Allometric degree distributions facilitate food-web stability

In natural ecosystems, species are linked by feeding interactions that determine energy fluxes and create complex food webs. The stability of these food webs enables many species to coexist and to form diverse ecosystems. Recent theory finds predator-prey body-mass ratios to be critically important for food-web stability. However, the mechanisms responsible for this stability are unclear. Here we use a bioenergetic consumer-resource model to explore how and why only particular predator-prey body-mass ratios promote stability in tri-trophic (three-species) food chains. We find that this 'persistence domain' of ratios is constrained by bottom-up energy availability when predators are much smaller than their prey and by enrichment-driven dynamics when predators are much larger. We also find that 97% of the tri-trophic food chains across five natural food webs exhibit body-mass ratios within the predicted persistence domain. Further analyses of randomly rewired food webs show that body mass and allometric degree distributions in natural food webs mediate this consistency. The allometric degree distributions hold that the diversity of species' predators and prey decreases and increases, respectively, with increasing species' body masses. Our results demonstrate how simple relationships between species' body masses and feeding interactions may promote the stability of complex food webs.     

Universal scaling relations in food webs

The structure of ecological communities is usually represented by food webs. In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks. Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs are different from those found in large ones. Furthermore, food webs (except in isolated cases) do not share general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character and a scale-free (power-law) distribution of the degree (the number of links per vertex). Here we propose to describe food webs as transportation networks by extending to them the concept of allometric scaling (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.     

Structural asymmetry and the stability of diverse food webs

Untangling the influence of human activities on food-web stability and persistence is complex given the large numbers of species and overwhelming number of interactions within ecosystems. Although biodiversity has been associated with stability, the actual structures and processes that confer stability to diverse food webs remain largely unknown. Here we show that real food webs are structured such that top predators act as couplers of distinct energy channels that differ in both productivity and turnover rate. Our theoretical analysis shows that coupled fast and slow channels convey both local and non-local stability to food webs. Alarmingly, the same human actions that have been implicated in the loss of biodiversity also directly erode the very structures and processes that we show to confer stability on food webs.     

Compartments revealed in food-web structure

Compartments in food webs are subgroups of taxa in which many strong interactions occur within the subgroups and few weak interactions occur between the subgroups. Theoretically, compartments increase the stability in networks, such as food webs. Compartments have been difficult to detect in empirical food webs because of incompatible approaches or insufficient methodological rigour. Here we show that a method for detecting compartments from the social networking science identified significant compartments in three of five complex, empirical food webs. Detection of compartments was influenced by food web resolution, such as interactions with weights. Because the method identifies compartmental boundaries in which interactions are concentrated, it is compatible with the definition of compartments. The method is rigorous because it maximizes an explicit function, identifies the number of non-overlapping compartments, assigns membership to compartments, and tests the statistical significance of the results. A graphical presentation reveals systemic relationships and taxa-specific positions as structured by compartments. From this graphic, we explore two scenarios of disturbance to develop a hypothesis for testing how compartmentalized interactions increase stability in food webs.     

Ecosystem-level patterns of primary productivity and herbivory in terrestrial habitats

Ecosystems are structurally organized as food webs within which energy is transmitted between trophic levels and dissipated into the environment. Energy flow between two trophic levels is given by the amount of production at the lower level and by the proportion of production that is consumed, assimilated and respired at the higher level. Considerable evidence indicates that food-web structure varies predictably in different habitats, but much less is known about quantitative relationships among food web fluxes. Many of the energetic properties of herbivores in African game parks are associated with rainfall and, by inference, with net primary productivity. Respiratory costs per unit production at the consumer trophic level are higher for homeotherms than for heterotherms. Plant secondary chemicals affect herbivore dietary choices and the allocation of plant resources to those chemicals varies with resource availability. How these phenomena are translated into ecosystem fluxes is unknown. We present evidence that herbivore biomass, consumption and productivity are closely correlated with plant productivity, suggesting that the latter is a principal integrator and indicator of functional processes in food webs.     

内蒙古草原锡林河流域植物群落生物量及多样性沿土壤水分含量梯度的变化

在内蒙古草原锡林河流域土壤水分含量梯度上,测定土壤含水量并调查植物群落样方,探讨植物群落生物量及多样性沿水分梯度的变化.发现植物群落地上生物量和物种丰富度与土壤含水量之间呈显著的单峰关系;而香侬威纳指数和Pielous均匀度指数与土壤含水量之间不存在显著的相关关系.植物群落物种丰富度和香侬威纳指数与地上生物量之间呈显著的正相关关系;而Pielous均匀度指数与地上生物量之间不存在显著的相关关系.结果表明土壤含水量对半干旱草原植物群落的丰富度和生产力的影响极为显著,但不同土壤含水量对群落均匀性的影响有限,说明除土壤含水量外还有其他因素影响草原植物群落的结构.     

Stability criteria for complex ecosystems

Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (for example predator-prey, mutualistic or competitive). Here we extend May's results to these relationships and find remarkable differences between predator-prey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predator-prey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predator-prey networks can be arbitrarily large and complex, provided that predator-prey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.     

Predator diversity dampens trophic cascades

Food web complexity is thought to weaken the strength of terrestrial trophic cascades in which strong impacts of natural enemies on herbivores cascade to influence primary production indirectly. Predator diversity can enhance food web complexity because predators may feed on each other and on shared prey. In such cases, theory suggests that the impact of predation on herbivores relaxes and cascading effects on basal resources are dampened. Despite this view, no empirical studies have explicitly investigated the role of predator diversity in mediating primary productivity in a natural terrestrial system. Here we compare, in a coastal marsh community, impacts of arthropod predators on herbivores and plant productivity between a simple food web with a single predator species and a complex food web with a diverse predator assemblage. We show that enhancing predator diversity dampens enemy effects on herbivores and weakens trophic cascades. Consequently, changes in diversity at higher trophic levels can significantly alter ecosystem function in natural systems.     

Symbiotic fungal endophytes control insect host-parasite interaction webs

Symbiotic microorganisms that live intimately associated with terrestrial plants affect both the quantity and quality of resources, and thus the energy supply to consumer populations at higher levels in the food chain. Empirical evidence on resource limitation of food webs points to primary productivity as a major determinant of consumer abundance and trophic structure. Prey quality plays a critical role in community regulation. Plants infected by endophytic fungi are known to be chemically protected against herbivore consumption. However, the influence of this microbe-plant association on multi-trophic interactions remains largely unexplored. Here we present the effects of fungal endophytes on insect food webs that reflect limited energy transfer to consumers as a result of low plant quality, rather than low productivity. Herbivore-parasite webs on endophyte-free grasses show enhanced insect abundance at alternate trophic levels, higher rates of parasitism, and increased dominance by a few trophic links. These results mirror predicted effects of increased productivity on food-web dynamics. Thus 'hidden' microbial symbionts can have community-wide impacts on the pattern and strength of resource-consumer interactions.     

Consumer versus resource control of species diversity and ecosystem functioning

A key question in ecology is which factors control species diversity in a community. Two largely separate groups of ecologists have emphasized the importance of productivity or resource supply, and consumers or physical disturbance, respectively. These variables show unimodal relationships with diversity when manipulated in isolation. Recent multivariate models, however, predict that these factors interact, such that the disturbance diversity relationship depends on productivity, and vice versa. We tested these models in marine food webs, using field manipulations of nutrient resources and consumer pressure on rocky shores of contrasting productivity. Here we show that the effects of consumers and nutrients on diversity consistently depend on each other, and that the direction of their effects and peak diversity shift between sites of low and high productivity. Factorial meta-analysis of published experiments confirms these results across widely varying aquatic communities. Furthermore, our experiments demonstrate that these patterns extend to important ecosystem functions such as carbon storage and nitrogen retention. This suggests that human impacts on nutrient supply and food-web structure have strong and interdependent effects on species diversity and ecosystem functioning, and must therefore be managed together.     

Dimensionality of consumer search space drives trophic interaction strengths

Trophic interactions govern biomass fluxes in ecosystems, and stability in food webs. Knowledge of how trophic interaction strengths are affected by differences among habitats is crucial for understanding variation in ecological systems. Here we show how substantial variation in consumption-rate data, and hence trophic interaction strengths, arises because consumers tend to encounter resources more frequently in three dimensions (3D) (for example, arboreal and pelagic zones) than two dimensions (2D) (for example, terrestrial and benthic zones). By combining new theory with extensive data (376 species, with body masses ranging from 5.24 × 10(-14) kg to 800 kg), we find that consumption rates scale sublinearly with consumer body mass (exponent of approximately 0.85) for 2D interactions, but superlinearly (exponent of approximately 1.06) for 3D interactions. These results contradict the currently widespread assumption of a single exponent (of approximately 0.75) in consumer-resource and food-web research. Further analysis of 2,929 consumer-resource interactions shows that dimensionality of consumer search space is probably a major driver of species coexistence, and the stability and abundance of populations.     

棉田叶螨亚群落营养结构初步研究

本文报道了新疆棉田螨类群落中的叶螨科（Ｔｅｔｒａｎｙｃｈｉｄａｅ）亚群落营养结构。从采到的标本中已鉴定出棉叶螨５种，天敌２６种。初步探索了叶螨亚群落的食物网络关系，比较了棉田不同施药水平与天敌数量关系。     

Simple rules yield complex food webs

Several of the most ambitious theories in ecology describe food webs that document the structure of strong and weak trophic links that is responsible for ecological dynamics among diverse assemblages of species. Early mechanism-based theory asserted that food webs have little omnivory and several properties that are independent of species richness. This theory was overturned by empirical studies that found food webs to be much more complex, but these studies did not provide mechanistic explanations for the complexity. Here we show that a remarkably simple model fills this scientific void by successfully predicting key structural properties of the most complex and comprehensive food webs in the primary literature. These properties include the fractions of species at top, intermediate and basal trophic levels, the means and variabilities of generality, vulnerability and food-chain length, and the degrees of cannibalism, omnivory, looping and trophic similarity. Using only two empirical parameters, species number and connectance, our 'niche model' extends the existing 'cascade model and improves its fit ten-fold by constraining species to consume a contiguous sequence of prey in a one-dimensional trophic niche.     

Robustness of the BMP morphogen gradient in Drosophila embryonic patterning

Developmental patterning relies on morphogen gradients, which generally involve feedback loops to buffer against perturbations caused by fluctuations in gene dosage and expression. Although many gene components involved in such feedback loops have been identified, how they work together to generate a robust pattern remains unclear. Here we study the network of extracellular proteins that patterns the dorsal region of the Drosophila embryo by establishing a graded activation of the bone morphogenic protein (BMP) pathway. We find that the BMP activation gradient itself is robust to changes in gene dosage. Computational search for networks that support robustness shows that transport of the BMP class ligands (Scw and Dpp) into the dorsal midline by the BMP inhibitor Sog is the key event in this patterning process. The mechanism underlying robustness relies on the ability to store an excess of signalling molecules in a restricted spatial domain where Sog is largely absent. It requires extensive diffusion of the BMP-Sog complexes, coupled with restricted diffusion of the free ligands. We show experimentally that Dpp is widely diffusible in the presence of Sog but tightly localized in its absence, thus validating a central prediction of our theoretical study.     

具反馈控制和Holling Ⅳ功能性反应捕食非自治系统的持久性和全局稳定性

目的研究一类具反馈控制和HollingⅣ功能性反应捕食非自治系统。方法通过应用微分方程比较原理和构造适当的Lyapunov泛函进行研究。结果得到保证该系统解的持久性和全局稳定性的充分条件。结论与具反馈控制和HollingⅡ功能性反应捕食系统相比,当功能性反应函数非单调增加时,该系统仍可保持其持久性和全局稳定性。     

食饵具有阶段结构的时滞捕食系统的Hopf 分支控制

为研究一类食饵具有阶段结构的时滞捕食系统的 Hopf 分支控制问题,利用状态反馈和参数扰动方法设计Hopf 分支控制器,以延迟捕食系统 Hopf 分支的发生,得到了受控捕食系统的局部稳定性和产生 Hopf 分支的充分条件。最后,给出仿真实例,验证了控制器的有效性。     

Ecosystem stability and compensatory effects in the Inner Mongolia grassland

Numerous studies have suggested that biodiversity reduces variability in ecosystem productivity through compensatory effects; that is, a species increases in its abundance in response to the reduction of another in a fluctuating environment. But this view has been challenged on several grounds. Because most studies have been based on artificially constructed grasslands with short duration, long-term studies of natural ecosystems are needed. On the basis of a 24-year study of the Inner Mongolia grassland, here we present three key findings. First, that January-July precipitation is the primary climatic factor causing fluctuations in community biomass production; second, that ecosystem stability (conversely related to variability in community biomass production) increases progressively along the hierarchy of organizational levels (that is, from species to functional group to whole community); and finally, that the community-level stability seems to arise from compensatory interactions among major components at both species and functional group levels. From a hierarchical perspective, our results corroborate some previous findings of compensatory effects. Undisturbed mature steppe ecosystems seem to culminate with high biodiversity, productivity and ecosystem stability concurrently. Because these relationships are correlational, further studies are necessary to verify the causation among these factors. Our study provides new insights for better management and restoration of the rapidly degrading Inner Mongolia grassland.     

Systemic risk in banking ecosystems

In the run-up to the recent financial crisis, an increasingly elaborate set of financial instruments emerged, intended to optimize returns to individual institutions with seemingly minimal risk. Essentially no attention was given to their possible effects on the stability of the system as a whole. Drawing analogies with the dynamics of ecological food webs and with networks within which infectious diseases spread, we explore the interplay between complexity and stability in deliberately simplified models of financial networks. We suggest some policy lessons that can be drawn from such models, with the explicit aim of minimizing systemic risk.