Transient dynamics and food-web complexity in the Lotka-Volterra cascade model

How does the long-term behaviour near equilibrium of model food webs correlate with their short-term transient dynamics? Here, simulations of the Lotka -Volterra cascade model of food webs provide the first evidence to answer this question. Transient behaviour is measured by resilience, reactivity, the maximum amplification of a perturbation and the time at which the maximum amplification occurs. Model food webs with a higher probability of local asymptotic stability may be less resilient and may have a larger transient growth of perturbations. Given a fixed connectance, the sizes and durations of transient responses to perturbations increase with the number of species. Given a fixed number of species, as connectance increases, the sizes and durations of transient responses to perturbations may increase or decrease depending on the type of link that is varied. Reactivity is more sensitive to changes in the number of donor-controlled links than to changes in the number of recipient-controlled links, while resilience is more sensitive to changes in the number of recipient-controlled links than to changes in the number of donor-controlled links. Transient behaviour is likely to be one of the important factors affecting the persistence of ecological communities.     

Food web stability and weighted connectance: the complexity-stability debate revisited

How the complexity of food webs relates to stability has been a subject of many studies. Often, unweighted connectance is used to express complexity. Unweighted connectance is measured as the proportion of realized links in the network. Weighted connectance, on the other hand, takes link weights (fluxes or feeding rates) into account and captures the shape of the flux distribution. Here, we used weighted connectance to revisit the relation between complexity and stability. We used 15 real soil food webs and determined the feeding rates and the interaction strength matrices. We calculated both versions of connectance, and related these structural properties to food web stability. We also determined the skewness of both flux and interaction strength distributions with the Gini coefficient. We found no relation between unweighted connectance and food web stability, but weighted connectance was positively correlated with stability. This finding challenges the notion that complexity may constrain stability, and supports the ‘complexity begets stability’ notion. The positive correlation between weighted connectance and stability implies that the more evenly flux rates were distributed over links, the more stable the webs were. This was confirmed by the Gini coefficients of both fluxes and interaction strengths. However, the most even distributions of this dataset still were strongly skewed towards small fluxes or weak interaction strengths. Thus, incorporating these distribution with many weak links via weighted instead of unweighted food web measures can shed new light on classical theories.     

Effects of partitioning allochthonous and autochthonous resources on food web stability

The flux of energetic and nutrient resources across habitat boundaries can exert major impacts on the dynamics of the recipient food web. Competition for these resources can be a key factor structuring many ecological communities. Competition theory suggests that competing species should exhibit some partitioning to minimize competitive interactions. Species should partition both in situ (autochthonous) resources and (allochthonous) resources that enter the food web from outside sources. Allochthonous resources are important sources of energy and nutrients in many low productivity systems and can significantly influence community structure. The focus of this paper is on: (i) the influence of resource partitioning on food web stability, but concurrently we examine the compound effects of; (ii) the trophic level(s) that has access to allochthonous resources; (iii) the amount of allochthonous resource input; and (iv) the strength of the consumer–resource interactions. We start with a three trophic level food chain model (resource–consumer–predator) and separate the higher two trophic levels into two trophospecies. In the model, allochthonous resources are either one type available to both consumers and predators or two distinct types, one for consumers and one for predators. The feeding preferences of the consumer and predator trophospecies were varied so that they could either be generalists or specialists on allochthonous and/or autochthonous resources. The degree of specialization influenced system persistence by altering the structure and, therefore, the indirect effects of the food web. With regard to the trophic level(s) that has access to allochthonous resources, we found that a single allochthonous resource available to both consumers and predators is more unstable than two allochthonous resources. The results demonstrate that species populating food webs that experience low to moderate allochthonous resources are more persistent. The results also support the notion that strong links destabilize food web dynamics, but that weak to moderate strength links stabilize food web dynamics. These results are consistent with the idea that the particular structure, resource availability, and relative strength of links of food webs (such as degree of specialization) can influence the stability of communities. Given that allochthonous resources are important resources in many ecosystems, we argue that the influence of such resources on species and community persistence needs to be examined more thoroughly to provide a clearer understanding of food web dynamics.     

Major food web properties of two sandy beaches with contrasting morphodynamics, and effects on the stability

We determined major structural properties influencing the food webs of two sandy beaches with contrasting morphodynamics in the Atlantic coast of Uruguay: reflective (narrow and steep) and dissipative beaches (wide and flat). Furthermore, we evaluated how these characteristics could influence the stability of the local food webs. To this end, we examined the correlation of several food web properties with different ecosystem types (including freshwater habitats, estuary, marine, and terrestrial environments) using a principal components analysis. Sandy beach food web components included detritus, phytoplankton, zooplankton, benthic invertebrates, fishes, and seabirds. Our results revealed that the dissipative beach presented higher trophic levels, a higher number of trophic species, more links per species, as well as a higher proportion of intermediate trophic species, but lower connectance and proportion of omnivorous species than the reflective beach. The variation in the food web properties was explained by two principal components. Sandy beach food webs contribute mainly to one dimension of the principal components analysis that was determined by the number of trophic species, links per species, the trophic similarity, and the characteristic path length. We suggest that species and link characteristics, such as predominance of scavengers and detritivorous, the relatively high connectance and the short path length are drivers in the food web structure and may play a role in the community dynamic.     

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.     

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.     

Interplay between the paradox of enrichment and nutrient cycling in food webs

Nutrient cycling is fundamental to ecosystem functioning. Despite recent major advances in the understanding of complex food web dynamics, food web models have so far generally ignored nutrient cycling. However, nutrient cycling is expected to strongly impact food web stability and functioning. To make up for this gap, we built an allometric and size structured food web model including nutrient cycling. By releasing mineral nutrients, recycling increases the availability of limiting resources for primary producers and links each trophic level to the bottom of food webs. We found that nutrient cycling can provide a significant part of the total nutrient supply of the food web, leading to a strong enrichment effect that promotes species persistence in nutrient poor ecosystems but leads to a paradox of enrichment at high nutrient inputs. The presence of recycling loops linking each trophic level to the basal resources weakly affects species biomass temporal variability in the food web. Recycling loops tend to slightly dampen the destabilising effect of nutrient enrichment on consumer temporal variability while they have opposite effects for primary producers. By considering nutrient cycling, this new model improves our understanding of the response of food webs to nutrient availability and opens perspectives to better link studies on food web dynamics and ecosystem functioning.     

On the generality of stability-complexity relationships in Lotka-Volterra ecosystems

Understanding how complexity persists in nature is a long-standing goal of ecologists. In theoretical ecology, local stability is a widely used measure of ecosystem persistence and has made a major contribution to the ecosystem stability-complexity debate over the last few decades. However, permanence is coming to be regarded as a more satisfactory definition of ecosystem persistence and has relatively recently become available as a tool for assessing the global stability of Lotka-Volterra communities. Here we document positive relationships between permanence and Lotka-Volterra food web complexity and report a positive correlation between the probability of local stability and permanence. We investigate further the frequency of discrepancy (attributed to fragile systems that are locally stable but not permanent or locally unstable systems that are permanent and have cyclic or chaotic dynamics), associate non-permanence with the local stability or instability of equilibria on the boundary of the state-space, and investigate how these vary with aspects of ecosystem complexity. We find that locally stable interior equilibria tend to have all locally unstable boundary equilibria. Since a locally stable boundary is inconsistent with permanent dynamics, this can explain the observed positive correlation between local interior stability and permanence. Our key finding is that, at least in Lotka-Volterra model ecosystems, local stability may be a better measure of persistence than previously thought.     

Food web complexity and stability across habitat connectivity gradients

The effects of habitat connectivity on food webs have been studied both empirically and theoretically, yet the question of whether empirical results support theoretical predictions for any food web metric other than species richness has received little attention. Our synthesis brings together theory and empirical evidence for how habitat connectivity affects both food web stability and complexity. Food web stability is often predicted to be greatest at intermediate levels of connectivity, representing a compromise between the stabilizing effects of dispersal via rescue effects and prey switching, and the destabilizing effects of dispersal via regional synchronization of population dynamics. Empirical studies of food web stability generally support both this pattern and underlying mechanisms. Food chain length has been predicted to have both increasing and unimodal relationships with connectivity as a result of predators being constrained by the patch occupancy of their prey. Although both patterns have been documented empirically, the underlying mechanisms may differ from those predicted by models. In terms of other measures of food web complexity, habitat connectivity has been empirically found to generally increase link density but either reduce or have no effect on connectance, whereas a unimodal relationship is expected. In general, there is growing concordance between empirical patterns and theoretical predictions for some effects of habitat connectivity on food webs, but many predictions remain to be tested over a full connectivity gradient, and empirical metrics of complexity are rarely modeled. Closing these gaps will allow a deeper understanding of how natural and anthropogenic changes in connectivity can affect real food webs.     

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.     

Community assembly and food web stability

The ecological assembly of food web is considered as a process of predator colonizations and extinctions. The results of computer simulations using predator-prey equations allow us to identify three types of food web stability and examine how they may change through development of food webs. Species turnover stability increases, stability to extensive species extinction remains constant, and local stability to population fluctuations decreases as food web assembly proceeds.     

The effects of energy input,immigration and habitat size on food web structure: a microcosm experiment

It has been hypothesised that larger habitats should support more complex food webs. We consider three mechanisms which could lead to this pattern. These are increased immigration rates, increased total productivity and spatial effects on the persistence of unstable interactions. Experiments designed to discriminate between these mechanisms were carried out in laboratory aquatic microcosm communities of protista and bacteria, by independently manipulating habitat size, total productivity and immigration rate. Larger habitats supported more complex food webs, with more species, more links per species and longer maximum and mean food chains, even in the absence of differences in total energy input. Increased immigration rate resulted in more complex food webs, but habitats with higher energy input per unit area supported less complex food webs. We conclude that spatial effects on the persistence of unstable interactions, and variation in immigration rates, are plausible mechanisms by which habitat size could affect food web structure. Variation in total productivity with habitat area seems a less likely explanation for variation in food web structure.     

Relative ascendency predicts food web robustness

Threats to ecosystems globally from anthropogenic disturbance and climate change requires us to urgently identify the most sensitive biological communities to ensure they are effectively preserved. It is for this reason that understanding and predicting food web stability has been topical within ecology. Food web stability is a multi-faceted concept that represents the ability of a food web to maintain its integrity following disturbance, it includes resistance, resilience and fragility. In this study, we examine the ability of four food web metrics to predict the fragility to random species extinctions in 120 qualitative food webs. We show that three information-based indices out performed food web connectance in predicting fragility, with relative ascendency having the strongest relationship. Relative ascendency was a much stronger predictor of fragility than MacArthur’s stability metric, Average Mutual Information and connectance as it accounted for both the distribution and number of links between species. We also find that most qualitative food webs persist around a central tendency of relative ascendency.     

Body size and food web structure: testing the equiprobability assumption of the cascade model

The cascade model successfuly predicts many patterns in reported food webs. A key assumption of this model is the existence of a predetermined trophic hierarchy; prey are always lower in the hierarchy than their predators. At least three studies have suggested that, in animal food webs, this hierarchy can be explained to a large extent by body size relationships. A second assumption of the standard cascade model is that trophic links not prohibited by the hierarchy occur with equal probability. Using nonparametric contingency table analyses, we tested this ”equiprobability hypothesis” in 16 published animal food webs for which the adult body masses of the species had been estimated. We found that when the hierarchy was based on body size, the equiprobability hypothesis was rejected in favor of an alternative, ”predator-dominance” hypothesis wherein the probability of a trophic link varies with the identity of the predator. Another alternative to equiprobabilty is that the probability of a trophic link depends upon the ratio of the body sizes of the two species. Using nonparametric regression and liklihood ratio tests, we show that a size-ratio based model represents a significant improvement over the cascade model. These results suggest that models with heterogeneous predation probabilities will fit food web data better than the homogeneous cascade model. They also suggest a new way to bridge the gap between static and dynamic food web models. Received: 3 February 1999 / Accepted: 26 October 1999     

Parasites Affect Food Web Structure Primarily through Increased Diversity and Complexity

Comparative research on food web structure has revealed generalities in trophic organization, produced simple models, and allowed assessment of robustness to species loss. These studies have mostly focused on free-living species. Recent research has suggested that inclusion of parasites alters structure. We assess whether such changes in network structure result from unique roles and traits of parasites or from changes to diversity and complexity. We analyzed seven highly resolved food webs that include metazoan parasite data. Our analyses show that adding parasites usually increases link density and connectance (simple measures of complexity), particularly when including concomitant links (links from predators to parasites of their prey). However, we clarify prior claims that parasites “dominate” food web links. Although parasites can be involved in a majority of links, in most cases classic predation links outnumber classic parasitism links. Regarding network structure, observed changes in degree distributions, 14 commonly studied metrics, and link probabilities are consistent with scale-dependent changes in structure associated with changes in diversity and complexity. Parasite and free-living species thus have similar effects on these aspects of structure. However, two changes point to unique roles of parasites. First, adding parasites and concomitant links strongly alters the frequency of most motifs of interactions among three taxa, reflecting parasites'' roles as resources for predators of their hosts, driven by trophic intimacy with their hosts. Second, compared to free-living consumers, many parasites'' feeding niches appear broader and less contiguous, which may reflect complex life cycles and small body sizes. This study provides new insights about generic versus unique impacts of parasites on food web structure, extends the generality of food web theory, gives a more rigorous framework for assessing the impact of any species on trophic organization, identifies limitations of current food web models, and provides direction for future structural and dynamical models.     

Genetic variation, predator-prey interactions and food web structure

Food webs are networks of species that feed on each other. The role that within-population phenotypic and genetic variation plays in food web structure is largely unknown. Here, I show via simulation how variation in two key traits, growth rates and phenology, by influencing the variability of body sizes present through time, can potentially affect several structural parameters in the direction of enhancing food web persistence: increased connectance, decreased interaction strengths, increased variation among interaction strengths and increased degree of omnivory. I discuss other relevant traits whose variation could affect the structure of food webs, such as morphological and additional life-history traits, as well as animal personalities. Furthermore, trait variation could also contribute to the stability of food web modules through metacommunity dynamics. I propose future research to help establish a link between within-population variation and food web structure. If appropriately established, such a link could have important consequences for biological conservation, as it would imply that preserving (functional) genetic variation within populations could ensure the preservation of entire communities.     

Permanence does not predict the commonly measured food web structural attributes

Food web assembly algorithms show great promise for investigating issues involving the dynamics of whole webs, such as succession, rehabilitation, and invasibility. Permanence, which requires that all species densities remain positive and finite, has been suggested as a good stability constraint. This study tests the validity of the permanence constraint by comparing real webs and model webs from the literature to the predictions of three assembly algorithms: one constrained by permanence and feasibility, one constrained by feasibility alone, and one with no dynamical constraint. It is found that the addition of the permanence constraint does not improve the predictive ability of the algorithm. Its main effect is to increase the efficiency of species selected for the web. Dynamically constrained webs have lower connectance and indistinct trophic levels compared to real webs and webs from other models, which is a consequence of omitting species' physiology. Although webs are less likely to be permanent if they have high omnivory and cycling, the web-building process circumvents this constraint. The challenges of testing and justifying system-level hypotheses, including isolating and detecting their effects, are discussed.