Disentangling nestedness from models of ecological complexity

Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant–pollinator networks, we show that this statement is incorrect. A simpler metric—the number of mutualistic partners a species has—is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.     

Ecological networks and their fragility

Darwin used the metaphor of a 'tangled bank' to describe the complex interactions between species. Those interactions are varied: they can be antagonistic ones involving predation, herbivory and parasitism, or mutualistic ones, such as those involving the pollination of flowers by insects. Moreover, the metaphor hints that the interactions may be complex to the point of being impossible to understand. All interactions can be visualized as ecological networks, in which species are linked together, either directly or indirectly through intermediate species. Ecological networks, although complex, have well defined patterns that both illuminate the ecological mechanisms underlying them and promise a better understanding of the relationship between complexity and ecological stability.     

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.     

有毒物影响的阶段结构捕食模型的稳定性

建立了有毒物影响的阶段结构捕食模型.利用微分方程定性与稳定性理论,讨论了该模型解的非负性和平衡点的局部渐近稳定性,获得了正平衡点全局渐近稳定的充分性条件.揭示了当食饵种群增长率和捕食者种群增长率均足够大时,模型中两种群将持续生存.     

具有扩散的年龄阶段结构捕食模型的渐近性

研究一类2种群都具有扩散的捕食-被捕食系统年龄阶段结构模型．首先通过构造Lyapunov泛函证明了惟一正平衡态的局部渐近稳定性,再利用方程组的比较原理给出正平衡态全局渐近稳定的充分条件．     

Strong contributors to network persistence are the most vulnerable to extinction

The architecture of mutualistic networks facilitates coexistence of individual participants by minimizing competition relative to facilitation. However, it is not known whether this benefit is received by each participant node in proportion to its overall contribution to network persistence. This issue is critical to understanding the trade-offs faced by individual nodes in a network. We address this question by applying a suite of structural and dynamic methods to an ensemble of flowering plant/insect pollinator networks. Here we report two main results. First, nodes contribute heterogeneously to the overall nested architecture of the network. From simulations, we confirm that the removal of a strong contributor tends to decrease overall network persistence more than the removal of a weak contributor. Second, strong contributors to collective persistence do not gain individual survival benefits but are in fact the nodes most vulnerable to extinction. We explore the generality of these results to other cooperative networks by analysing a 15-year time series of the interactions between designer and contractor firms in the New York City garment industry. As with the ecological networks, a firm's survival probability decreases as its individual nestedness contribution increases. Our results, therefore, introduce a new paradox into the study of the persistence of cooperative networks, and potentially address questions about the impact of invasive species in ecological systems and new competitors in economic systems.     

含两种捕食者和两种竞争食饵的扩散系统的稳定性

讨论一类含两种捕食者和两种竞争食饵的捕食者-食饵模型解的存在性和一致有界性.应用线性化方法研究了该模型非负平衡点的局部渐近稳定性;应用Lyapunov方法给出了该模型正平衡点全局渐近稳定的充分条件.     

An ecological and evolutionary perspective on human-microbe mutualism and disease

The microbial communities of humans are characteristic and complex mixtures of microorganisms that have co-evolved with their human hosts. The species that make up these communities vary between hosts as a result of restricted migration of microorganisms between hosts and strong ecological interactions within hosts, as well as host variability in terms of diet, genotype and colonization history. The shared evolutionary fate of humans and their symbiotic bacteria has selected for mutualistic interactions that are essential for human health, and ecological or genetic changes that uncouple this shared fate can result in disease. In this way, looking to ecological and evolutionary principles might provide new strategies for restoring and maintaining human health.     

具有放养率的时滞捕食模型的分岔行为

考虑一类具有常数放养率的时滞捕食种群模型,研究了种群稳定性和分岔行为。通过对特征方程的研究,得到种群稳定及发生分岔行为的充分条件;利用MATLAB软件进行数值模拟,给出相空间的轨迹,得到时滞与放养率是影响种群稳定的两个重要因素,验证了理论分析所得结果的正确性。     

Reproductive pair correlations and the clustering of organisms.

Clustering of organisms can be a consequence of social behaviour, or of the response of individuals to chemical and physical cues. Environmental variability can also cause clustering: for example, marine turbulence transports plankton and produces chlorophyll concentration patterns in the upper ocean. Even in a homogeneous environment, nonlinear interactions between species can result in spontaneous pattern formation. Here we show that a population of independent, random-walking organisms ('brownian bugs'), reproducing by binary division and dying at constant rates, spontaneously aggregates. Using an individual-based model, we show that clusters form out of spatially homogeneous initial conditions without environmental variability, predator-prey interactions, kinesis or taxis. The clustering mechanism is reproductively driven-birth must always be adjacent to a living organism. This clustering can overwhelm diffusion and create non-poissonian correlations between pairs (parent and offspring) or organisms, leading to the emergence of patterns.     

一类带有时滞和时滞耦合复杂网络的脉冲同步

研究了耦合项和非线性项含有时滞的复杂网络的脉冲同步问题.根据可控的复杂网络达到同步时耦合项会自动消失,可以得到含有脉冲影响复杂网络的误差动态网络.根据脉冲微分方程的稳定性分析,建立合适的Lyapunov Krasovskii泛函,得到含有脉冲影响的复杂网络新的脉冲同步准则.最后,复杂网络的微分方程模型和误差系统仿真图说明了脉冲同步准则的有效性和正确性.     

植食性昆虫、植物和共生微生物的功能关联

植食性昆虫和植物均能与微生物形成密切关系，它们各自的生态功能及相互关系也常被共生微生物所影响。近年来，随着分子水平研究方法的进展，植食性昆虫和植物中很多可遗传共生微生物（细菌、真菌等）被发现。共生微生物能够在营养、生殖、防御和解毒等方面给宿主带来显著影响，并与宿主形成竞争、互利或寄生等关系。植食性昆虫体内的含菌胞、肠道、血淋巴、唾液腺等常含有重要功能的共生微生物。新的分子生物学手段和高通量测序技术的应用使得我们能够增加对宿主和共生微生物（即使处于低丰度）之间关系的了解。本文尝试总结了植食性昆虫和植物共生微生物的多样性及其关系、昆虫和植物互作机制、昆虫共生菌解毒植物毒素等方面的近期证据，突出强调了应以系统观思维来理解共生微生物、植食性昆虫和植物间的功能关联，并就将来值得研究的问题提出了建议。     

一类具有强食饵和弱食饵的捕食系统分析

提出并研究了一类具有两个相互竞争的食饵种群与一个以这两个物种为食的捕食者种群的捕食系统.首先通过比较原理研究了该系统解的正有界性及系统平衡点的存在性,并运用特征值方法对可能存在的平衡点的局部渐近稳定性进行了讨论.其次利用微分方程的基本理论,得到了系统持久性的充分条件.然后通过构造Lyapunov函数讨论了系统平衡点的全局稳定性.最后,利用数值模拟验证本文的主要结论.     

无线传感器网络初始化簇头选举算法

利用节点初始分布后,对无线传感器网络具有的极少确知信息,建立了初始的异步通信模型;同时给出一种简单产生临时ID号的方法,保证相互间较大概率的互异性.基于此,提出了一种有效初始簇头选举方法,通过局部比较本地ID与邻居ID,实现快速簇头选举.实验表明,该方法能在无线传感器网络初始分布的无序、空白的环境下,迅速建立起有效的簇头,完成网络初级结构的建立,为后续接入资源的分配乃至协议的应用,提供了前提.多组仿真结果表明,算法的稳定性较好,具有较强的实用性.     

Weak pairwise correlations imply strongly correlated network states in a neural population

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.     

非自治一食饵-两竞争捕食者模型的动力学行为

研究了非自治的食饵-捕食模型,该系统是一食饵种群被两个具有竞争关系的捕食者种群捕食.其动力学行为包括:持久性、全局渐近稳定性、正周期解和正概周期解的存在唯一性.     

Non-random coextinctions in phylogenetically structured mutualistic networks

The interactions between plants and their animal pollinators and seed dispersers have moulded much of Earth's biodiversity. Recently, it has been shown that these mutually beneficial interactions form complex networks with a well-defined architecture that may contribute to biodiversity persistence. Little is known, however, about which ecological and evolutionary processes generate these network patterns. Here we use phylogenetic methods to show that the phylogenetic relationships of species predict the number of interactions they exhibit in more than one-third of the networks, and the identity of the species with which they interact in about half of the networks. As a consequence of the phylogenetic effects on interaction patterns, simulated extinction events tend to trigger coextinction cascades of related species. This results in a non-random pruning of the evolutionary tree and a more pronounced loss of taxonomic diversity than expected in the absence of a phylogenetic signal. Our results emphasize how the simultaneous consideration of phylogenetic information and network architecture can contribute to our understanding of the structure and fate of species-rich communities.     

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.     

一类捕食者-食饵模型的定性分析

本文应用常微分方程定性分析的方法来研究一类捕食者-食饵模型,讨论了系统平衡点存在性、局部渐近稳定性、极限环存在性。     

带有保护区域的加法Allee效应捕食-食饵模型的共存解

讨论了一类带有保护区域和加法Allee效应的扩散捕食-食饵模型。首先讨论了平凡解和半平凡解的稳定性, 接着考察了非常数正解的不存在性, 最后运用全局分歧理论得到了非常数正解的存在性条件。研究结果表明,在弱Allee效应下,当扩散系数适当且参数满足一定条件时,两物种能共存而且共存解稳定;当扩散系数充分大时两物种不共存。