A landscape theory for food web architecture

Ecologists have long searched for structures and processes that impart stability in nature. In particular, food web ecology has held promise in tackling this issue. Empirical patterns in food webs have consistently shown that the distributions of species and interactions in nature are more likely to be stable than randomly constructed systems with the same number of species and interactions. Food web ecology still faces two fundamental challenges, however. First, the quantity and quality of food web data required to document both the species richness and the interaction strengths among all species within food webs is largely prohibitive. Second, where food webs have been well documented, spatial and temporal variation in food web structure has been ignored. Conversely, research that has addressed spatial and temporal variation in ecosystems has generally ignored the full complexity of food web architecture. Here, we incorporate empirical patterns, largely from macroecology and behavioural ecology, into a spatially implicit food web structure to construct a simple landscape theory of food web architecture. Such an approach both captures important architectural features of food webs and allows for an exploration of food web structure across a range of spatial scales. Finally, we demonstrated that food webs are hierarchically organized along the spatial and temporal niche axes of species and their utilization of food resources in ways that stabilize ecosystems.     

Integrating food web diversity, structure and stability

Given the unprecedented rate of species extinctions facing the planet, understanding the causes and consequences of species diversity in ecosystems is of paramount importance. Ecologists have investigated both the influence of environmental variables on species diversity and the influence of species diversity on ecosystem function and stability. These investigations have largely been carried out without taking into account the overarching stabilizing structures of food webs that arise from evolutionary and successional processes and that are maintained through species interactions. Here, we argue that the same large-scale structures that have been purported to convey stability to food webs can also help to understand both the distribution of species diversity in nature and the relationship between species diversity and food web stability. Specifically, the allocation of species diversity to slow energy channels within food webs results in the skewed distribution of interactions strengths that has been shown to confer stability to complex food webs. We end by discussing the processes that might generate and maintain the structured, stable and diverse food webs observed in nature.     

Re-evaluating the omnivory–stability relationship in food webs

Under equilibrium conditions, previous theory has shown that the presence of omnivory destabilizes food webs. Correspondingly, omnivory ought to be rare in real food webs. Although, early food web data appeared to verify this, recently many ecologists have found omnivory to be ubiquitous in food web data gathered at a high taxonomic resolution. In this paper, we re-investigate the role of omnivory in food webs using a non-equilibrium perspective. We find that the addition of omnivory to a simple food chain model (thus a simple food web) locally stabilizes the food web in a very complete way. First, non-equilibrium dynamics (e.g. chaos) tend to be eliminated or bounded further away from zero via period-doubling reversals invoked by the omnivorous trophic link. Second, food chains without interior attractors tend to gain a stable interior attractor with moderate amounts of omnivory.     

食物网稳定性机制研究进展:一个基于等级系统的框架

食物网理论沟通了群落生态学和生态系统生态学,将生物多样性和生态系统功能的研究统一起来,是理解生态系统运作机制的关键。自从1973年Robert May的经典研究引发著名的"复杂性-稳定性"论辩之后,人们认识到食物网的稳定性是其结构维持、功能发挥和动态演化的一个重要前提,并开始了对食物网稳定性机制的探索。早期研究主要关注只包含拓扑关系的定性食物网,但后来人们逐渐认识到相互作用强度的重要性,并提出了诸如自限性、弱相互作用、适应性捕食等一系列机制。本文系统梳理了过往研究中模块层面的各类稳定性机制和全网层面对各模块的整合机制,从而清晰地展示了"模块-全网"双层框架的全貌。通过在其基础上的扩展,进而提出了一个基于等级系统的食物网稳定性框架,并从动力学和能量学角度,对各层级内部的稳定性机制以及层级之间的关系进行了探讨,以期为建立普适的食物网稳定性理论提供一些思路。未来的研究方向包括：①将稳定性机制的研究从食物网扩展到更一般的生态网络;②综合考虑生物物理要素、动力学稳定性、系统对能流功率的追求、环境的平稳程度、演化历史等影响因素,从而得到关于食物网结构和动态的更为深刻的认识。     

基于土壤食物网的生态系统复杂性-稳定性关系研究进展

复杂性-稳定性关系是生态学核心问题之一。作为模式食物网,土壤食物网在探索生态系统复杂性-稳定性关系中起了极大的作用。总结了以Moore、de Ruiter、Neutel等为代表的理论生态学家以土壤食物网为工具研究生态系统复杂性-稳定性关系的方法、结论及不足之处,并展望了未来的发展方向。Moore、de Ruiter、Neutel等将土壤食物网功能群生物量数据、土壤食物网Lotka-Volterra模型和面向过程模型三者结合起来,描述相互作用强度大小格局、分室、能流组织形式等复杂性特征;将土壤食物网Lotka-Volterra模型与群落矩阵结合起来分析局域稳定性,进而探讨生态系统复杂性-稳定性关系的一般规律。在此基础上,Moore、de Ruiter、Neutel等证明了与随机食物网相比,真实食物网的相互作用强度格局、分室等复杂性特征提高了生态系统稳定性,生产力与稳定性共同决定了食物链的长度,并指出建立在平衡态基础上的静态土壤食物网模型在探索生态系统复杂性-稳定性关系方面具有较大的不足,动态土壤食物网是未来以土壤食物网为工具研究生态系统复杂性-稳定性关系的发展方向。     

Antagonistic and Synergistic Interactions Among Predators

The structure and dynamics of food webs are largely dependent upon interactions among consumers and their resources. However, interspecific interactions such as intraguild predation and interference competition can also play a significant role in the stability of communities. The role of antagonistic/synergistic interactions among predators has been largely ignored in food web theory. These mechanisms influence predation rates, which is one of the key factors regulating food web structure and dynamics, thus ignoring them can potentially limit understanding of food webs. Using nonlinear models, it is shown that critical aspects of multiple predator food web dynamics are antagonistic/synergistic interactions among predators. The influence of antagonistic/synergistic interactions on coexistence of predators depended largely upon the parameter set used and the degree of feeding niche differentiation. In all cases when there was no effect of antagonism or synergism (a _ij =1.00), the predators coexisted. Using the stable parameter set, coexistence occurred across the range of antagonism/synergism used. However, using the chaotic parameter strong antagonism resulted in the extinction of one or both species, while strong synergism tended to coexistence. Whereas using the limit cycle parameter set, coexistence was strongly dependent on the degree of feeding niche overlap. Additionally increasing the degree of feeding specialization of the predators on the two prey species increased the amount of parameter space in which coexistence of the two predators occurred. Bifurcation analyses supported the general pattern of increased stability when the predator interaction was synergistic and decreased stability when it was antagonistic. Thus, synergistic interactions should be more common than antagonistic interactions in ecological systems.     

Global stability, local stability and permanence in model food webs

The dynamical theory of food webs has been based typically on local stability analysis. The relevance of local stability to food web properties has been questioned because local stability holds only in the immediate vicinity of the equilibrium and provides no information about the size of the basin of attraction. Local stability does not guarantee persistence of food webs in stochastic environments. Moreover, local stability excludes more complex dynamics such as periodic and chaotic behaviors, which may allow persistence. Global stability and permanence could be better criteria of community persistence. Our simulation analysis suggests that these three stability measures are qualitatively consistent in that all three predict decreasing stability with increasing complexity. Some new predictions on how stability depends on food web configurations are generated here: a consumer-victim link has a smaller effect on the probabilities of stability, as measured by all three stability criteria, than a pair of recipient-controlled and donor-controlled links; a recipient-controlled link has a larger effect on the probabilities of local stability and permanence than a donor-controlled link, while they have the same effect on the probability of global stability; food webs with equal proportions of donor-controlled and recipient-controlled links are less stable than those with different proportions.     

Local stability properties of complex,species‐rich soil food webs with functional block structure

Ecologists have long debated the properties that confer stability to complex, species‐rich ecological networks. Species‐level soil food webs are large and structured networks of central importance to ecosystem functioning. Here, we conducted an analysis of the stability properties of an up‐to‐date set of theoretical soil food web models that account both for realistic levels of species richness and the most recent views on the topological structure (who is connected to whom) of these food webs. The stability of the network was best explained by two factors: strong correlations between interaction strengths and the blocked, nonrandom trophic structure of the web. These two factors could stabilize our model food webs even at the high levels of species richness that are typically found in soil, and that would make random systems very unstable. Also, the stability of our soil food webs is well‐approximated by the cascade model. This result suggests that stability could emerge from the hierarchical structure of the functional organization of the web. Our study shows that under the assumption of equilibrium and small perturbations, theoretical soil food webs possess a topological structure that allows them to be complex yet more locally stable than their random counterpart. In particular, results strongly support the general hypothesis that the stability of rich and complex soil food webs is mostly driven by correlations in interaction strength and the organization of the soil food web into functional groups. The implication is that in real‐world food web, any force disrupting the functional structure and distribution pattern of interaction strengths (i.e., energy fluxes) of the soil food webs will destabilize the dynamics of the system, leading to species extinction and major changes in the relative abundances of species.     

Reconciling the omnivory-stability debate

Despite attempts at reconciliation, the role of omnivory in food web stability remains unclear. Here we develop a novel community matrix approach that is analogous to the bifurcation method of modular food web theory to show that the stability of omnivorous food chains depends critically on interaction strength. We find that there are only six possible ways that omnivorous interaction strengths can influence the stability of linear food chains. The results from these six cases suggest that: (1) strong omnivory is always destabilizing, (2) stabilization by weak to intermediate omnivorous interaction strengths dominates the set of possible stability responses, and, (3) omnivory can be occasionally strictly destabilizing or intermittently destabilizing. We then revisit the classical results of Pimm and Lawton to show that although their parameterization tends to produce a low percentage of stable omnivorous webs, the same parameterization shows strong theoretical support for the weak interaction effect. Finally, we end by arguing that our current empirical knowledge of omnivory resonates with this general theory.     

The effects of space and diversity of interaction types on the stability of complex ecological networks

The relationship between structure and stability in ecological networks and the effect of spatial dynamics on natural communities have both been major foci of ecological research for decades. Network research has traditionally focused on a single interaction type at a time (e.g. food webs, mutualistic networks). Networks comprising different types of interactions have recently started to be empirically characterized. Patterns observed in these networks and their implications for stability demand for further theoretical investigations. Here, we employed a spatially explicit model to disentangle the effects of mutualism/antagonism ratios in food web dynamics and stability. We found that increasing levels of plant-animal mutualistic interactions generally resulted in more stable communities. More importantly, increasing the proportion of mutualistic vs. antagonistic interactions at the base of the food web affects different aspects of ecological stability in different directions, although never negatively. Stability is either not influenced by increasing mutualism—for the cases of population stability and species’ spatial distributions—or is positively influenced by it—for spatial aggregation of species. Additionally, we observe that the relative increase of mutualistic relationships decreases the strength of biotic interactions in general within the ecological network. Our work highlights the importance of considering several dimensions of stability simultaneously to understand the dynamics of communities comprising multiple interaction types.     

Sustainability without coexistence state in Durrett–Levin hawk–dove model

Models that explain the sustainability of an exploiter–victim ecosystem admit, generally, a coexistence state of both species in the well-mixed limit. Even if this state is unstable, the extinction-prone system may acquire stability on spatial domains where different patches oscillate incoherently around the coexistence state. New experiments, however, suggest that a spatially segregated system may be stable even in the absence of such a coexistence state. Here we revisit the hawk–dove (case 3) model of Durrett and Levin, which has been shown to support persistent population for system of interacting particles. It turns out that this model does not admit a (stable or unstable) coexistence state on a single habitat. We analyze the peculiar mechanism that leads to persistence in this case and the role of demographic stochasticity with and without self-interaction, using numerical simulations and exact solutions in the infinite diffusion limit.     

Why allometric scaling enhances stability in food web models

It has recently been shown that the incorporation of allometric scaling into the dynamic equations of food web models enhances network stability if predators are assigned a higher body mass than their prey. We investigate the underlying mechanisms leading to this stability increase. The dynamic equations can be written such that allometric scaling influences these equations at three places: the time scales of predator and prey dynamics become separated, the energy outflow to the predators is decreased, and intraspecific competition is increased relative to metabolic rates. For five food web topologies and various network sizes (i.e., species richness), we study the effect of each of these modifications on the percentage of surviving species separately and find that the decreased interaction strengths and the increased intraspecific competition are responsible for the enhanced stability. We also investigate the range of parameter values for which an enhanced stability is observed.     

Complex shifts between food web states in response to whole‐ecosystem manipulations

Food webs can respond in surprising and complex ways to temporary alterations in their species composition. When such a perturbation is reversed, food webs have been shown to either return to the pre‐perturbation community state or remain in the food web configuration that established during the perturbation. Here we report findings from a replicated whole‐lake experiment investigating food web responses to a perturbation and its consecutive reversal. We could identify three distinct community states in the food web that corresponded to the periods before, during and after the perturbation. Most importantly, we demonstrate the establishment of a distinct post‐perturbation food web configuration that differed from both the pre‐ and during‐perturbation communities in phytoplankton biomass and micro‐ and mesozooplankton species composition. We suggest that the pre‐ and post‐perturbation food web configurations may represent two alternative stable community states. We provide explanations for how each of the contrasting communities may be maintained through altered species interactions. These findings add to the discussion of how natural food webs react to environmental change and imply that the range of potential ecosystem dynamics in response to perturbations can be wider and more complex than is often recognized.     

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.     

Current food web models cannot explain the overall topological structure of observed food webs

Topological food webs illustrating “who eats whom” in different systems exhibit similar, non‐random, structures suggesting that general rules govern food web structure. Current food web models correctly predict many measures of food web topology from knowledge of species richness and connectance (fraction of possible predator–prey links that actually occur), together with assumptions about the ecological rules governing “who eats whom”. However, current measures are relatively insensitive to small changes in topology. Improvement of, and discrimination among, current models requires development of new measures of food web structure. Here I examine whether current food web models (cascade, niche, and nested hierarchy models, plus a random null model) can predict a new measure of food web structure, structural stability. Structural stability complements other measures of food web topology because it is sensitive to changes in topology that other measures often miss. The cascade and null models respectively over‐ and underpredict structural stability for a set of 17 high‐quality food webs. While the niche and nested hierarchy models provide unbiased predictions on average, their 95% confidence intervals frequently fail to include the observed data. Observed structural stabilities for all models are overdispersed compared to model predictions, and predicted and observed structural stabilities are uncorrelated, indicating that important sources of variation in structural stability are not captured by the models. Crucially, poor model performance arises because observed variation in structural stability is unrelated to variation in species richness and connectance. In contrast, almost all other measures of food web topology vary with species richness and connectance in natural webs. No model that takes species richness and connectance as the only input parameters can reproduce observed variation in structural stability. Further progress in predicting and explaining food web topology will require fundamentally new models based on different input parameters.     

The relative importance of herbivory and carnivory on the distribution of energy in a stochastic tri-trophic food web

A three-state, discrete-time Markov chain is used to model the dynamics of energy flow in a tri-trophic food web. The distribution of energy in the three trophic levels is related to the rates of flow between the trophic levels and calculated for the entire range of possible flow values. These distributions are then analysed for stability and used to test the idea that plants are resource-limited and herbivores are predation-limited. Low rates of death and decomposition, when coupled with low rates of herbivory and carnivory, tend to destabilize this food web. Food webs with higher rates of death and decomposition are relatively more stable regardless of rates of herbivory and carnivory. Plants are more prone to resource-limitation and herbivores are, in general, limited by their predators, which supports Hairston et al. (Am. Nat. 94 (1960) 421). The rate of decomposition often mediates the roles of top-down and bottom-up control of energy flow in the food web.     

The dynamics of multispecies, multi-life-stage models of aquatic food webs

We investigated the dynamics of models of aquatic food webs using stability analysis methods previously applied to other types of food web models. Our models expanded traditional Lotka-Volterra models of predator-prey interactions in several ways. We added life history structure to these models in order to investigate its effects. Life history omnivory is different life history stages of a species feeding in trophically different positions in a food web. Such a species might appear omnivorous, integrating across all stages, but the individual stage might not be. Other important additions to the basic models included stock-recruitment relationships between adults and young and food-dependent maturation rates for early life history stages. Complex models of multispecies interactions were built from basic ones by adding new features sequentially. Our analysis revealed five major features of our multispecies, multi-life-stage models. Omnivory reduces stability, as it does in food web models without life history structure. However, life history omnivory reduces stability much less than single life stage omnivory does. Stock recruitment relationships affect the likelihood of finding stable models. If the maturation rate of young varies with their food supply, the chance of finding stable models decreases. Finally, predation loops of the type A eats B, B eats A, or A eats B, B eats C, C eats A greatly reduce model stability. We present both biological and mathematical explanations for these findings. We also discuss their implications for management of marine resources.     

The reduction of food web robustness by parasitism: fact and artefact

A robust food web is one which suffers few secondary extinctions after primary species losses. While recent research has shown that a food web with parasitism is less robust than one without, it still remains unclear whether the reduction in robustness is due to changes in network complexity or unique characteristics associated with parasitism. Here, using several published food webs, simulation experiments with different food web models and extinction scenarios were conducted to elucidate how such reduction can be achieved. Our results show that, regardless of changes in network complexity and preferential parasitism, the reduction in food web robustness is mainly due to the life cycle constraint of parasites. Our findings further demonstrate that parasites are prone to secondary extinctions and that their extinctions occur earlier than those involving free-living species. These findings suggest that the vulnerable nature of parasites to species loss makes them highly sensitive indicators of food web integrity.     

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.