Biodiversity and persistence of ecological communities in variable environments

ecological complexity 5 (2008) 99–105

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Biodiversity and persistence of ecological communities in variable environments Charlotte Borrvall, Bo Ebenman * Department of Biology, IFM, Linko¨ping University, S-581 83 Linko¨ping, Sweden

article info

abstract

Article history:

Recent analyses of climate data indicate that the intensity and frequency of different

Received 2 February 2007

weather extremes have increased. Such increased environmental variability may lead to

Received in revised form

increased species extinction rates and hence have important consequences for the long-

26 June 2007

term persistence of ecological communities. Here we use model communities in order to

Accepted 28 June 2007

investigate the relationship between species richness and community persistence in a

Published on line 19 March 2008

fluctuating environment. We model two scenarios: (1) correlated species responses to environmental fluctuations and (2) uncorrelated (independent) species responses. We

Keywords:

quantify the risk and extent of species extinctions using the so-called community viability

Biodiversity

analysis. It is shown that species-rich communities are more sensitive to environmental

Community persistence

stochasticity than species-poor communities. Specifically, per species risk of extinction is

Ecological community

higher in species-rich communities than in species-poor ones. Moreover, for a given species

Environmental stochasticity

richness, communities with uncorrelated species responses to environmental variation run

Extinction

a considerable higher risk of losing a fixed proportion of species compared with commu-

Risk assessment

nities with correlated species responses. We discuss the compatibility of these results with the ecological insurance hypothesis. # 2008 Elsevier B.V. All rights reserved.

1.

Introduction

Analyses of climate data indicate that the intensity and frequency of weather extremes have increased (Boyce et al., 2006; Easterling et al., 2000; Meehl and Tebaldi, 2004; Hoyos et al., 2006; Goswami et al., 2006). How will such an increasingly variable environment affect the long-term persistence of species in ecological communities? Theory suggest that the extinction risk of a species will depend both on its intrinsic sensitivity to environmental variation and on its interactions with other species, that is, on the trophic structure of the community where it is embedded (Xu and Li, 2002; Ripa and Ives, 2003; Ives and Cardinale, 2004; Sabo, 2005; Brassil, 2006; Jonsson et al., 2006). Moreover, owing to interdependences among species in ecological communities the loss of one species could lead to a cascade of secondary

extinctions (Paine, 1966; Estes and Palmisano, 1974; Pimm, 1979; Borrvall et al., 2000; Dunne et al., 2002; Ebenman et al., 2004; Ebenman and Jonsson, 2005; Eklo¨f and Ebenman, 2006). Hence, increased environmental variability might have potentially dramatic consequences for the robustness and functioning of the communities (see Chapin et al., 2000; Balvanera et al., 2006 for reviews). It has been argued that biodiversity can act as insurance against environmental fluctuations (Walker, 1992; Naeem, 1998; Yachi and Loreau, 1999; Elmqvist et al., 2003; The´bault and Loreau, 2005). If species with similar functional roles respond differently to environmental perturbations (response diversity) theory predicts that the temporal variability in aggregate community properties (such as total biomass) should decline with increasing species richness (Yachi and Loreau, 1999; Ives et al., 1999, 2000). Adding more species to a

* Corresponding author. E-mail addresses: [email protected] (C. Borrvall), [email protected] (B. Ebenman). 1476-945X/$ – see front matter # 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ecocom.2008.02.004

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ecological complexity 5 (2008) 99–105

community increases the probability of finding tolerant species (insurance hypothesis) and species-rich communities could therefore be able to cope with environmental fluctuations in a better way than species-poor ones. Theoretical studies of ecological communities in variable environments have shown that communities with a higher number of species often are more stable in the sense of having lower variation in combined biomass even though variation in biomass of individual species may increase with increasing species richness (May, 1974; Tilman, 1996; Hughes and Roughgarden, 2000; Lehman and Tilman, 2000; Ives and Hughes, 2002). A few experimental studies have supported these predictions showing negative relationships between species number and the variability of ecosystem processes (McGrady-Steed et al., 1997; Naeem and Li, 1997; Morin and McGrady-Steed, 2004; Steiner et al., 2006). Earlier theoretical studies of the relationship between biodiversity (species richness) and community variability have assumed low environmental variation. More specifically, they have investigated the variability in species and community biomass for persisting communities, rather than having explored how environmental fluctuations might change the composition of a community. In other words, it is assumed that no species goes extinct. As environmental variance increases, the probability of species extinction increases (May, 1973; Lande, 1993). It is therefore important to explore the risk and extent of extinctions in ecological communities subjected to a more highly variable environment. To our knowledge there are no theoretical studies that explicitly have investigated the relationship between species number and community persistence in fluctuating environments. Here we use model communities in order to explore how biodiversity (species number) affects the persistence of ecological communities in a stochastic environment. We focus on the effects of environmental stochasticity (demographic stochasticity is treated implicitly). We model two scenarios, one in which species are assumed to respond similarly (i.e., in a correlated way) to environmental fluctuations, and one in which species are totally uncorrelated in their responses. We show that the risk and extent of extinctions is higher in species-rich than in species-poor communities, specifically, the per species risk of extinction increases with increasing species number. Further, there is a much higher risk of extinction when species respond independently to environmental fluctuations than when they respond in a correlated way.

links divided by the number of species raised to two) is kept constant at C = 0.11, which is within the range observed for real food webs (Dunne et al., 2002). Links are distributed randomly but within certain constraints. Basal species are allowed to exist without having predators preying upon them. Consumers, on the other hand, cannot exist without at least one prey. An herbivore feeds on at least one basal species and a carnivore feeds on at least one herbivore. Carnivores could also feed on basal species (carnivores are potentially omnivorous). The generalized Lotka-Volterra model with stochasticity is used to describe community dynamics: 0 1 s X dNi ¼ Ni @bi ðtÞ þ a˜ i j N j A for i ¼ 1; . . . ; s dt j¼1 where dNi/dt is the rate of change of density of species i with respect to time in a community with s species, bi(t) is the intrinsic per capita growth (mortality) rate for basal (consumer) species i at time t, and a˜ i j is the per capita effect of species j on the per capita growth rate of species i. We use type 2 functional response in which: 8 a˜ i j ¼ ai j ; j 2 LðiÞ; > > > > hi j ai j > < a˜ ¼  P ; j 2 CðiÞ; ij 1 þ T n 2 Rð jÞ hn j an j Nn > > h ji a ji > > > P ; j 2 RðiÞ: : a˜ i j ¼ e 1 þ T n 2 RðiÞ hni ani Nn Here hij is the preference of predator j for prey i, aij is the intrinsic attack rate of predator j on prey i, T is the handling time needed for the predator to catch and consume the prey, and e is a measure of conversion efficiency, that is, the rate at which resources are converted into new consumers. L(i) is the set of species belonging to the same trophic level as species i, C(i) contains the species that consume species i, and R(i) contains the species being resources to species i. All species have intra-specific competition, given by aii, and basal species also have interspecific competition, given by aij. We have chosen to incorporate environmental stochasticity as white noise (i.e., no serial correlation) in the per capita species growth rates, bi, given by: bi ðtÞ ¼ b¯i ð1 þ ei ðtÞÞ Here b¯i is the mean value of the per capita growth rate of species i and ei(t) is a stochastic process given as ei ðtÞ ¼ eik ; k  t < k þ 1 for k ¼ 0; 1; . . .

2.

Model and methods

We consider triangular food webs (decreasing number of species with increasing trophic level) with three trophic levels: basal species, herbivores and carnivores. We vary the number of species in the webs, allowing there to be 6, 9, 12 or 15 species. The smallest web contains three basal species, two herbivores and one carnivore. Web size is increased one step by adding three more species, one at each level, resulting finally in the 15 species web containing 6 basal species, 5 herbivores and 4 carnivores. Connectance (C = L/S2, number of

and eik are independent and uniformly distributed stochastic variables in the interval [1.3, 1.3]. This corresponds to a variance in e of 0.563, a variance that is higher than that used in most earlier theoretical studies. We use a high variance compared to earlier studies because the aim of our study is to investigate how communities respond to an increasingly variable environment. Only basal species experience stochasticity and we analyze two scenarios: (1) species respond to environmental fluctuations in the same way (perfect positive correlation) and (2) species respond independently (correlation equals zero). The second scenario – independent

ecological complexity 5 (2008) 99–105

responses of species to environmental fluctuations – might seem unrealistic. However, this scenario has been analyzed in earlier studies (Yachi and Loreau, 1999; Ives et al., 1999, 2000; Hughes and Roughgarden, 2000; Ives and Hughes, 2002) and in order to be able to compare our results with results from these earlier studies we have chosen to include this scenario in our analysis. In order to achieve some generality we generate a large number of replicate communities in which model parameters are sampled from predefined distributions (see below). We keep generating replicates until 500 ‘persistent’ deterministic replicate communities have been found. Communities are considered persistent if all species densities remain above a predefined threshold (see below) following numerical integration over 1000 time units using a deterministic model with per capita growth rates set to the mean values (as initial species densities we use the equilibrium densities of the corresponding system with type 1 functional response). In this way we check that the communities would be persistent in a deterministic setting (constant environment). Then, for each of the 500 persistent deterministic replicate communities environmental stochasticity is added to all basal species in the community and the system is then integrated over 25,000 time units. During the integration all species are checked for extinction. Demographic stochasticity is not treated explicitly. Instead we implicitly include demographic stochasticity by defining absolute extinction thresholds below which species are considered extinct. The threshold densities used are 2  102 for basal species, 104 for herbivores and 105 for carnivores. These extinction thresholds are approximately two orders of magnitude smaller than the equilibrium densities of the respective species categories in six-species communities (for plants somewhat higher). Of course, species extinction risks will depend on the size of the extinction thresholds, so if thresholds are high extinction risks will be high. However, here we are not primarily interested in predicting absolute extinction risks, rather we are interested in relative extinc-

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tion risks for different scenarios (species-rich vs. speciespoor communities; correlated vs. uncorrelated species responses). We record the time of each extinction event and quantify the risk and extent of extinctions in differentsized communities using the so-called risk curves. The risk curves show the probability that the number of species (or fraction of species of the original community) remaining will fall down to or below a certain level within a given period of time (see Ebenman et al., 2004). We also calculate the per species probability of extinction for species at different trophic levels. Model parameters were chosen as follows. For basal species mean intrinsic growth rate, b¯i , is set to 1. For consumers mean intrinsic mortality rate, b¯i , is randomly drawn from the uniform distribution [0.01, 0]. Mortality rates for consumers are sorted, resulting in lower carnivores compared with their prey hrates for i i:e:; absðbherbivore Þ > absðbcarnivore Þ . This is because body size often increases with trophic level (Jonsson et al., 2005), and larger body sizes often confer lower mortality rates (Roff, 1992). The strength of intra-specific competition is set equal to 1 for all basal species. The strength of interspecific competition among basal species is drawn at random from the uniform interval [0.7, 0.3]. Each predator has a maximum prey preference equal to 1 (meaning that predators with only one prey has hij = 1). Predators with several prey species are assumed to have a high preference (0.9) for one of their prey species (assigned randomly) and equal lower preferences (0.1 shared equally among the rest of the prey) for the others. High preference for one prey will on average lead to a skew distribution of per capita interaction strengths, reflecting a pattern found in natural communities (see Wootton and Emmerson, 2005 for a review). For each consumer–prey interaction the intrinsic attack rate, aij, is taken at random from the uniform distribution [0, 1]. Handling time, T, is assumed to be the same for all consumers on all prey and is given the value of 0.01. Conversion efficiency, e, is set to 0.2 for

Fig. 1 – Risk curves for communities with different number of species showing the probability that the post-extinction community will contain =s species. Number of species in original communities varies from 6 to 15. Circles, 15 species; triangles, 12 species; squares, 9 species; diamonds, 6 species. The length of the vertical dashed lines shows resistance against extinctions. (a) Correlated response scenario; (b) uncorrelated response scenario.

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ecological complexity 5 (2008) 99–105

Table 1 – Risk and number of extinctions for different-sized communities for the correlated response scenario (and the uncorrelated response scenario) Species number

6

9

12

Probability of at least one extinction Mean number of extinctions

0.12 (1.0) 0.27 (4.02)

0.43 (1.0) 1.02 (6.52)

0.73 (1.0) 2.22 (9.07)

0.95 (1.0) 3.96 (11.63)

Per species extinction risk Overall Basal Herbivore Carnivore

0.045 0.042 0.057 0.028

0.11 0.12 0.12 0.08

0.18 0.20 0.20 0.14

0.26 0.30 0.29 0.18

(0.67) (0.67) (0.70) (0.62)

links between adjacent trophic levels (e < 1 when the size of the consumer is larger than that of its prey). Omnivory links are assumed to be less efficient and we therefore use e = 0.02 for these links. The intervals for the parameters in the present study are similar to the ones used and motivated in earlier theoretical studies of food webs (see Borrvall et al., 2000; Borrvall and Ebenman, 2006; Ebenman et al., 2004).

(0.72) (0.75) (0.73) (0.67)

(0.76) (0.80) (0.75) (0.69)

3.

Results and discussion

3.1.

Risk and extent of extinctions

15

(0.78) (0.83) (0.76) (0.71)

Risk and extent of species extinctions differs between species-rich and species-poor communities and between the scenarios of correlated and uncorrelated responses of species to environmental fluctuations. For the correlated

Fig. 2 – Risk curves for communities with different number of species showing the probability that the proportion of species of the original community remaining in the post-extinction community will be =s/so, where so is the number of species in the original community. Number of species in original communities varies from 6 to 15. Circles, 15 species; triangles, 12 species; squares, 9 species; diamonds, 6 species. (a) Correlated response scenario; (b) uncorrelated response scenario; (c) comparison of the 15-species communities from the two scenarios (solid circles, correlated response scenario; open circles, uncorrelated response scenario).

ecological complexity 5 (2008) 99–105

response scenario the probability that at least one species goes extinct increases with species richness meaning that community resistance decreases with species richness (vertical dashed lines in Fig. 1a, Table 1). For the uncorrelated response scenario resistance is zero for all webs (Fig. 1b, Table 1). The average number of extinctions increases with species richness in both scenarios (Table 1). Moreover, species-rich communities run the risk of losing a greater proportion of species compared with species-poor communities (Fig. 2a and b). In other words there is a higher per species extinction risk in larger webs than in smaller ones (Table 1). There may be several reasons why the rate of species extinction increases with species richness in a stochastic environment. First, theory suggests that variation in species abundances increases with increasing species richness, at least in competition communities (May, 1973, 1974; Tilman, 1999). Increased variance in abundance is likely to lead to increased extinction risk (e.g., Lande, 1993). Second, densities of species are on average lower in species-rich communities than in species-poor communities (Fig. 3). Such density compensation has also been found in real communities (see McGrady-Steed and Morin, 2000). Hence, densities of species in species-rich communities lie closer to the extinction threshold from the start and are therefore likely to reach this threshold faster than species in species-poor communities with higher population densities. Thus, this negative relationship between population sizes and species diversity makes species-rich communities more vulnerable to environmental stochasticity. For a given species richness, communities with uncorrelated species responses run a considerable higher risk of losing a fixed proportion of species compared with communities with correlated species responses (Fig. 2a–c, Table 1). Thus, the average number of extinctions as well as the per species extinction risk are significantly higher in the uncorrelated response scenario. Extinctions occur from all trophic levels with a somewhat higher risk for species at lower trophic levels (Table 1). Why are extinction rates higher when species responses to environmental fluctuations are uncorrelated? The most likely reason is that the

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Fig. 3 – Species densities in communities with different number of species at t = 0 (note log-scale of y-axis). Diamonds, basal species; squares, herbivores; triangles, carnivores.

variance in the densities of individual populations increases with decreasing degree of correlation (May, 1973; Ives et al., 2000). It is interesting to contrast this finding with the prediction of the insurance hypothesis (Walker, 1992; Yachi and Loreau, 1999; Ives et al., 1999, 2000; Elmqvist et al., 2003). This hypothesis states that if species respond differently to environmental fluctuations, that is, in an uncorrelated way, the variation in the combined densities of all species should decrease with increasing species richness. Our study indicates that this positive effect of species richness on community-level stability may be offset by a high risk of extinction in species-rich communities when environmental variation is large and species respond to this variation in an uncorrelated way.

Fig. 4 – (a) Time to primary extinction for communities with different number of species (note log-scale of y-axis). (b) Time between first and last extinction (based on median values of all replicates in which at least two extinctions occurred). Solid circles, correlated response scenario; open circles, uncorrelated response scenario.

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3.2.

ecological complexity 5 (2008) 99–105

Time to and order of extinctions

The time to the first extinction event (primary extinction) decreases with increasing species number (Fig. 4a). This is probably due to the negative relationship between species richness and species abundances (Fig. 3) (see above). Irrespective of species richness it is always a basal species that goes extinct first, thereby unleashing the extinction cascade that often follows. It would be interesting to further investigate the risk and pattern of such extinction cascades in communities with different number of species. Earlier studies of the response of communities in constant (deterministic) environments to species loss suggest that top-down and bottom-up extinction cascades are more likely to occur in species-poor than in species-rich communities (Ebenman et al., 2004). Time elapsed between the first and the final extinction (calculated from those replicates showing at least two extinctions) increases with species richness (Fig. 4b). This is in line with an earlier study showing that time to secondary species extinctions, following initial deletion of one species, increases with species richness (Borrvall and Ebenman, 2006). Time to primary species extinction is substantially shorter when species show uncorrelated response to environmental fluctuations compared with the case of correlated species response (Fig. 4a). Time between first and last extinction is, on the other hand, longer for the uncorrelated species response scenario compared with the correlated species response scenario (Fig. 4b).

4.

Future directions

In this study we assume that the relative response range is the same for all basal species, that is, all basal species are equally sensitive to environmental fluctuations. It would be interesting also to study the scenario in which the stochastic terms are drawn from different intervals for the different species. It might be the case that the range of tolerances among species is larger in species-rich than in species-poor communities. Thus, it might be more likely that species-rich communities contain species that are tolerant (less affected) to different kinds of environmental fluctuations. On the other hand, they might also contain species that are more sensitive to environmental fluctuations. We have chosen to incorporate stochasticity in the growth and mortality rate of species. Environmental variation might also affect per capita interaction strengths. The consequences of variable interaction strengths on community stability deserve further study (see Navarrete and Berlow, 2006). Recent theoretical work on multitrophic communities suggests that the relationship between diversity and mean trophic interaction strength can have important effects on the relationship between diversity and temporal variability of total biomass of the different trophic levels (The´bault and Loreau, 2005). It would be interesting to further study the impact of mean strength of trophic interactions on the persistence of multitrophic communities in variable environments.

Acknowledgements We thank Maria Christianou for valuable discussions. B.E. is also grateful to the organizers and participants of the interesting workshop ‘‘Advances in Food-Web Theory and its Applications to Ecological Risk Assessment’’ in Yokohama, 12–14 September 2006, for stimulating discussions and great hospitality. The research was funded by the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning.

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