Foraging Adaptation and the Relationship Between Food-Web Complexity and Stability

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Science  28 Feb 2003:
Vol. 299, Issue 5611, pp. 1388-1391
DOI: 10.1126/science.1079154


Ecological theory suggests that complex food webs should not persist because of their inherent instability. “Real” ecosystems often support a large number of interacting species. A mathematical model shows that fluctuating short-term selection on trophic links, arising from a consumer's adaptive food choice, is a key to the long-term stability of complex communities. Without adaptive foragers, food-web complexity destabilizes community composition; whereas in their presence, complexity may enhance community persistence through facilitation of dynamical food-web reconstruction that buffers environmental fluctuations. The model predicts a linkage pattern consistent with field observations.

Ecological theory (1–5) suggests that complexity (high species richness, dense trophic links) destabilizes food webs. “Real” ecosystems often support large numbers of species interacting in highly complex networks of direct and indirect pathways (6–9). To resolve this apparent paradox, several hypotheses have been proposed, including ones attributing “real” food-web stability to dominance of stabilizing food-web architecture (10, 11). These studies have considered relatively static topological food-web features such as distribution of interaction strength (10) and trophic links (11). I propose that “flexibility” in food-web structure, arising from the consumers' adaptive behavioral (12, 13) or evolutionary (14,15) switches in food choice in response to qualitative and quantitative resource changes, stabilizes complex food webs.

Adaptation is critical to food-web dynamics (16) and influences food-web stability (17). This study considers food-web models having more realistic and wide-ranging complexity, where the degree of flexibility is manipulated by systematically changing both the fraction of adaptive foragers and their adaptation rate. This provides a comprehensive picture of the synergistic effects of food-web complexity and adaptation on food-web stability.

Consider a food web comprising N species, any pair of which are connected to each other with probability C (≤1; connectance). In determining trophic link direction, I used two models, random (18) and cascade (4, 18), which generate different substructures (19). Suppose that consumers cannot consume different resource species simultaneously because of the prey's patchy distribution (12), the capturing strategy for different prey (12), or the consumer's sensory and cognitive constraints for discriminating between prey (20). Consumers allocate their foraging effort among possible resources and, given a fixed total foraging effort (measured by energy or time), per capita consumption rate would increase with increasing foraging efficiency and increased foraging effort allocated to the resource (21).

The dynamics of species i (1… N) biomass,Xi , is described by:Embedded Image Embedded Image Embedded Image(1)where ri is an intrinsic reproductive rate; si a self-regulation intensity; fij the foraging efficiency of species i on resource species j, defined as a per capita foraging rate when all foraging efforts are allocated to resource j; aij the foraging effort of species i allocated to resourcej Embedded Imagewhen species i does not feed on speciesj); and eij the metabolic rate of species i consuming species j. Hereafter, eij is, for simplicity, set to a biologically feasible (22, 23) constant value,e (here e = 0.15, but for e= 0.01 to 0.35 the value does not alter the main result).

I used community persistence, the probability that all species persist for a given time in fluctuating environments, as an index of food-web stability. As biological parameters change over space and time by environmental disturbances, the community persisting in the wider parameter region is more likely to be observed in nature (3). To estimate the effects of complexity on community persistence, I calculated the probability of community persistence in an ensemble of stochastically generated food-web models with varying complexity (N, C) (24). When species population density becomes very low (Xi < 10−13), the species is permanently removed, which represents extinction.

Consider an extreme case where a food web contains no adaptive foragers. As no individual species discriminate between resources, foraging efforts are equally allocated among all possible resource species [aij = 1/(the potential number of species i's resource species)]. Irrespective of the food-web model, persistence decreases with increasing species richness or connectance (Fig. 1, A, B, and G), agreeing with previous models (1–5) that use different stability indices and/or food-web structures. The negative effect of species richness on stability is detectable even if persistence is measured by a species' extinction probability [ln(persistence probability)/N], and results in rejection of the null hypothesis that ascribes this negative relationship to an increased number of species with the same extinction probability.

Figure 1

Relationships between food-web complexity and stability. (A to D) Complexity-stability relationship in food webs without (A, B) or with (C, D) adaptive foragers in random (A, C) and cascade (B, D) models. (E toI) Complexity-stability relationships with varying (E to G) fraction of adaptive foragers (F) or (E, H, and I) adaptation rate (G) in the random model. Parameters are (F, G) = (A, B) (0.0, 0.0), (C, D) (1.0, 0.25).

In reality, trophic link strength is not a fixed property. Consumers switch foraging behavior at individual levels (12,13, 25, 26) and foraging-related traits may evolve at population levels (14,27). In the presence of adaptive foragers, the observed connection probability {“realized connectance”; (total number of links)2/[N(N–1)]} can be smaller thanC (renamed “potential connectance”), as some potential resources may not be used. The dynamics of the foraging effort of an adaptive consumer i to resource species j(aij ) is given by (21): Embedded Image Embedded Image(2)where j is the potential prey of species i; Gi the adaptation rate of consumer i, which is higher when species change their diet behaviorally rather than evolutionarily, when the evolutionary speed is higher, or when the species that shifts its diet behaviorally has more detailed and complete information about resources or better information-processing ability (12). Eq. 2represents a simple food-choice rule that maximizes energy gain (21): a consumer species i increases its foraging effort allocated to resource j if resource profitability, energy gain per unit effort (eij fijXj ), is higher than the average profitability of resources that the consumer is currently foraging Embedded ImageIt will decrease its effort if profitability is lower than average. A consumer will only feed on the most profitable prey if adaptation is extremely rapid; slow adaptation leads to time delay in food choice and, in a fluctuating environment, may cause asynchrony between food choice and food profitability.

To investigate how adaptive food choice alters the complexity-stability relationship, consider a fraction, F, of randomly chosen species shifting their diet (Gi > 0), while the remaining fraction (1 – F) cannot (Gi = 0); for simplicity, adaptation rates are set to a constant (G). The population dynamics of such a food web is governed by combining population dynamics (Eq. 1) and adaptive dynamics (Eq. 2). With adaptive foragers, there is a critical level of complexity [the line along the diagonal ridge of parameter space of species richness and connectance (Fig. 1E)], where stability is prohibited below and promoted above by increasing complexity. With decreasing fraction of adaptive foragers, F (Fig. 1, E to G), or adaptation rate, G (Fig. 1, E, H, and I), the region of positive relationship decreases and the relationship becomes less clear. Regardless of model used, these outcomes were not altered qualitatively, which suggests that the robustness of the basic premise that increasing the fraction of adaptive foragers or their adaptive ability can turn negative complexity-stability relationships into positive ones.

The model predicts that realized connectance should depend on the observation time scale (28, 29). Suppose biological parameters change intermittently with sufficiently long intervals. Within a short time range, the realized connectance may be represented by a single parameter set. At this scale, complex food webs with adaptive foragers are characterized by a few strong (high foraging effort, aij ) and many weak (low foraging effort) links (Fig. 2A). This is a consistent pattern recorded from observations (6,30–32) of natural food webs. The realized connectance becomes upper-bounded (Fig. 2B) with increasing potential connectance (C), and its maximum level decreases with increasing fraction of adaptive forgers (F) (Fig. 2B). This pattern implies that adaptive foragers use only a part of their potential resources. At a longer time scale, environmental disturbances lead to fluctuating selection on interaction strength and consequently food-web reconstruction (Fig. 3, supporting online text). The realized connectance should increase with observation time as the probability of a potential link's activation increases and will approach potential connectance (C) when the observation period is infinitely long. This time scale–dependent linkage pattern indicates that high complexity affords food webs high “flexibility”; potential links are activated or inactivated while realized connectance is kept low in response to environmental changes and population fluctuations to enhance community persistence.

Figure 2

Short-term linkage patterns of food webs. (A) Frequency distribution of realized foraging efforts (aij ; in 1000 persistent communities) in food webs with adaptive foragers (F = 1.0). Parameters:N = 12, C = 1.0, G = 0.25, t = 105. (B) The effect of potential connectance (C) on the realized connectance (fraction of links with aij > 10−6 averaged over 100 simulations) of food web with low (circle; F = 0.5), intermediate (square; 0.75), and high (triangle; 1.0) proportion of adaptive foragers. Without adaptive foragers (F = 0.0), realized connectance ≡ potential connectance (dotted line). Parameters: N = 12,C = 1.0, G = 2.5,t = 105.

Figure 3

An example of long-term food-web dynamics. A random model with parameters N = 12, C= 1.0, F = 1.0, G = 0.025. Disturbance (indicated by red arrow at t = 2 × 105), which randomly changes parameters,ri and fi , leads to (A) population fluctuation accompanied by (B) dynamical changes in foraging efforts. Different colors represent (A) 12 species and (B) 66 trophic links between them. (C andD) Food-web architecture and interaction strength before (C,t = 2 × 105) and after (D,t = 2 × 106) the disturbance. Red and blue arrows are trophic links with foraging effort (aij ) of larger and smaller than 0.9, respectively. Thickness of arrows and circle sizes represent foraging efforts (aij ) and species densities (Xi ), respectively. Links with foraging efforts smaller than 0.1 are not depicted.

This mechanism demands sufficiently high adaptation speed to induce quick food-web reconstruction when disturbance takes place. Empirical evidence of fast evolution of foraging-related traits (14,15, 27, 33) indicates that evolution and population dynamics may overlap temporally. Changes in adaptive learning associated with foraging behavior is not restricted to higher animals but is frequently observed in arthropods (25,26), this suggests that behavioral diet shifts, which occur over shorter time scales than a generation, may be widespread to those taxa. Adaptive diet choice may potentially have a major influence on community dynamics. Precise empirical studies are required to test explicitly whether the dynamic changes in food-web linkage observed in nature (6, 28, 29,34) are attributed to adaptation.

This study has implications for conservation. Biodiversity loss effects on community stability will be influenced by the focal community's evolutionary history, as complexity-stability relationships depend on the developmental levels of foraging-adjustment ability that are shaped through natural selection (13). Introduced species, which do not share an evolutionary history with local organisms, can influence community stability in a manner different from that of resident species or populations. A positive relationship between species richness and community stability suggests that high biodiversity is self-sustaining. In such cases, losses of species may catalyze further losses for system instability and the effort required to prevent the next loss would increase as the number of loss increases. If present species diversity levels are maintained through natural selection on foraging behavior, the genetic structure of populations may influence community level dynamics through change in adaptation rate. This implies an important link between the genetic and community levels of biology.

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