Positive complexity-stability relations in food web models without foraging adaptation

May's [1972. Will a large complex system be stable? Nature 238, 413-414] local stability analysis of random food web models showed that increasing network complexity leads to decreasing stability, a result that is contradictory to earlier empirical findings. Since this seminal work, research of complexity-stability relations became one of the most challenging issues in theoretical ecology. We investigate conditions for positive complexity-stability relations in the niche, cascade, nested hierarchy, and random models by evaluating the network robustness, i.e., the fraction of surviving species after population dynamics. We find that positive relations between robustness and complexity can be obtained when resources are large, Holling II functional response is used and interaction strengths are weighted with the number of prey species, in order to take foraging efforts into account. In order to obtain these results, no foraging dynamics needs to be included. However, the niche model does not show positive complexity-stability relations under these conditions. By comparing to empirical food web data, we show that the niche model has unrealistic distributions of predator numbers. When this distribution is randomized, positive complexity-stability relations can be found also in the niche model.     

Species dynamics alter community diversity–biomass stability relationships

The relationship between community diversity and biomass variability remains a crucial ecological topic, with positive, negative and neutral diversity–stability relationships reported from empirical studies. Theory highlights the relative importance of Species–Species or Species–Environment interactions in driving diversity–stability patterns. Much previous work is based on an assumption of identical (stable) species‐level dynamics. We studied ecosystem models incorporating stable, cyclic and more complex species‐level dynamics, with either linear or non‐linear density dependence, within a locally stable community framework. Species composition varies with increasing diversity, interacting with the correlation of species' environmental responses to drive either positive or negative diversity–stability patterns, which theory based on communities with only stable species‐level dynamics fails to predict. Including different dynamics points to new mechanisms that drive the full range of diversity–biomass stability relationships in empirical systems where a wider range of dynamical behaviours are important.     

Increasing community size and connectance can increase stability in competitive communities

The relationship between community complexity and stability has been the subject of an enduring debate in ecology over the last 50 years. Results from early model communities showed that increased complexity is associated with decreased local stability. I demonstrate that increasing both the number of species in a community and the connectance between these species results in an increased probability of local stability in discrete-time competitive communities, when some species would show unstable dynamics in the absence of competition. This is shown analytically for a simple case and across a wider range of community sizes using simulations, where individual species have dynamics that can range from stable point equilibria to periodic or more complex. Increasing the number of competitive links in the community reduces per-capita growth rates through an increase in competitive feedback, stabilising oscillating dynamics. This result was robust to the introduction of a trade-off between competitive ability and intrinsic growth rate and changes in species interaction strengths. This throws new light on the discrepancy between the theoretical view that increased complexity reduces stability and the empirical view that more complex systems are more likely to be stable, giving one explanation for the relative lack of complex dynamics found in natural systems. I examine how these results relate to diversity-biomass stability relationships and show that an analytical solution derived in the region of stable equilibrium dynamics captures many features of the change in biomass fluctuations with community size in communities including species with oscillating dynamics.     

The role of behavioral dynamics in determining the patch distributions of interacting species

The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single-species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two-species-two-patch model of competition, where the population dynamical equilibrium in the absence of movement is often not a behavioral equilibrium in the presence of adaptive movement. The population dynamics of this system are explored for several different movement rules and different parameter values, producing a variety of outcomes. Other systems of interacting species that may lack a dynamically stable distribution among patches are discussed, and it is argued that such systems are not rare. The sensitivity of community properties to individual movement behavior in this and earlier studies argues that there is a great need for empirical investigation to determine the applicability of different models of the behavioral dynamics of habitat selection.     

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。     

Towards novel approaches to modelling biotic interactions in multispecies assemblages at large spatial extents

Aim Biotic interactions – within guilds or across trophic levels – have widely been ignored in species distribution models (SDMs). This synthesis outlines the development of ‘species interaction distribution models’ (SIDMs), which aim to incorporate multispecies interactions at large spatial extents using interaction matrices. Location Local to global. Methods We review recent approaches for extending classical SDMs to incorporate biotic interactions, and identify some methodological and conceptual limitations. To illustrate possible directions for conceptual advancement we explore three principal ways of modelling multispecies interactions using interaction matrices: simple qualitative linkages between species, quantitative interaction coefficients reflecting interaction strengths, and interactions mediated by interaction currencies. We explain methodological advancements for static interaction data and multispecies time series, and outline methods to reduce complexity when modelling multispecies interactions. Results Classical SDMs ignore biotic interactions and recent SDM extensions only include the unidirectional influence of one or a few species. However, novel methods using error matrices in multivariate regression models allow interactions between multiple species to be modelled explicitly with spatial co‐occurrence data. If time series are available, multivariate versions of population dynamic models can be applied that account for the effects and relative importance of species interactions and environmental drivers. These methods need to be extended by incorporating the non‐stationarity in interaction coefficients across space and time, and are challenged by the limited empirical knowledge on spatio‐temporal variation in the existence and strength of species interactions. Model complexity may be reduced by: (1) using prior ecological knowledge to set a subset of interaction coefficients to zero, (2) modelling guilds and functional groups rather than individual species, and (3) modelling interaction currencies and species’ effect and response traits. Main conclusions There is great potential for developing novel approaches that incorporate multispecies interactions into the projection of species distributions and community structure at large spatial extents. Progress can be made by: (1) developing statistical models with interaction matrices for multispecies co‐occurrence datasets across large‐scale environmental gradients, (2) testing the potential and limitations of methods for complexity reduction, and (3) sampling and monitoring comprehensive spatio‐temporal data on biotic interactions in multispecies communities.     

Allometric scaling enhances stability in complex food webs

Classic local stability theory predicts that complex ecological networks are unstable and are unlikely to persist despite empiricists' abundant documentation of such complexity in nature. This contradiction has puzzled biologists for decades. While some have explored how stability may be achieved in small modules of a few interacting species, rigorous demonstrations of how large complex and ecologically realistic networks dynamically persist remain scarce and inadequately understood. Here, we help fill this void by combining structural models of complex food webs with nonlinear bioenergetic models of population dynamics parameterized by biological rates that are allometrically scaled to populations' average body masses. Increasing predator–prey body mass ratios increase population persistence up to a saturation level that is reached by invertebrate and ectotherm vertebrate predators when being 10 or 100 times larger than their prey respectively. These values are corroborated by empirical predator–prey body mass ratios from a global data base. Moreover, negative effects of diversity (i.e. species richness) on stability (i.e. population persistence) become neutral or positive relationships at these empirical ratios. These results demonstrate that the predator–prey body mass ratios found in nature may be key to enabling persistence of populations in complex food webs and stabilizing the diversity of natural ecosystems.     

Population stability is higher in more diverse annual plant communities

Abstract Theoretical work suggests a paradoxical effect of diversity on the temporal stability of ecological systems: increasing diversity should result in decreased stability of populations while community stability is enhanced. While empirical work indicates that community stability tends to increase with diversity, investigations of the effect of diversity on populations have resulted in few clear patterns. Here, we examine relationships between community diversity and population stability in unmanipulated annual plant communities. We show that, counter to theory, the temporal stability of annual plant populations increases with diversity. In addition, and again counter to theoretical assumptions, mean population size tends to increase with diversity, a pattern most likely due to variation in local productivity. The fact that community diversity, population size and the temporal stability of populations covaried positively suggests that abiotic factors such as productivity may govern population stability to such an extent as to override potential effects of diversity.     

Qualitative stability and ambiguity in model ecosystems

Qualitative analysis of stability in model ecosystems has previously been limited to determining whether a community matrix is sign stable or not with little analytical means to assess the impact of complexity on system stability. Systems are seen as either unconditionally or conditionally stable with little distinction and therefore much ambiguity in the likelihood of stability. First, we reexamine Hurwitz's principal theorem for stability and propose two "Hurwitz criteria" that address different aspects of instability: positive feedback and insufficient lower-level feedback. Second, we derive two qualitative metrics based on these criteria: weighted feedback (wF(n)) and weighted determinants (wDelta(n)). Third, we test the utility of these qualitative metrics through quantitative simulations in a random and evenly distributed parameter space in models of various sizes and complexities. Taken together they provide a practical means to assess the relative degree to which ambiguity has entered into calculations of stability as a result of system structure and complexity. From these metrics we identify two classes of models that may have significant relevance to system research and management. This work helps to resolve some of the impasse between theoretical and empirical discussions on the complexity and stability of natural communities.     

Predator decline leads to decreased stability in a coastal fish community

Fisheries exploitation has caused widespread declines in marine predators. Theory predicts that predator depletion will destabilise lower trophic levels, making natural communities more vulnerable to environmental perturbations. However, empirical evidence has been limited. Using a community matrix model, we empirically assessed trends in the stability of a multispecies coastal fish community over the course of predator depletion. Three indices of community stability (resistance, resilience and reactivity) revealed significantly decreasing stability concurrent with declining predator abundance. The trophically downgraded community exhibited weaker top‐down control, leading to predator‐release processes in lower trophic levels and increased susceptibility to perturbation. At the community level, our results suggest that high predator abundance acts as a stabilising force to the naturally stochastic and highly autocorrelated dynamics in low trophic species. These findings have important implications for the conservation and management of predators in marine ecosystems and provide empirical support for the theory of predatory control.     

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 ecology and evolution of host-plant resistance to insects

Genetic techniques have yielded new insights into plant-herbivore coevolution. Quantitative genetic tests of herbivory theory reveal that in some cases insect herbivores impose selection on resistance traits. Also, some resistance traits are costly while others appear not to be, and genetic models can explain these results. Genetic variation in plant resistance influences insect community structure by modifying interactions of herbivores with competitors and natural enemies. Therefore, models of multispecies coevolution are more realistic than pairwise coevolutionary models. Ecological genetics will facilitate further theoretical and empirical exploration of multispecies coevolution of plants and herbivores.     

Experimental evidence rejects pairwise modelling approach to coexistence in plant communities

Competition is often invoked as the cause of plant species loss with increasing system productivity. Experimental results for multispecies assemblages are virtually absent and mathematical models are thus used to explore the relationship between competition and coexistence. Modelling approaches to coexistence and diversity in competitive communities commonly employ Lotka-Volterra-type (LV) models with additive pairwise competitive effects.Using pairwise plant competition experiments, we calibrate the LV system and use it to predict plant biomass and coexistence in six three-species and one seven-species experimental mixture. Our results show that five out of the six three-species sets and the seven-species set deviate significantly from LV model predictions. Fitting an additional non-additive competition coefficient resulted in predictions that more closely matched the experimental results, with stable coexistence suggested in all but one case. These results are discussed with particular reference to the possible underlying mechanisms of coexistence in our experimental community. Modelling the effect of competition intensity on stability indicates that if non-additive effects occur, they will be relevant over a wide range of community sizes. Our findings caution against relying on coexistence predictions based on LV models.     

A method to determine rates and patterns of variability in ecological communities

It is well known that ecological communities are spatially and temporally dynamic. Quantifying temporal variability in ecological communities is challenging, however, especially for time-series data sets of less than 40 measurement intervals. In this paper, we describe a method to quantify temporal variability in multispecies communities over time frames of 10–40 measurement intervals. Our approach is a community-level extension of autocorrelation analysis, but we use Euclidean distance to measure similarity of community samples at increasing time lags rather than the correlation coefficient. Regressing Euclidean distances versus increasing time lags yields a measure of the rate and nature of community change over time. We demonstrate the method with empirical data sets from shortgrass steppe, old-field succession and zooplankton dynamics in lakes, and we investigate properties of the analysis using simulation models. Results indicate that time-lag analysis provides a useful quantitative measurement of the rate and pattern of temporal dynamics in communities over time frames that are too short for more traditional autocorrelation approaches.     

Individual species–area relationships and spatial patterns of species diversity in a Great Basin,semi‐arid shrubland

Traditional biodiversity metrics operate at the level of a plant community but do not capture spatial variation in diversity from a ‘plant's‐eye view’ of a community. Recently‐developed statistics consider the spatial patterns of plants as well as the number and distribution of species in local plant neighborhoods to quantitatively assess multispecies spatial patterns from a ‘plant's‐eye view’. We used one such statistic, the individual species area relationship (ISAR), to assess spatial patterns of species diversity in a Great Basin (USA) semi‐arid shrubland through an analysis of a spatial dataset on shrub species and locations. In conjunction with appropriate null models, the ISAR blends species area relationships with second‐order spatial statistics to measure the expected species richness in local neighborhoods of variable size around the individuals of a focal species within a community. We found that, contrary to a previous analysis using more traditional methods, the community was well‐mixed with a typical shrub surrounded on average by 4.9 shrub neighbors of 2.1 species at a neighborhood scale of 1.0 m. We also found statistically significant fine‐scale variation in diversity patterns, such that neighborhoods of two species were more diverse than expected by a heterogeneous Poisson null model that accounted for larger‐scale habitat heterogeneity. However, this effect was caused by intraspecific aggregation of these species and was not due to positive interspecific association. Contrary to previous findings in other semi‐arid shrublands, our analysis suggests that the spatial pattern of the shrub community was not significantly structured by interspecific facilitation. This result supports growing evidence for balanced species patterns of adult plants in multispecies communities. Our approach may be used in other communities to describe complex multispecies spatial patterns, quantify species‐specific associations with diversity patterns, and to generate hypotheses regarding relationships between patterns and community‐structuring processes.     

Contrasting effects of diversity on the temporal stability of plant populations

Recent theoretical and empirical work suggests that diversity enhances the temporal stability of a community. However, the effect of diversity on the stability of the individual populations within the community remains unclear. Some models predict a decrease of population stability with diversity, whereas others suggest that diversity has a stabilizing effect on populations. Empirical evidence for either relationship between population stability and diversity is weak. The few studies that directly assessed the stability of populations reported contradicting results. We used a six-year data-set from a plant diversity experiment to examine the relationships between diversity and temporal stability of plant biomass. Our results show that stability increased with diversity at the community-level, while the stability of populations, averaged over all species, decreased with diversity. However, when examining species separately we found positive, negative and neutral relationships between population stability and diversity. Our findings suggest that diversity may contribute to the stability of ecosystem services at the community level, but the effect of diversity on the stability of the individual populations within the community are generally negative. However, different species within the community may show strikingly different relationships between diversity and stability.     

Disentangling the effect of hybrid interactions and of the constant effort hypothesis on ecological community stability

In the last years, a remarkable theoretical effort has been made in order to understand the relation between stability and complexity in ecological communities. Yet, what maintains species diversity in real ecological communities is still an open question. The non‐random structures of ecological interaction networks have been recognized as one key ingredient impacting the maximum number of coexisting species within the ecological community. However most of the earlier theoretical studies have considered communities with only one interaction type (either antagonistic, competitive or mutualistic). Recently, it has been proposed that multiple interaction types might stabilize ecosystems and that, in this hybrid case, increasing complexity increases stability. Here we show that these results depend on ad hoc hypothesis that the authors used in their model and we highlight the need to disentangle the role of multiple interaction types and constant interaction effort allocation on community stability. Indeed, we find that mixing of mutualistic and predator–prey interaction types does not stabilize the community dynamics and we demonstrate that a positive correlation between complexity and stability is observed only if a constant effort allocation is imposed in the ecological interactions. Synthesis In recent years a sparkling research has been devoted to the search of new theoretical mechanisms to explain way ecosystems may persist despite their complexity. Here we show that, contrary to what recently suggested (Mougi et al. 2012), the mismatch between theoretical results and empirical evidences on the stability of ecological community is still there also for communities with both mutualistic and antagonistic interactions, and the ‘complexity‐stability’ paradox is still alive. Indeed, we demonstrate that their results arise as an artifact of the peculiar rescaling of the interaction strengths they imposed. Our study suggests that further theoretical studies and experimental evidences are still needed to better understand the role of interaction strengths in real ecological communities.     

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.     

Coral reef fisheries stock assessment

Summary Although all fisheries are multispecies and spatially heterogeneous, coral reef fisheries are an extreme in both respects. The two main approaches to stock assessment have been either to consider individual species separately or to lump all species together. Both are limited in their predictive power. The lack of ecological knowledge and the large number of parameters required make methods based on single species often impractical or expensive. However, where the appropriate information is available, ecological studies do not provide significant improvements on yield-per-recruit or surplus yield models currently used.Alternative community models based on aggregates of species lack predictive power, empirical support and relative data. Models are further limited because they do not address various economic aspects, fish movement and recruitment, all of which must be spatially resolved. However, the ECOPATH model, based on trophic compartments, represents a new approach useful to multispecies assessment, and the only way at present to include predation in stock models. In practice the data available will be the most important factor in the choice of stock assessment model.The major concern for management of many coral reefs is conservation of the habitat and stocks. In some cases this has been achieved with little reference to stock assessment, by using community management and closed areas, which are receiving increasing support. However, once the objective of conservation is achieved, stock assessment should have an important role in improving the economic performance of the fisheries. The wider problems of management have no simple solutions, but managers should look to adaptive management, designing their own experiments to choose between management models.     

Does predator interference cause alternative stable states in multispecies communities?

Whereas it is well known that simple ecological mechanisms may promote stability in simple species models, their consequences for stability and resilience in multispecies communities are largely unexplored. Here, we studied the effect of predator interference on the occurrence of alternative attractors and complex dynamics in randomly constructed multispecies predator-prey communities. We studied three types of interference: random interference (“asymmetric”), random interference but symmetrical between pairs of predators (“symmetric”), and interference among only the same species (“conspecific”). In all cases predator interference increased the average number of alternative attractors, whereas at the same time it reduced the emergence of oscillatory or chaotic dynamics. Our findings demonstrate a contrasting effect of predator interference on the stability of a community: on the one hand it reduces cycles and chaos in the dynamics, on the other hand predator interference increases the likelihood that communities may undergo critical transitions between multiple stable states.