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.     

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.     

Nutritional constraints in terrestrial and freshwater food webs

Biological and environmental contrasts between aquatic and terrestrial systems have hindered analyses of community and ecosystem structure across Earth's diverse habitats. Ecological stoichiometry provides an integrative approach for such analyses, as all organisms are composed of the same major elements (C, N, P) whose balance affects production, nutrient cycling, and food-web dynamics. Here we show both similarities and differences in the C:N:P ratios of primary producers (autotrophs) and invertebrate primary consumers (herbivores) across habitats. Terrestrial food webs are built on an extremely nutrient-poor autotroph base with C:P and C:N ratios higher than in lake particulate matter, although the N:P ratios are nearly identical. Terrestrial herbivores (insects) and their freshwater counterparts (zooplankton) are nutrient-rich and indistinguishable in C:N:P stoichiometry. In both lakes and terrestrial systems, herbivores should have low growth efficiencies (10-30%) when consuming autotrophs with typical carbon-to-nutrient ratios. These stoichiometric constraints on herbivore growth appear to be qualitatively similar and widespread in both environments.     

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.     

Reconciling complexity with stability in naturally assembling food webs

Understanding how complex food webs assemble through time is fundamental both for ecological theory and for the development of sustainable strategies of ecosystem conservation and restoration. The build-up of complexity in communities is theoretically difficult, because in random-pattern models complexity leads to instability. There is growing evidence, however, that nonrandom patterns in the strengths of the interactions between predators and prey strongly enhance system stability. Here we show how such patterns explain stability in naturally assembling communities. We present two series of below-ground food webs along natural productivity gradients in vegetation successions. The complexity of the food webs increased along the gradients. The stability of the food webs was captured by measuring the weight of feedback loops of three interacting 'species' locked in omnivory. Low predator-prey biomass ratios in these omnivorous loops were shown to have a crucial role in preserving stability as productivity and complexity increased during succession. Our results show the build-up of food-web complexity in natural productivity gradients and pin down the feedback loops that govern the stability of whole webs. They show that it is the heaviest three-link feedback loop in a network of predator-prey effects that limits its stability. Because the weight of these feedback loops is kept relatively low by the biomass build-up in the successional process, complexity does not lead to instability.     

单组元聚集体的聚集--迁移的模型

提出了可逆迁移过程和不可逆聚集过程共存的聚集体生长模型.假定聚集反应速率核为I(i;j)=2I,迁移反应速率核为K(i;j)=Jij或K(i;j)=Jj.建立Smoluchowski速率方程,由此求出了系统的集团浓度分布的精确解.结果表明,集团浓度分布符合标度特性.     

Whole-lake carbon-13 additions reveal terrestrial support of aquatic food webs

Ecosystems are supported by organic carbon from two distinct sources. Endogenous carbon is produced by photosynthesis within an ecosystem by autotrophic organisms. Exogenous carbon is produced elsewhere and transported into ecosystems. Consumers may use exogenous carbon with consequent influences on population dynamics, predator-prey relationships and ecosystem processes. For example, exogenous inputs provide resources that may enhance consumer abundance beyond levels supported by within-system primary production. Exogenous fluxes of organic carbon to ecosystems are often large, but this material is recalcitrant and difficult to assimilate, in contrast to endogenously produced organic matter, which is used more easily. Here we show, by the experimental manipulation of dissolved inorganic (13)C in two lakes, that internal primary production is insufficient to support the food webs of these ecosystems. Additions of NaH(13)CO(3) enriched the (13)C content of dissolved inorganic carbon, particulate organic carbon, zooplankton and fish. Dynamics of (13)C indicate that 40-55% of particulate organic carbon and 22-50% of zooplankton carbon are derived from terrestrial sources, showing that there is significant subsidy of these ecosystems by organic carbon produced outside their boundaries.     

单种群模型的混沌分析

通过对单种群模型的混沌分析,以期对混沌行为有较为清晰的了解,得到了在参数范围内的模型分别是分布混沌,Martelli-混沌、Devaney-混沌、Block-Coppel混沌,为此模型在生态学诸领域中的应用提供理论指导。     

Ecosystem consequences of species richness and composition in pond food webs

Resolving current concerns about the role of biodiversity on ecosystems calls for understanding the separate roles of changes in species numbers and of composition. Recent work shows that primary productivity often, but not always, saturates with species richness within single trophic levels. However, any interpretation of such patterns must consider that variation in biodiversity is necessarily associated with changes in species composition (identity), and that changes in biodiversity often occur across multiple trophic levels. Here we present results from a mesocosm experiment in which we independently manipulated species richness and species composition across multiple trophic levels in pond food webs. In contrast to previous studies that focused on single trophic levels, we found that productivity is either idiosyncratic or increases with respect to species richness, and that richness influences trophic structure. However, the composition of species within richness levels can have equally or more marked effects on ecosystems than average effects of richness per se. Indirect evidence suggests that richness and associated changes in species composition affect ecosystem attributes through indirect effects and trophic interactions among species, features that are highly characteristic of natural, complex ecosystems.     

一类具三阶段结构的单种群模型的最优收获策略

研究一生中有三个阶段——卵、幼年及成年的单种群生长模型,该模型收获成年种群,得到了正平衡点全局渐近稳定的充分条件,给出了收获成年种群的最优收获策略.     

带有变异的离散的单种群持久性

文章对离散状态下单种群演化模型进行研究,利用分析方法并结合Lyapunov函数给出单种群在变异下持久性的充分条件.     

生态环境受污染的单种群持续生存的研究

利用微分方程的定性与稳定性理论以及种群动力学理论建立了在污染环境中单种群的数学模型.利用Dulac函数方法推断了模型在地方病平衡点的全局稳定性充分条件,并从生态学的角度对模型进行了生物解释。     

阶段结构单种群模型的全局渐近稳定性

研究了一类具有三个阶段的阶段结构单种群生长模型，得到了该模型正平衡点全局渐近稳定性的充分条件．     

具密度依赖和生育脉冲的单种群阶段结构模型

给出了具有密度依赖和生育脉冲的单种群阶段结构模型,通过研究其对应的离散系统,得到周期解及其稳定性的阀值.当系统的参数超过阀值,系统存在一系列的分支并最终走向混沌.     

具有性别结构和不育控制的单种群模型

建立了一个简单的具有性别结构和不育控制的单种群模型,判断了平衡点存在和稳定的条件,得到了种群一致持续生存和正平衡点全局渐近稳定的充分条件.     

具有3阶段结构的自食单种群征税模型

在运用微分方程理论研究具有3个年龄阶段的自食单种群模型的基础上将税收考虑进去,分析了一类具有阶段结构的自食单种群征税模型,讨论了平衡点的存在性．在适当的假设条件下,采用Routh-Hurwitz判别法证明了系统正平衡点是局部渐近稳定的,并通过构造Lyapunov函数得到了系统正平衡点的稳定吸引域．同时利用Pontryagin最大值原理给出了最优征税策略,得出了贴现率能够影响捕获种群的利润水平．目的在于既保护生态系统又能使经济收益最大,为生物资源的开发和利用提供可靠的理论依据．     

一类具有收获系数的单种群模型的混沌分析及反馈控制

分析了一类具有收获系数的单种群模型的差分方程,得到了该模型的不动点及其稳定的参数区域和吸引的参数区域,利用混沌动力学知识分析其2-周期解的稳定区域,根据Li-York定理和邓小炎的方法得到了模型的3-周期解的存在性,即存在混沌现象。利用一种基于Lyapunov指数的状态反馈控制策略,使混沌状态的单种群模型变为可测。该控制策略可将混沌状态的单种群模型快速地收敛于给定的任意值。