Relation between complexity and stability in food webs with adaptive behavior

We investigate the influence of functional responses (Lotka-Volterra or Holling type), initial topological web structure (randomly connected or niche model), adaptive behavior (adaptive foraging and predator avoidance) and the type of constraints on the adaptive behavior (linear or nonlinear) on the stability and structure of food webs. Two kinds of stability are considered: one is the network robustness (i.e., the proportion of species surviving after population dynamics) and the other is the species deletion stability. When evaluating the network structure, we consider link density as well as the trophic level structure. We show that the types of functional responses and initial web structure do not have a large effect on the stability of food webs, but foraging behavior has a large stabilizing effect. It leads to a positive complexity-stability relationship whenever higher "complexity" implies more potential prey per species. The other type of adaptive behavior, predator avoidance behavior, makes food webs only slightly more stable. The observed link density after population dynamics depends strongly on the presence or absence of adaptive foraging, and on the type of constraints used. We also show that the trophic level structure is preserved under population dynamics with adaptive foraging.     

Predation risk influences food‐web structure by constraining species diet choice

The foraging behaviour of species determines their diet and, therefore, also emergent food‐web structure. Optimal foraging theory (OFT) has previously been applied to understand the emergence of food‐web structure through a consumer‐centric consideration of diet choice. However, the resource‐centric viewpoint, where species adjust their behaviour to reduce the risk of predation, has not been considered. We develop a mechanistic model that merges metabolic theory with OFT to incorporate the effect of predation risk on diet choice to assemble food webs. This ‘predation‐risk‐compromise’ (PR) model better captures the nestedness and modularity of empirical food webs relative to the classical optimal foraging model. Specifically, compared with optimal foraging alone, risk‐mitigated foraging leads to more‐nested but less‐modular webs by broadening the diet of consumers at intermediate trophic levels. Thus, predation risk significantly affects food‐web structure by constraining species’ ability to forage optimally, and needs to be considered in future work.     

Interactive effects of body-size structure and adaptive foraging on food-web stability

Body-size structure of food webs and adaptive foraging of consumers are two of the dominant concepts of our understanding how natural ecosystems maintain their stability and diversity. The interplay of these two processes, however, is a critically important yet unresolved issue. To fill this gap in our knowledge of ecosystem stability, we investigate dynamic random and niche model food webs to evaluate the proportion of persistent species. We show that stronger body-size structures and faster adaptation stabilise these food webs. Body-size structures yield stabilising configurations of interaction strength distributions across food webs, and adaptive foraging emphasises links to resources closer to the base. Moreover, both mechanisms combined have a cumulative effect. Most importantly, unstructured random webs evolve via adaptive foraging into stable size-structured food webs. This offers a mechanistic explanation of how size structure adaptively emerges in complex food webs, thus building a novel bridge between these two important stabilising mechanisms.     

Effects of evolutionary changes in prey use on the relationship between food web complexity and stability

The relationship between food web complexity and stability has been the subject of a long-standing debate in ecology. Although rapid changes in the food web structure through adaptive foraging behavior can confer stability to complex food webs, as reported by Kondoh (Science 299:1388–1391, 2003), the exact mechanisms behind this adaptation have not been specified in previous studies; thus, the applicability of such predictions to real ecosystems remains unclear. One mechanism of adaptive foraging is evolutionary change in genetically determined prey use. We constructed individual-based models of evolution of prey use by predators assuming explicit population genetics processes, and examined how this evolution affects the stability (i.e., the proportion of species that persist) of the food web and whether the complexity of the food web increased the stability of the prey–predator system. The analysis showed that the stability of food webs decreased with increasing complexity regardless of evolution of prey use by predators. The effects of evolution on stability differed depending on the assumptions made regarding genetic control of prey use. The probabilities of species extinctions were associated with the establishment or loss of trophic interactions via evolution of the predator, indicating a clear link between structural changes in the food web and community stability.     

The impact of nonlinear functional responses on the long-term evolution of food web structure

We investigate the long-term web structure emerging in evolutionary food web models when different types of functional responses are used. We find that large and complex webs with several trophic layers arise only if the population dynamics is such that it allows predators to focus on their best prey species. This can be achieved using modified Lotka-Volterra or Holling/Beddington functional responses with effective couplings that depend on the predator's efficiency at exploiting the prey, or a ratio-dependent functional response with adaptive foraging. In contrast, if standard Lotka-Volterra or Holling/Beddington functional responses are used, long-term evolution generates webs with almost all species being basal, and with additionally many links between these species. Interestingly, in all cases studied, a large proportion of weak links result naturally from the evolution of the food webs.     

Effects of heterogeneous interaction strengths on food web complexity

Using a bioenergetic model we show that the pattern of foraging preferences greatly determines the complexity of the resulting food webs. By complexity we refer to the degree of richness of food-web architecture, measured in terms of some topological indicators (number of persistent species and links, connectance, link density, number of trophic levels, and frequency of weak links). The poorest food-web architecture is found for a mean-field scenario where all foraging preferences are assumed to be the same. Richer food webs appear when foraging preferences depend on the trophic position of species. Food-web complexity increases with the number of basal species. We also find a strong correlation between the complexity of a trophic module and the complexity of entire food webs with the same pattern of foraging preferences.     

Does foraging adaptation create the positive complexity-stability relationship in realistic food-web structure?

The adaptive food-web hypothesis suggests that an adaptive foraging switch inverses the classically negative complexity-stability relationships of food webs into positive ones, providing a possible resolution for the long-standing paradox of how populations persist in a complex natural food web. However, its applicability to natural ecosystems has been questioned, because the positive relationship does not emerge when a niche model, a realistic "benchmark" of food-web models, is used. I hypothesize that, in the niche model, increasing connectance influences the fraction of basal species to destabilize the system and this masks the inversion of the negative complexity-stability relationship in the presence of adaptive foraging. A model analysis shows that, if this confounding effect is eliminated, then, even in a niche model, a population is more likely to persist in a more complex food web. This result supports the robustness of adaptive food-web hypothesis and reveals the condition in which the hypothesis should be tested.     

Emergence of complexity in evolving niche-model food webs

We have analysed mechanisms that promote the emergence of complex structures in evolving model food webs. The niche model is used to determine predator-prey relationships. Complexity is measured by species richness as well as trophic level structure and link density. Adaptive dynamics that allow predators to concentrate on the prey species they are best adapted to lead to a strong increase in species number but have only a small effect on the number and relative occupancy of trophic levels. The density of active links also remains small but a high number of potential links allows the network to adjust to changes in the species composition (emergence and extinction of species). Incorporating effects of body size on individual metabolism leads to a more complex trophic level structure: both the maximum and the average trophic level increase. So does the density of active links. Taking body size effects into consideration does not have a measurable influence on species richness. If species are allowed to adjust their foraging behaviour, the complexity of the evolving networks can also be influenced by the size of the external resources. The larger the resources, the larger and more complex is the food web it can sustain. Body size effects and increasing resources do not change size and the simple structure of the evolving networks if adaptive foraging is prohibited. This leads to the conclusion that in the framework of the niche model adaptive foraging is a necessary but not sufficient condition for the emergence of complex networks. It is found that despite the stabilising effect of foraging adaptation the system displays elements of self-organised critical behaviour.     

Food-web complexity emerging from ecological dynamics on adaptive networks

Food webs are complex networks describing trophic interactions in ecological communities. Since Robert May's seminal work on random structured food webs, the complexity-stability debate is a central issue in ecology: does network complexity increase or decrease food-web persistence? A multi-species predator-prey model incorporating adaptive predation shows that the action of ecological dynamics on the topology of a food web (whose initial configuration is generated either by the cascade model or by the niche model) render, when a significant fraction of adaptive predators is present, similar hyperbolic complexity-persistence relationships as those observed in empirical food webs. It is also shown that the apparent positive relation between complexity and persistence in food webs generated under the cascade model, which has been pointed out in previous papers, disappears when the final connection is used instead of the initial one to explain species persistence.     

Food web structure in Mediterranean streams: exploring stabilizing forces in these ecosystems

We constructed the food webs of six Mediterranean streams in order to determine ecological generalities derived from analysis of their structure and to explore stabilizing forces within these ecosystems. Fish, macroinvertebrates, primary producers and detritus are the components of the studied food webs. Analysis focused on a suite of food web properties that describe species’ trophic habits, linkage complexity and food chains. A great structural similarity was found in analyzed food webs; we therefore suggest average values for the structural properties of Mediterranean stream food webs. Percentage of omnivorous species was positively correlated with connectance, and there was a predominance of intermediate trophic level species that had established simple links with detritus. In short, our results suggest that omnivory and the weak interactions of detritivores have a stabilizing role in these food webs.     

Metabolic adjustment enhances food web stability

Understanding ecosystem stability is one of the greatest challenges of ecology. Over several decades, it has been shown that allometric scaling of biological rates and feeding interactions provide stability to complex food web models. Moreover, introducing adaptive responses of organisms to environmental changes (e.g. like adaptive foraging that enables organisms to adapt their diets depending on resources abundance) improved species persistence in food webs. Here, we introduce the concept of metabolic adjustment, i.e. the ability of species to slow down their metabolic rates when facing starvation and to increase it in time of plenty. We study the reactions of such a model to nutrient enrichment and the adjustment speed of metabolic rates. We found that increasing nutrient enrichment leads to a paradox of enrichment (increase in biomasses and oscillation amplitudes and ultimately extinction of species) but metabolic adjustment stabilises the system by dampening the oscillations. Metabolic adjustment also increases the average biomass of the top predator in a tri‐trophic food chain. In complex food webs, metabolic adjustment has a stabilising effect as it promotes species survival by creating a large diversity of metabolic rates. However, this stabilising effect is mitigated in enriched ecosystems. Phenotypic plasticity of organisms must be considered in food web models to better understand the response of organisms to their environment. As metabolic rate is central in describing biological rates, we must pay attention to its variations to fully understand the population dynamics of natural communities.     

Predator and detritivore niche width helps to explain biocomplexity of experimental detritus-based food webs in four aquatic and terrestrial ecosystems

In the study of food webs, the existence and explanation of recurring patterns, such as the scale invariance of linkage density, predator–prey ratios and mean chain length, constitute long-standing issues. Our study focused on litter-associated food webs and explored the influence of detritivore and predator niche width (as δ¹³C range) on web topological structure. To compare patterns within and between aquatic and terrestrial ecosystems and take account of intra-habitat variability, we constructed 42 macroinvertebrate patch-scale webs in four different habitats (lake, lagoon, beech forest and cornfield), using an experimental approach with litterbags. The results suggest that although web differences exist between ecosystems, patterns are more similar within than between aquatic and terrestrial web types. In accordance with optimal foraging theory, we found that the niche width of predators and prey increased with the number of predators and prey taxa as a proportion of total taxa in the community. The tendency was more marked in terrestrial ecosystems and can be explained by a lower per capita food level than in aquatic ecosystems, particularly evident for predators. In accordance with these results, the number of links increased with the number of species but with a significantly sharper regression slope for terrestrial ecosystems. As a consequence, linkage density, which was found to be directly correlated to niche width, increased with the total number of species in terrestrial webs, whereas it did not change significantly in aquatic ones, where connectance scaled negatively with the total number of species. In both types of ecosystem, web robustness to rare species removal increased with connectance and the niche width of predators. In conclusion, although limited to litter-associated macroinvertebrate assemblages, this study highlights structural differences and similarities between aquatic and terrestrial detrital webs, providing field evidence of the central role of niche width in determining the structure of detritus-based food webs and posing foraging optimisation constraints as a general mechanistic explanation of food web complexity differences within and between ecosystem types.     

Predicting the effects of temperature on food web connectance

Few models concern how environmental variables such as temperature affect community structure. Here, we develop a model of how temperature affects food web connectance, a powerful driver of population dynamics and community structure. We use the Arrhenius equation to add temperature dependence of foraging traits to an existing model of food web structure. The model predicts potentially large temperature effects on connectance. Temperature-sensitive food webs exhibit slopes of up to 0.01 units of connectance per 1°C change in temperature. This corresponds to changes in diet breadth of one resource item per 2°C (assuming a food web containing 50 species). Less sensitive food webs exhibit slopes down to 0.0005, which corresponds to about one resource item per 40°C. Relative sizes of the activation energies of attack rate and handling time determine whether warming increases or decreases connectance. Differences in temperature sensitivity are explained by differences between empirical food webs in the body size distributions of organisms. We conclude that models of temperature effects on community structure and dynamics urgently require considerable development, and also more and better empirical data to parameterize and test them.     

Difference in Web Construction Behavior at Newly Occupied Web Sites Between Two Cyclosa Species

Animals make decisions based on subjective assessments of their environment. To determine their future foraging activities, animals probably assess food availability from past foraging experiences. Thus, foraging also functions as a way for animals to collect information, with the uncertainty of an assessment decreasing as foraging activity increases. This suggests that different needs for a correct assessment may affect the investment made in foraging activities. Orb‐web spiders sometimes relocate their webs and relocation rate differs among species. After web relocation, several spider species have been reported to construct the first webs at newly occupied web sites using less silk than usual, possibly to avoid the risk of an overinvestment at sites where food availability has not been determined. Nevertheless, they may pay a cost, because of inadequate decision‐making, if webs constructed with less silk convey less information and increase the uncertainty of an assessment. We expect that stronger site tenacity necessitates a greater requirement for correct assessment of web site and the degree to which spiders reduce the amount of web silk in the first web after web relocation is smaller in species that use the same site longer. To test this hypothesis, we examined web construction in two orb‐web spiders, Cyclosa octotuberculata and C. argenteoalba. At the same time we found that these two species exhibit different web‐site tenacity, as C. octotuberculata does not relocate its webs as frequently as does C. argenteoalba. After artificially induced web relocation, C. argenteoalba constructed webs that were initially smaller and contained only about 2/3 of the silk in control webs that were constructed at the original site. In contrast, C. octotuberculata did not exhibit such decreases in web size or in the amount of web silk used. This result is consistent with our hypothesis.     

Food web structure in a tropical stream ecosystem

Abstract This study investigated the structure and properties of a tropical stream food web in a small spatial scale, characterizing its planktonic, epiphytic and benthic compartments. The study was carried out in the Potreirinho Creek, a second‐order stream located in the south‐east of Brazil. Some attributes of the three subwebs and of the conglomerate food web, composed by the trophic links of the three compartments plus the fish species, were determined. Among compartments, the food webs showed considerable variation in structure. The epiphytic food web was consistently more complex than the planktonic and benthic webs. The values of number of species, number of links and maximum food chain length were significantly higher in the epiphytic compartment than in the other two. Otherwise, the connectance was significantly lower in epiphyton. The significant differences of most food web parameters were determined by the increase in the number of trophic species, represented mainly by basal and intermediate species. High species richness, detritus‐based system and high degree of omnivory characterized the stream food web studied. The aquatic macrophytes probably provide a substratum more stable and structurally complex than the sediment. We suggest that the greater species richness and trophic complexity in the epiphytic subweb might be due to the higher degree of habitat complexity supported by macrophyte substrate. Despite differences observed in the structure of the three subwebs, they are highly connected by trophic interactions, mainly by fishes. The high degree of fish omnivory associated with their movements at different spatial scales suggests that these animals have a significant role in the food web dynamic of Potreirinho Creek. This interface between macrophytes and the interconnections resultant from fish foraging, diluted the compartmentalization of the Potreirinho food web.     

Persistence increases with diversity and connectance in trophic metacommunities

Background

We are interested in understanding if metacommunity dynamics contribute to the persistence of complex spatial food webs subject to colonization-extinction dynamics. We study persistence as a measure of stability of communities within discrete patches, and ask how do species diversity, connectance, and topology influence it in spatially structured food webs.

Methodology/Principal Findings

We answer this question first by identifying two general mechanisms linking topology of simple food web modules and persistence at the regional scale. We then assess the robustness of these mechanisms to more complex food webs with simulations based on randomly created and empirical webs found in the literature. We find that linkage proximity to primary producers and food web diversity generate a positive relationship between complexity and persistence in spatial food webs. The comparison between empirical and randomly created food webs reveal that the most important element for food web persistence under spatial colonization-extinction dynamics is the degree distribution: the number of prey species per consumer is more important than their identity.

Conclusions/Significance

With a simple set of rules governing patch colonization and extinction, we have predicted that diversity and connectance promote persistence at the regional scale. The strength of our approach is that it reconciles the effect of complexity on stability at the local and the regional scale. Even if complex food webs are locally prone to extinction, we have shown their complexity could also promote their persistence through regional dynamics. The framework we presented here offers a novel and simple approach to understand the complexity of spatial food webs.     

Connectance and parasite diet breadth in flea-mammal webs

The number of links in webs of species interactions, which lies at the heart of the biodiversity-stability debate, has given rise to controversy during the last 20 yr. Studies exploring these web properties have mainly focused on symmetric webs where each species can potentially feed on any other species; asymmetric webs such as host-parasite webs, where one set of species feed on another set of species, have been overlooked. However, food webs are incomplete without parasites and the study of parasite-host sub-web properties deserves attention. Here, using a large database involving 33 regional interaction webs between mammals and their flea parasites, we found a negative relationship between species richness and host-parasite connectance. We suggest that some phylogenetic constraints on flea diet may explain our observed patterns because we found that parasite diet breadth, measured as host taxonomic diversity, was invariant along our host richness gradient. We found that the slope of the logarithmic relationship between the number of realized links and species richness is lower than slope values reported for food webs. We suggest that connectance may not respond to increasing species richness as rapidly in host-parasite webs as in predator-prey food webs due to stronger coevolutionary requirements.     

Evidence for the existence of a robust pattern of prey selection in food webs

Food webs aim to provide a thorough representation of the trophic interactions found in an ecosystem. The complexity of empirical food webs, however, is leading many ecologists to focus dynamic ecosystem studies on smaller microcosm or mesocosm studies based upon community modules, which comprise three to five species and the interactions likely to have ecological relevance. We provide here a structural counterpart to community modules. We investigate food-web 'motifs' which are n-species connected subgraphs found within the food web. Remarkably, we find that the over- and under-representation of three-species motifs in empirical food webs can be understood through comparison to a static food-web model, the niche model. Our result conclusively demonstrates that predation upon species with some 'characteristic' niche value is the prey selection mechanism consistent with the structural properties of empirical food webs.     

Emergence of non-random structure in local food webs generated from randomly structured regional webs

Previous studies have shown that high-resolution, empirical food webs possess a non-random network structure, typically characterized by uniform or exponential degree distributions. However, the empirical food webs that have been investigated for their structural properties represent local communities that are only a subset of a larger pool of regionally coexisting species. Here, we use a simple model to investigate the effects of regional food web structure on local food webs that are assembled by two simple processes: random immigration of species from a source web (regional food web), and random extinction of species within the local web. The model shows that local webs with non-random degree distributions can arise from randomly structured source webs. A comparison of local webs assembled from randomly structured source webs with local webs assembled from source webs generated by the niche model shows that the former have higher species richness at equilibrium, but have a nonlinear response to changing extinction rates. These results imply that the network structure of regional food webs can play a significant role in the assembly and dynamics of local webs in natural ecosystems. With natural landscapes becoming increasingly fragmented, understanding such structure may be a necessary key to understanding the maintenance and stability of local species diversity.