Exploring the temporal variability of a food web using long‐term biomonitoring data

Ecological communities are constantly being reshaped in the face of environmental change and anthropogenic pressures. Yet, how food webs change over time remains poorly understood. Food web science is characterized by a trade‐off between complexity (in terms of the number of species and feeding links) and dynamics. Topological analysis can use complex, highly resolved empirical food web models to explore the architecture of feeding interactions but is limited to a static view, whereas ecosystem models can be dynamic but use highly aggregated food webs. Here, we explore the temporal dynamics of a highly resolved empirical food web over a time period of 18 years, using the German Bight fish and benthic epifauna community as our case study. We relied on long‐term monitoring ecosystem surveys (from 1998 to 2015) to build a metaweb, i.e. the meta food web containing all species recorded over the time span of our study. We then combined time series of species abundances with topological network analysis to construct annual food web snapshots. We developed a new approach, ‘node‐weighted’ food web metrics by including species abundances to represent the temporal dynamics of food web structure, focusing on generality and vulnerability. Our results suggest that structural food web properties change through time; however, binary food web structural properties may not be as temporally variable as the underlying changes in species composition. Further, the node‐weighted metrics enabled us to detect that food web structure was influenced by changes in species composition during the first half of the time series and more strongly by changes in species dominance during the second half. Our results demonstrate how ecosystem surveys can be used to monitor temporal changes in food web structure, which are important ecosystem indicators for building marine management and conservation plans.     

Peak-to-peak dynamics in food chain models

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the forecast concerns the population at the top of the food chain and that peaks variability often increases from bottom to top. All these findings bring naturally to the conclusion that top populations should be sampled in order to have higher chances to detect peak-to-peak dynamics. The analysis is carried out by studying ditrophic food chain models with seasonally varying parameters, tritrophic food chain models with constant parameters, and more complex food chain and food web models.     

Bimodal trait distributions with large variances question the reliability of trait-based aggregate models

Functionally diverse communities can adjust their species composition to altered environmental conditions, which may influence food web dynamics. Trait-based aggregate models cope with this complexity by ignoring details about species identities and focusing on their functional characteristics (traits). They describe the temporal changes of the aggregate properties of entire communities, including their total biomasses, mean trait values, and trait variances. The applicability of aggregate models depends on the validity of their underlying assumptions that trait distributions are normal and exhibit small variances. We investigated to what extent this can be expected to work by comparing an innovative model that accounts for the full trait distributions of predator and prey communities to a corresponding aggregate model. We used a food web structure with well-established trade-offs among traits promoting mutual adjustments between prey edibility and predator selectivity in response to selection. We altered the shape of the trade-offs to compare the outcome of the two models under different selection regimes, leading to trait distributions increasingly deviating from normality. Their biomass and trait dynamics agreed very well for stabilizing selection and reasonably well for directional selection, under which different trait values are favored at different times. However, for disruptive selection, the results of the aggregate model strongly deviated from the full trait distribution model that showed bimodal trait distributions with large variances. Hence, the outcome of aggregate models is reliable under ideal conditions but has to be questioned when confronted with more complex selection regimes and trait distributions, which are commonly observed in nature.     

Does structural sensitivity alter complexity–stability relationships?

Structural sensitivity, namely the sensitivity of a model dynamics to slight changes in its mathematical formulation, has already been studied in some models with a small number of state variables. The aim of this study is to investigate the impact of structural sensitivity in a food web model. Especially, the importance of structural sensitivity is compared to that of trophic complexity (number of species, connectance), which is known to strongly influence food web dynamics. Food web structures are built using the niche model. Then food web dynamics are modeled using several type II functional responses parameterized to fit the same predation fluxes. Food web persistence was found to be mostly determined by trophic complexity. At the opposite, even if food web connectance promotes equilibrium dynamics, their occurrence is mainly driven by the choice of the functional response. These conclusions are robust to changes in some parameter values, the fitting method and some model assumptions. In a one-prey/one-predator system, it was shown that the possibility that multiple stable states coexist can be highly structural sensitive. Quantifying this type of uncertainty at the scale of ecosystem models will be both a natural extension to this work and a challenging issue.     

Stability of complex food webs: resilience, resistance and the average interaction strength

In the face of stochastic climatic perturbations, the overall stability of an ecosystem will be determined by the balance between its resilience and its resistance, but their relative importance is still unknown. Using aquatic food web models we study ecosystem stability as a function of food web complexity. We measured three dynamical stability properties: resilience, resistance, and variability. Specifically, we evaluate how a decrease in the strength of predator-prey interactions with food web complexity, reflecting a decrease in predation efficiency with the number of prey per predator, affects the overall stability of the ecosystem. We find that in mass conservative ecosystems, a lower interaction strength slows down the mass cycling rate in the system and this increases its resistance to perturbations of the growth rate of primary producers. Furthermore, we show that the overall stability of the food webs is mostly given by their resistance, and not by their resilience. Resilience and resistance display opposite trends, although they are shown not to be simply opposite concepts but rather independent properties. The ecological implication is that weaker predator-prey interactions in closed ecosystems can stabilize food web dynamics by increasing its resistance to climatic perturbations.     

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.     

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.     

Aphids indirectly increase virulence and transmission potential of a monarch butterfly parasite by reducing defensive chemistry of a shared food plant

Parasites and hosts live in communities consisting of many interacting species, but few studies have examined how communities affect parasite virulence and transmission. We studied a food web consisting of two species of milkweed, two milkweed herbivores (monarch butterfly and oleander aphid) and a monarch butterfly-specific parasite. We found that the presence of aphids increased the virulence and transmission potential of the monarch butterfly's parasite on one milkweed species. These increases were associated with aphid-induced decreases in the defensive chemicals of milkweed plants. Our experiment suggests that aphids can indirectly increase the virulence and transmission potential of monarch butterfly parasites, probably by altering the chemical composition of a shared food plant. These results indicate that species that are far removed from host-parasite interactions can alter such interactions through cascading indirect effects in the food web. As such, indirect effects within ecological communities may drive the dynamics and evolution of parasites.     

复杂性-稳定性研究: 数学模型的进展

对自然生态系统的观察给人们以复杂的群落更稳定的直观印象, 但数学模型却得出了截然相反的结论。这一“悖论”使得复杂性-稳定性研究自20世纪70年代以来成为长期的热点。本文对这一领域的数学模型研究进行简要综述。首先对这一论题进行概念剖析, 然后将各类模型分为线性和非线性两大类, 前者即群落矩阵法, 后者包括相互作用矩阵法、复杂网络数值模拟法和食物网构件动力学法。它们分别基于不同的群落构建方法和稳定性判断标准, 探求各物种是如何相互作用并实现共存的。总体而言, 在随机构建的群落模型中, 多样性和连接度的增长不利于系统稳定; 而在更接近真实自然群落的模型中, 相互作用方式、网络拓扑结构、相互作用强度分布等方面的机制提供了稳定效应, 按此组织的生态网络可达到很高的复杂度。然而, 复杂性-稳定性的研究还远未结束, 当前的模型仍不足以反映自然群落中的复杂相互作用, 稳定性的概念也有待拓展。对这一议题的深入研究在生态学理论和生态系统管理实践方面都具有重大价值。     

The concepts of elasticity, invulnerability and invadability

Users of mathematical models in ecological research have emphasized mathematical elegance in elucidating the dynamics of ecosystem models with fixed collections of state variables instead of addressing the equally important question of what effects a changing ecosystem structure has on the system's dynamics. Our work addresses the effect of invasion on the species composition of communities. In the context of a linear model, we found that as communities were made more complex (in terms of the number of species they contained and the number of interactions among these species) the probability of their being stable decreased, but the probability of their being invulnerable to invasion by other species increased. These results are consistent with the hypothesis that, through time, communities approach an intermediate complexity at which the influences of environmental stochasticity (which tends to destabilize complex communities) and invasion pressure (which tends to add species to simple communities) counterbalance one another. At this intermediate complexity the average rate of change of species composition is low.     

Self-organized instability in complex ecosystems

Why are some ecosystems so rich, yet contain so many rare species? High species diversity, together with rarity, is a general trend in neotropical forests and coral reefs. However, the origin of such diversity and the consequences of food web complexity in both species abundances and temporal fluctuations are not well understood. Several regularities are observed in complex, multispecies ecosystems that suggest that these ecologies might be organized close to points of instability. We explore, in greater depth, a recent stochastic model of population dynamics that is shown to reproduce: (i) the scaling law linking species number and connectivity; (ii) the observed distributions of species abundance reported from field studies (showing long tails and thus a predominance of rare species); (iii) the complex fluctuations displayed by natural communities (including chaotic dynamics); and (iv) the species-area relations displayed by rainforest plots. It is conjectured that the conflict between the natural tendency towards higher diversity due to immigration, and the ecosystem level constraints derived from an increasing number of links, leaves the system poised at a critical boundary separating stable from unstable communities, where large fluctuations are expected to occur. We suggest that the patterns displayed by species-rich communities, including rarity, would result from such a spontaneous tendency towards instability.     

Omnivory as a stabilizing feature of natural communities

Abstract Omnivory-defined broadly as feeding on more than one trophic level-occupies a prominent position in discussions of food web architecture and dynamics, due in large part to an enduring conflict regarding omnivory's role in community dynamics. According to classical results from mathematical food web theory, omnivory destabilizes ecological communities, whereas more recent conceptual syntheses suggest that omnivory should be a strongly stabilizing factor in food webs. Working with an arthropod assemblage at Mount Saint Helens, I experimentally addressed this controversy using a two-way factorial design that crossed a manipulation of the degree of omnivory with another "disturbance" manipulation that targeted a specific component of the assemblage. In this statistical design, significant interaction effects (i.e., how the community impacts of the disturbance varied with the degree of omnivory) identified key stabilizing or destabilizing influences of omnivory. Overall, my experimental results indicated that increasing the degree of omnivory stabilized community dynamics, in keeping with recent conceptual syntheses.     

Winter is coming: Food web structure and seasonality in a subtropical freshwater coastal lake

Food web studies provide a useful tool to assess the organization and complexity of natural communities. Nevertheless, the seasonal dynamics of food web properties, their environmental correlates, and potential association with community diversity and stability remain poorly studied. Here, we condensed an incomplete 6‐year community dataset of a subtropical coastal lake to examine how monthly variation in diversity impacts food web structure over an idealized time series for an averaged year. Phytoplankton, zooplankton, macroinvertebrates, and fish were mostly resolved to species level (n = 120 trophospecies). Our results showed that the seasonal organization of the food web could be aggregated into two clusters of months grouped here as ‘summer’ and ‘winter’. During ‘winter’, the food web decreases in size and complexity, with the number of trophospecies dropping from 106 to 82 (a 22.6% decrease in the number of nodes) and the trophic interactions from 1,049 to 637 between month extremes (a 39.3% drop in the number of links). The observed simplification in food web structure during ‘winter’ suggests that community stability is more vulnerable to the impact of any change during this period.     

Food chains in the chemostat: Relationships between mean yield and complex dynamics

Atritrophic food-chain chemostat model composed of a prey with Monod-type nutrient uptake, a Holling Type II predator and a Holling Type II exploited superpredator is considered in this paper. The bifurcations of the model show that dynamic complexity first increases and then decreases with the nutrient supplied to the bottom of the food chain. Extensive simulations prove that the same holds for food yield, i.e., there exists an optimum nutrient supply which maximizes mean food yield. Finally, a comparative analysis of the results points out that the optimum nutrient supply practically coincides with the nutrient supply separating chaotic dynamics from high-frequency cyclic dynamics. This reinforces the idea, already known for simpler models, that food yield maximization requires that the system behaves on the edge of chaos.     

The more polluted the environment,the more important biodiversity is for food web stability

Human activities have led to massive influxes of pollutants, degrading the habitat of species and simplifying their biodiversity. However, the interaction between food web complexity, pollution and stability is still poorly understood. In this study we evaluate the effect exerted by accumulable pollutants on the relationship between complexity and stability of food webs. We built model food webs with different levels of richness and connectance, and used a bioenergetic model to project the dynamics of species biomasses. Further, we developed appropriate expressions for the dynamics of bioaccumulated and environmental pollutants. We additionally analyzed attributes of organisms’ and communities as determinants of species persistence (stability). We found that the positive effect of complexity on stability was enhanced as pollutant stress increased. Additionally we showed that the number of basal species and the maximum trophic level shape the complexity–stability relationship in polluted systems, and that in‐degree of consumers determines species extinction in polluted environments. Our study indicates that the form of biodiversity and the complexity of interaction networks are essential to understand and project the effects of pollution and other ecosystem threats.     

Quantifying the relative importance of variation in predation and the environment for species coexistence

Coexistence and food web theory are two cornerstones of the long‐standing effort to understand how species coexist. Although competition and predation are known to act simultaneously in communities, theory and empirical study of these processes continue to be developed largely independently. Here, we integrate modern coexistence theory and food web theory to simultaneously quantify the relative importance of predation and environmental fluctuations for species coexistence. We first examine coexistence in a theoretical, multitrophic model, adding complexity to the food web using machine learning approaches. We then apply our framework to a stochastic model of the rocky intertidal food web, partitioning empirical coexistence dynamics. We find the main effects of both environmental fluctuations and variation in predator abundances contribute substantially to species coexistence. Unexpectedly, their interaction tends to destabilise coexistence, leading to new insights about the role of bottom‐up vs. top‐down forces in both theory and the rocky intertidal ecosystem.     

Drought decreases incorporation of recent plant photosynthate into soil food webs regardless of their trophic complexity

Theory suggests that more complex food webs promote stability and can buffer the effects of perturbations, such as drought, on soil organisms and ecosystem functions. Here, we tested experimentally how soil food web trophic complexity modulates the response to drought of soil functions related to carbon cycling and the capture and transfer below‐ground of recent photosynthate by plants. We constructed experimental systems comprising soil communities with one, two or three trophic levels (microorganisms, detritivores and predators) and subjected them to drought. We investigated how food web trophic complexity in interaction with drought influenced litter decomposition, soil CO₂ efflux, mycorrhizal colonization, fungal production, microbial communities and soil fauna biomass. Plants were pulse‐labelled after the drought with ¹³C‐CO₂ to quantify the capture of recent photosynthate and its transfer below‐ground. Overall, our results show that drought and soil food web trophic complexity do not interact to affect soil functions and microbial community composition, but act independently, with an overall stronger effect of drought. After drought, the net uptake of ¹³C by plants was reduced and its retention in plant biomass was greater, leading to a strong decrease in carbon transfer below‐ground. Although food web trophic complexity influenced the biomass of Collembola and fungal hyphal length, ¹³C enrichment and the net transfer of carbon from plant shoots to microbes and soil CO₂ efflux were not affected significantly by varying the number of trophic groups. Our results indicate that drought has a strong effect on above‐ground–below‐ground linkages by reducing the flow of recent photosynthate. Our results emphasize the sensitivity of the critical pathway of recent photosynthate transfer from plants to soil organisms to a drought perturbation, and show that these effects may not be mitigated by the trophic complexity of soil communities, at least at the level manipulated in this experiment.     

Network structure, predator–prey modules, and stability in large food webs

Large, complex networks of ecological interactions with random structure tend invariably to instability. This mathematical relationship between complexity and local stability ignited a debate that has populated ecological literature for more than three decades. Here we show that, when species interact as predators and prey, systems as complex as the ones observed in nature can still be stable. Moreover, stability is highly robust to perturbations of interaction strength, and is largely a property of structure driven by predator–prey loops with the stability of these small modules cascading into that of the whole network. These results apply to empirical food webs and models that mimic the structure of natural systems as well. These findings are also robust to the inclusion of other types of ecological links, such as mutualism and interference competition, as long as consumer–resource interactions predominate. These considerations underscore the influence of food web structure on ecological dynamics and challenge the current view of interaction strength and long cycles as main drivers of stability in natural communities. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The Effects of Spatial Scale on Trophic Interactions

Food chain models have dominated empirical studies of trophic interactions in the past decades, and have lead to important insights into the factors that control ecological communities. Despite the importance of food chain models in instigating ecological investigations, many empirical studies still show a strong deviation from the dynamics that food chain models predict. We present a theoretical framework that explains some of the discrepancies by showing that trophic interactions are likely to be strongly influenced by the spatial configuration of consumers and their resources. Differences in the spatial scale at which consumers and their resources function lead to uncoupling of the population dynamics of the interacting species, and may explain overexploitation and depletion of resource populations. We discuss how changed land use, likely the most prominent future stress on natural systems, may affect food web dynamics by interfering with the scale of interaction between consumers and their resource.     

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.