC int.,log(dbh+c2),dincest int.,dbh int.,log(dbh+c2),reldincest int.,dbh int.,log(dbh+c3),dincest int.,log(dbh+c5) int.,log(dbh+c4) int.,dbh int.,dbh int.,dbh int.,log(dbh+c1) Ǧ Ǧ  int.,log(dbh+c3),reldincest int.,log(dbh+c5) int.,log(dbh+c4) int.,dbh int.,dbh int.,dbh int.,log(dbh+c1) Ǧ Ǧ  int.,log(dbh+c3),[dincest], [log(dbh+c2)*dincest] int.,log(dbh+c5) int.,log(dbh+c4) int.,dbh int.,dbh int.,dbh int.,log(dbh+c1) Ǧ Ǧ 

Explanatoryvariables

-42(-57,-21) 6.2(3.4,10) -17(-20,-14) 2.3(1.6,3.1) -9.9(-11,-9.1) 0.029(0.0041,0.050) -10(-11,-9.2) 0.038(0.018,0.059) -11(-12,-10) 0.065(0.050,0.081) -3.7(-4.1,-3.3) -1.2(-1.4,-1.0) -

5.7(4.7,6.5) -3.1(-3.4,-2.8) 2.3(-3.2,6.6) -1.4(-2.9,0.55)

6.9(6.2,7.9) -3.5(-3.8,-3.3) -7.7(-14,-2.8) -42(-56,-22) 7.3(3.1,10) -17(-20,-14) 2.4(1.6,3.1) -9.9(-11,-8.9) 0.029(0.0038,0.050) -10(-11,-9.2) 0.039(0.017,0.059) -11(-12,-10) 0.063(0.047,0.080) -3.6(-4.1,-3.2) -1.2(-1.4,-1.0) -

1.8(1.2,2.5) -2.1(-2.4,-1.9) -1.4(-2.4,-0.45) -8.9(-10.0,-7.8) 0.052(0.035,0.072) 2.2(1.7,2.9) -2.3(-2.6,-2.1) -5.8(-12,-0.94) -9.0(-10,-7.6) 0.053(0.033,0.070) 5.9(5.1,6.7) -3.2(-3.5,-2.9) -1.8(-2.7,-1.0) -42(-57,-21) 7.3(2.9,11) -17(-20,-14) 2.4(1.7,3.1) -9.9(-11,-9.0) 0.029(0.0044,0.051) -10(-11,-9.2) 0.039(0.018,0.059) -11(-12,-10) 0.062(0.047,0.079) -3.7(-4.1,-3.2) -1.2(-1.4,-1.0) -

Parameterestimates:Median(95%CI)

stantsc1toc5wereassignedconstantvalues:1,8,16,20and40[cm]respectively;int.=intercept

TableS4.AUC,DIC(Spiegelhalteretal.2002)andparameterestimatesofcandidatemodels;insquaredbrackets:nonͲsignificantterms;additiveconͲ

72

Standingearly late Uprooted Uprooted&rot Snapped Snapped&rot Crushed Unknown Total DICSum Total Standing Uprooted Uprooted&rot Snapped Snapped&rot Crushed Unknown Total Total Standing Uprooted Uprooted&rot Snapped Snapped&rot Crushed Unknown Total

Beech “simpleͲgrowth” dincobs        Ash Ash        Hornbeam Hornbeam       

                           

 6226.5 450.0 160.8 168.1 208.8 1667.9 1092.6 8569.9 18544.5 241.2 92.7 58.8 77.2 39.3 49.5 16.3 6.7 236.9 208.4 119.6 52.4 15.5 15.5 37.0 37.2 4.3 205.7

0.72 0.89 0.68 0.81 0.76 0.68 0.73 0.71 0.84 0.71 0.66 0.82 0.77 0.68

AUC DIC int.,log(dbh+c3),dincobs int.,log(dbh+c5) int.,log(dbh+c4) int.,dbh int.,dbh int.,dbh int.,log(dbh+c1) Ǧ Ǧ  int.,log(dbh) int.,log(dbh) int. int. int. int. int. Ǧ Ǧ int.,dbh int,dbh int.,log(dbh) int int. int. int. Ǧ Ǧ

Explanatoryvariables



-0.083(-3.3,2.9) -1.2(-1.9,-0.37) 4.0(0.71,7.0) -2.4(-3.3,-1.5) -11(-16,-6.7) 0.10 (0.0081,0.21) -8.3(-11,-6.8) -8.3(-11,-6.7) -7.1(-8.5,-6.1) -7.0(-8.8,-6.1) -

1.3(-0.20,2.8) -1.6(-2.0,-1.2) 3.1(1.7,4.5) -2.4(-3.0,-2.0) -6.8(-7.7,-6.1) -6.5(-7.3,-5.8) -7.3(-8.7,-6.4) -7.0(-8.2,-6.2) -8.6(-11,-7.1) -

5.9(5.0,6.8) -3.2(-3.5,-2.9) -1.6(-2.5,-0.91) -41(-57,-22) 7.2(3.0,10) -17(-20,-14) 2.3(1.7,3.0) -9.9(-11,-9.0) 0.029(0.0048,0.050) -10(-11,-9.2) 0.038(0.019,0.058) -11(-12,-10) 0.063(0.046,0.080) -3.7(-4.1,-3.2) -1.2(-1.4,-0.97) -

Parameterestimates:Median(95%CI)

Spiegelhalter,D.J.,Best,N.G.,Carlin,B.R.&vanderLinde,A.(2002)Bayesianmeasuresofmodelcomplexityandfit.J.Roy.Stat.Soc.B,64,583̽616.

Reference



Model



73

Paper 2 Title:

Tree neighbourhood matters – Tree species composition drives diversity–productivity patterns in a near-natural beech forest

Journal: Forest Ecology and Management Authors: Ratcliffe S, Holzwarth F, Nadrowski K, Levick S, Wirth C

74

Forest Ecology and Management 335 (2015) 225–234

Contents lists available at ScienceDirect

Forest Ecology and Management journal homepage: www.elsevier.com/locate/foreco

Tree neighbourhood matters – Tree species composition drives diversity–productivity patterns in a near-natural beech forest Sophia Ratcliffe a,⇑, Frédéric Holzwarth a, Karin Nadrowski a, Shaun Levick b, Christian Wirth a,c a

University of Leipzig, Systematic Botany and Functional Biodiversity Lab, Johannisallee 21-23, 04103 Leipzig, Germany Max Planck Institute for Biogeochemistry, Hans-Knöll-Str. 10, 07745 Jena, Germany c German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5e, 04103 Leipzig, Germany b

a r t i c l e

i n f o

Article history: Received 15 April 2014 Received in revised form 15 September 2014 Accepted 17 September 2014

Keywords: Basal area increment Competition index Diversity–productivity Neighbourhood diversity

a b s t r a c t European beech forest with a variable admixture is one of the most important forest types in Central Europe. Growing evidence has demonstrated the positive effect of increased biodiversity on vital forest ecosystem functions and services such as productivity and nutrient cycling. Both complementarity in resource use and species identity are known to influence tree productivity but they have received relatively little attention in observational studies. Using a large dataset of repeat inventory trees in a nearnatural deciduous forest in Central Germany we test whether tree diversity enhances tree productivity at the tree and the stand level, whilst accounting for tree size, tree vitality, local topography and the potentially confounding effects of spatial autocorrelation and negative growth estimates. Beech and hornbeam individual tree growth was sensitive to their neighbourhood diversity and composition whilst ash trees were only sensitive to the neighbourhood tree density. Neighbourhood complementarity effects were driven by differences in species’ competitive strengths, whilst at the stand level productivity gains were primarily attributable to the density of ash and diversity effects were less prominent. We conclude that small-scale admixture with patches of different species promotes tree growth in European beech forest; congruent with current management plans for beech and hardwood forests. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction Forests provide us with a wealth of products and services. There is concern that the loss of biodiversity within forests is jeopardising these services (Aerts and Honnay, 2011). Growing empirical evidence demonstrates that biodiversity loss can affect major ecosystem properties such as primary productivity and nutrient cycling (Cardinale et al., 2012; Isbell et al., 2011). Unlike in grassland ecosystems, where clear productivity–diversity relationships have been identified (Balvanera et al., 2006; Hooper et al., 2005), the relationship between tree species diversity and tree productivity in forest ecosystems, and its underlying mechanisms, are less well understood (Nadrowski et al., 2010; Vilà et al., 2003). Both the diversity and the identity of species are known to influence ecosystem processes; complementarity (Tilman, 1988) and selection effects (Loreau, 2000) are the key mechanisms underpinning these relationships. In theory, diverse forest stands ⇑ Corresponding author. Tel.: +49 341 9738576; fax: +49 341 9738549. E-mail addresses: [email protected] (S. Ratcliffe), frederic. [email protected] (F. Holzwarth), [email protected] (K. Nadrowski), [email protected] (S. Levick), [email protected] (C. Wirth).

have a higher productivity due to species-specific differences in, for example, phenology or root architecture, so that interspecific competition is less intense than intraspecific (Kelty, 1992; Pretzsch and Schütze, 2009), or due to facilitation where positive interspecific interactions promote species’ performance (Cardinale et al., 2002). Diverse forests are also more likely to contain highly productive tree species that come to dominate, and most influence, community-level processes (selection effect: Loreau, 2000). A fundamental aspect of the selection effect is that it is the identity of the dominant species that most drives community-level processes. The extent to which complementarity and species identity control tree productivity has received relatively little attention in studies in natural and near-natural forests, and is a focus of this study. Current knowledge on biodiversity–productivity relationships in forest ecosystems stem from three approaches (classic forestry trials, experiments and observational studies), each with their own advantages and disadvantages with respect to resolving mechanisms and stand level representation (Baeten et al., 2013). Classic forestry trials explore the productivity of planted mixtures (Pretzsch, 2005). Their plot sizes are typically at a scale relevant for management but the focus is on a few selected merchantable tree

http://dx.doi.org/10.1016/j.foreco.2014.09.032 0378-1127/Ó 2014 Elsevier B.V. All rights reserved.

75

226

S. Ratcliffe et al. / Forest Ecology and Management 335 (2015) 225–234

species and diversity gradients are short (rarely more than 2 species). More recent biodiversity-ecosystem functioning experiments maximise the diversity gradient and avoid species identity effects by randomly selecting species from a large pool (Bruelheide et al., 2014; Scherer-Lorenzen et al., 2007). However, the plots are typically small (0.2 ha) and the trees are still young ( 2). Target species

Mnull

Mdiversity

Mconspecific

Mspecies

Ash

AIC R2

33.151 0.220

31.18 0.220

31.97 0.211

33.50 0.230

Beech

AIC R2

15023.78 0.466

15032.04 0.471

15034.79 0.472

15038.83 0.472

Hornbeam

AIC R2

459.52 0.171

463.78 0.195

462.87 0.209

450.59 0.231

78

229

S. Ratcliffe et al. / Forest Ecology and Management 335 (2015) 225–234

Table 4 Summary of the coefficients for the final model for ash (Mnull) and beech (Mspecies). The models predict the annual d.b.h. growth of individual trees. Predictor variables were centred and scaled, meaning that a one-unit change in each parameter (apart from the intercept) corresponds to a change in growth of one standard deviation. Coefficient

Estimate

Std. error

p-value

% variance explained

Estimate

Ash (Mnull) Intercept bd1 bd2 bnci bnci.beech bnci.ash bnci.acer bnci.hornbeam bdiv bvit belevation bwetness index

Std. error

p-value

% variance explained

0.140 0.145 0.024

0.006 0.002 0.001

2 indicates a more parsimonious model. For the three species the fixed radius method was the most suitable. For ash the selection of neighbouring trees of the same, or greater, canopy dominance was the most appropriate neighbourhood selection method, whilst the inclusion of all neighbouring trees was the most suitable for target beech and hornbeam trees. Species

Zone of influence

Ash Beech Hornbeam

Fixed radius

All trees

Larger trees

Radius (m)

All trees

Larger trees

13.67 14032.82 431.76

31.14 13745.26 431.75

20 15 15

8.7 14095.11 449.77

31.18 13740.42 433.42

Table A6 AIC values of the plot-level GLS spatial model testing each species identity effect (bid). Model selection was based on AIC comparison where a DAIC > 2 indicates a more parsimonious model. The presence of ash trees in the plot, as a factor present/absent, was also tested as an identity effect. The null model, with no identity or diversity effects, is included for comparision.

Table A3 AIC comparison of spatial and non-spatial GLS models (Mdiversity). The p-value is the probability from a likelihood ratio test. An exponential correlated error term was used for all the species. Species

Non-spatial

Spatial

P(t)

Ash Beech Hornbeam

31.18 14095.11 449.77

29.50 15032.04 463.78

0.313