Assessing competition intensity along productivity ... - UBC Botany

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Assessing competition intensity along productivity gradients using a simple model Ken Arii and Roy Turkington

Abstract: One of the most highly debated issues in plant ecology has been the manner in which competition intensity changes along productivity gradients. We have used a simple model to attempt to demonstrate that in theory, competition intensity can vary quite considerably along productivity gradients. Our model incorporates three key components: (i) changes in resource availability along a productivity gradient, (ii) changes in resource availability when neighbours are removed, and (iii) growth characteristics of the target species and (or) individuals to varying resource levels (i.e., response surface). Variation and interactions among these three components can potentially give rise to various, and occasionally complex, changes in competition intensity along productivity gradients. This partly explains the divergent, and sometimes contradictory, results reported in previous studies. Key words: competition intensity, productivity gradient, nutrient, light, model. Résumé : Une des questions les plus débattues en écologie végétale est de savoir comment l’intensité de la compétition change le long de gradients de productivité. Les auteurs ont tenté de démontrer que l’intensité de la compétition peut théoriquement varier considérablement le long de gradients de productivité, en utilisant un modèle simple. Ce modèle, développé par les auteurs, incorpore trois composantes critiques : (i) les changements dans la disponibilité des ressources le long du gradient de productivité; (ii) les changements de disponibilité des ressources lorsque les voisins sont éliminés; et (iii) les caractéristiques de croissance des espèces et (ou) individus ciblés, par rapport à des variations dans l’abondance des ressources (i.e. surface de réaction). La variation et les interactions de ces trois composantes pourraient vraisemblablement donner naissance à des changements variés, et complexes à l’occasion, dans l’intensité de la compétition le long de gradients de productivité. Ceci explique en partie les résultats divergents et parfois contradictoires rapportés dans des études précédentes. Mots clés : intensité de la compétition, gradient de productivité, nutriments, lumière, modèle. [Traduit par la Rédaction]

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Introduction One of the most highly debated issues in plant ecology has been the manner in which competition intensity (CI) changes along productivity gradients. Grime (1973, 1977, 1979) argued that CI should be highest in the most productive environments, while Newman (1973) and Tilman (1988) argued that CI should remain high and relatively constant at all points along a productivity gradient. A number of studies have demonstrated support of Grime’s predictions (Wilson and Keddy 1986; Gurevitch 1986; Gurevitch and Unnasch 1989; Reader and Best 1989; Reader 1990; Campbell and Grime 1992), while other studies have supported Tilman’s predictions (Fowler 1990; Goldberg and Miller 1990; Wilson Received June 27, 2001. Published on the NRC Research Press Web site at http://canjbot.nrc.ca on December 18, 2001. K. Arii.1 Department of Biology, McGill University, 1205 Avenue Docteur Penfield, Montréal, QC H3A 1B1, Canada. R. Turkington. Department of Botany, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada. 1

Corresponding author (e-mail: [email protected]).

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and Shay 1990; Wilson and Tilman 1991, 1993; Turkington et al. 1993; Wilson 1993; Belcher et al. 1995). Attempts have been made to clarify these conflicting results (Grace 1993; Markham and Chanway 1996), but they have not led to any definitive conclusions. In addition, recent studies have shown inconsistencies with respect to both hypotheses. For example, in an experiment carried out in a desert ecosystem, competition was found to be most intense in the lowest productivity habitats (Goldberg et al. 2001). In addition, Miller (1996) showed experimentally that CI may increase or decrease along a nutrient availability (i.e., productivity) gradient depending on the range of nutrients used in the experiment. Thus, no general relationship between CI and productivity gradient has been established to date. However, a recent meta-analysis (Goldberg et al. 1999) demonstrated that the relationship between CI and productivity is frequently negative. In addition, the effect of other factors, such as herbivory, has been proposed as a possible reason for the variety of results reported in previous studies (Goldberg et al. 1999; Van der Wal et al. 2000). Although other factors may indeed be contributing to the variation in experimental

DOI: 10.1139/cjb-79-12-1486

© 2001 NRC Canada


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Fig. 1. Three possible types of change in resource availability along productivity gradients. The solid line represents light availability and the dotted line represents nutrient availability. Functions for each of the three patterns are given in Table 1. See text for details. a)

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For each of the model components, we used several hypothetical functions. These functions are simplistic and do not represent any particular species or system, but they are nevertheless somewhat realistic, and provide insight into how the variation and interactions of these functions could influence CI along productivity gradients.

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The general method used to detect competition in field experiments is to remove one or several plant species or individuals and then measure the response of the remaining species or individuals (reviewed in Goldberg and Barton 1992). One can apply this method at several different productivity levels and assess the changes in CI along the productivity gradient. In this context, a productivity gradient is defined as a gradient of habitats from areas having low soil resource levels, low plant biomass, and high penetration of light to the soil surface, to areas with high soil resource levels, high plant biomass, and low penetration of light to the soil surface (sensu Tilman 1988, p. 6). When this method is applied, there are three key factors that have the potential to influene the outcome: (i) changes in resource availability along the productivity gradient, (ii) changes in resource availability when neighbours are removed, and (iii) the response of target plants to changes in resource availability. In our simulated model, we used three hypothetical species as targets to investigate changes in CI along a productivity gradient. Specifically, we first modeled changes in resource availability experienced by the three hypothetical species along a productivity gradient, as well as changes in resource levels when neighbours were removed. Using species-specific response surfaces, we then calculated biomass before and after neighbour removal at each productivity level for each of the hypothetical species. These biomass values (before and after neighbour removal) were then used to calculate CI at different points along the productivity gradient. In all cases, we calculated both the absolute competition intensity and the relative competition intensity to calculate our CI values. There were very few differences between them, so in all cases we present relative CI values (see Grace 1995).

Model description

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results, in this paper we attempt to show that in theory, CI can vary considerably along productivity gradients, without invoking other factors. We use a simple model to demonstrate this, and our results could reconcile some of the conflicting results reported in previous studies. It should be emphasized that the model is not intended to represent any specific cases (e.g., species or systems). Rather, it is used to demonstrate how variation and interactions among the key model components can profoundly influence the way CI changes along productivity gradients.

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According to the definition by Tilman (1988), availability of soil resources (nutrients) increases along a productivity gradient, while light availability decreases. Because the rate of change in resource availability along productivity gradients may differ depending on the composition, abundance, and characteristics (e.g., maximum growth rate, carbon allocation pattern, and form) of species present in the surroundings, we generated three possible types of change in resource availability that a target individual experiences along a productivity gradient (Figs. 1a–1c). For each of the three types we used, nutrient availability increases along the productivity gradient, while light availability decreases, and the nutrient and light availabilities at the lowest (0) and highest (10) productivity for each type are the same (Figs. 1a–1c). Thus, differences among the three types are ob© 2001 NRC Canada



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Table 1. Functions used in the model. Model components

Fig. 2. Response surfaces of three hypothetical species. Values on the response surfaces are biomass. The functions for each of the three surfaces are given in Table 1.

Simulated function

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 L N L N B = 15 .   − 0.5   15 .   − 0.5   10 10 10       10        3N    3L    B = 1 − exp  −   1 − exp  −   7   7       L  3     N  3  B = 1 − exp  −3    1 − exp  −3      5      5         

Note: B, biomass; L, light availability; Lnp, light availability with neighbours present; N, nutrient availability; Nnp, nutrient availability with neighbours present; Nna, nutrient availability after neighbour removal; P, productivity level. *0 ≤ L ≤ 10; 0 ≤ N ≤ 10.

served in the rates at which the nutrient and light availabilities change along the gradient. The equations that define these changes in resource availability are given in Table 1. In the real world, patterns of resource increase or decrease are likely to be numerous, depending on the neighbouring species’ composition, abundance, and characteristics; thus, there is no reason that the maximum value of resource availability should be 10 or that the change in availability of the two resources should be symmetric along the productivity gradient. Nonetheless, the three functions provide a somewhat realistic variation and allow us to examine how this variation may affect changes in CI along productivity gradients.

Changes in resource availability after neighbour removal When neighbours are removed, resources used by those neighbours then become available to a target individual, and light availability reaches the maximum value of 10. For nutrient availability, we used four different types of release functions (Table 1) because the degree to which released nutrients will be available to a target individual may differ depending on factors such as soil characteristics (e.g., leaching, adsorption: Ellis and Mellor 1995) and microbial activity (competition for released nutrients: Vitousek and Matson 1985). Release function 1 represents the base line, with no changes in nutrient availability after neighbour removal at any productivity level, while release functions 2–4 show increasing degrees of nutrient release. There is very little information in the literature on how the removal of neighbours influences resource (nutrient) availability (Goldberg 1996). The functions in Table 1 are quite simplistic and may not apply in some systems; however,

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Nutrient availability they serve our goal of providing variation and allow us to examine how variation in nutrient release patterns may affect changes in CI along productivity gradients. © 2001 NRC Canada



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Response of target individuals to changes in resource availability The last component in the model is the response of target individuals to changes in resource availability (i.e., response surface). We created three hypothetical response surfaces to varying levels of nutrients and light (Fig. 2). All three modeled species show increases in biomass as nutrient and light levels increase, but no inhibitory effects such as toxicity or photoinhibition are considered. Obviously, the response surface will have a much larger variation in the real world and could have as many variations as there are species. For all three hypothetical species in our model, the maximum attainable biomass is 1.0 (Table 1).

Calculating CI along a productivity gradient By combining the three components of the model we can calculate how CI changes along productivity gradients. Using the response surfaces, we can calculate the biomass of each species at each productivity level (i.e., resource level) before and after neighbour removal. Using these biomass values, we can then calculate CI along gradients at each productivity level using the formula:

CI =

Bna − Bnp Bna

where Bna is the biomass with neighbours absent and Bnp is the biomass with neighbours present (Grace 1995; Miller 1996). The CI values can then be then plotted against habitat productivity to examine trends in CI.

Results and discussion Based on the functions we used in the model, it is clear that there is profound variability in the way CI changes along productivity gradients (Fig. 3). All three modeled components have notable effects on CI values, but their influence depends on the combination of functions used. For example, differences in species’ response surfaces affect how CI values change along a gradient in certain combinations (e.g., Fig. 3e), but in other cases they do not influence the changes to the same extent (e.g., Fig. 3a). Some combinations of model functions show increasing CI values (e.g., Figs. 3a–3c) along the productivity gradient as predicted by Grime (1977, 1979), and other combinations show relatively consistent and high CI values (e.g., Figs. 3f and 3i) along the gradient as predicted by Newman (1973) and Tilman (1988). Figure 3 also illustrates the potential importance of the range of the productivity gradient assessed in the outcome of field experiments (Belcher et al. 1995; Miller 1996). In some instances (e.g., Figs. 3e and 3g; dotted line), depending on the range of the productivity gradient used, we may observe an increase or decrease in CI, or we may be able to detect both a decrease and an increase along the gradient. Similarly, if field experiments are conducted at only a few productivity levels, we can incorrectly interpret the changes in CI values along productivity gradients. For example, if we were to choose the three productivity levels represented by the dots in Fig. 3k, we would incorrectly conclude that CI is relatively high and consistent along the gradient. It should be noted that although most of the graphs in Fig. 3 show increasing CI values along the gradient, this is only a reflection of the hypothetical functions we used in this study. It does not mean that CI increases along the pro-

ductivity gradient in most cases. Moreover, depending on the functions used, and particularly if the nutrient release function is modeled so that nutrient availability decreases when neighbours are removed, we may actually observe a positive effect (facilitation) by the neighbouring species (Bertness and Callaway 1994). Although our simulations modeled the total removal of neighbours, they could also have modeled the partial removal of neighbours, as is done in many field experiments. In our model, this would have been made possible by assigning a function to describe how light intensity would change after the partial removal of neighbours. (Unlike the nutrient release function, there are some restrictions because the light intensity after neighbour removal cannot exceed the maximum light intensity of 10.) With the current functions used in the model, incorporating partial removal would have resulted in lower CI values at higher productivity levels. However, the partial removal of neighbours could give rise to considerably different patterns depending on how the other components are modeled. The variables used to construct the response function may also have a significant impact on the outcome of experiments (Belcher et al. 1995; Goldberg and Novoplansky 1997). In past studies, various characteristics were used to measure the response of targets after neighbour removal (e.g., biomass (Wedin and Tilman 1993), tiller production (DiTomasso and Aarssen 1991), shoot growth (Shevtsova et al. 1997), and percent cover (Jonasson 1992)). Even for a single target species, the response surface for each of these characteristics is likely to be different. Therefore, the characteristics measured may influence the outcome of competition studies. With this simple model, we have shown that in theory, variations and interactions among key model components can give rise to complex changes in CI along productivity gradients. These changes are a consequence of dynamic interactions between target individuals, neighbours, and resources. Thus, the divergent results reported in previous studies may be explained by considering the three model components simultaneously. The sets of functions used in this study are not representative of any particular species or system, but they are nevertheless reasonable. The emphasis in this study was not on the way each form of the functions influences CI, but rather on the way the variations and interactions of the functions give rise to changes in CI along productivity gradients. While it would be possible to apply this model to real systems, we currently lack appropriate empirical data that could be readily used to produce accurate functions (especially nutrient release functions and the changes in resource availability along productivity gradients) and to determine combinations of accurate functions for each component. Sets of functions used as model components are expected to be quite variable depending on the species or system used. To assess the validity of this model in a real system, preliminary experiments must first be conducted to construct the functions of the model, run it, and then compare it with the results of an actual competition experiment, preferably carried out in various systems. Such experiments may help us to better understand the mechanism behind CI changes along productivity gradients. © 2001 NRC Canada



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Fig. 3. Changes in competition intensity (CI, y axis) along productivity gradients (x axis). The broken lines represent species type 1; the solid lines represent species type 2, and the dotted lines represent species type 3. Each column of graphs represents different types of changes in resource availability, and each row of graphs represents the different types of nutrient release functions. The three circles in graph k represent hypothetical productivity levels. See text for details.

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Acknowledgements

References

This research was funded by Government of Canada (Department of Foreign Affairs and International Trade) Awards to K.A. and a Natural Sciences and Engineering Research Council of Canada operating grant to Martin J. Lechowicz. We are grateful to Mike Treberg for helpful comments on an earlier version of this manuscript.

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