一类捕食者与被捕食者模型的持久性与稳定性

研究了一类捕食者与被捕食者模型,该生态系统是一个食饵种群被一个捕食种群捕食.当给定参数满足一定条件下,利用比较原理和构造Lyapunov函数的方法,证明了系统的持久性和全局渐近稳定性,并讨论了正平衡点的渐近稳定性.     

高维“食饵—捕食者”模型周期解的存在性

一、引言文献对“Ⅱ类功能反应模型”进行了详细、完整的分析,给出了存在周期解的充分条件.但是在自然界中,就某一生态环境而言,往往同时存在上千种,甚至上万种“食饵-捕食者”系统,在食饵和捕食者之间都存在竞争关系.考虑到这些因素,本文将考虑更一般的高维“食饵-捕食者”模型.     

被捕食动物对捕食者的识别研究及在放归中的应用

对捕食者的认知能力是当前生态学研究的一个热点。一些物种具有对捕食者先天的识别能力,而一些物种必须通过后天学习才能获得对捕食者的认知能力,还有许多动物通过社会学习和文化传播获得对捕食者的识别能力。本文就国外被捕食动物对捕食者的识别的研究进展进行综述,并讨论了该项研究对野外放归工作提供的重要理论意义和应用价值。     

捕食者有病的食饵-捕食者模型

建立了捕食者有病的食饵-捕食者模型;由Hurwitz判据、LaSalle不变性原理获得了平衡点稳定的条件;并给出了模型的撮动解．     

富食悖论研究进展

Michael Rosenzweig于1971年首次提出＂富食悖论＂这一概念：在简单的被捕食者-捕食者系统中,随着营养物质供应的增加,系统变得不再稳定,并产生大振幅波动,最终导致系统内的物种灭亡。然而,许多实验结果并不支持Rosenzweig的理论。综述＂富食悖论＂的定义、理论和实验研究,同时综述各种解释实际与理论之间矛盾的机制,最后探讨＂富食悖论＂的研究前景。     

捕食者-猎物功能反应的统计模型研究

以往关于捕食者-猎者功能反应的数学模型大多是用微分方程和概率极限定理的方法来推导的.本文采用回归分析,系数显著性检验的方法,直接从实际统计数据出发,得出捕食者-猎物功能反应的统计模型,它是一种拟合得很好的不同以往的模型,为捕食者一猎物功能反应研究提供了一种新的方法.     

具有迁移效应的Hassell-Varley-Holling捕食者-食饵系统的持续生存

研究具有迁移效应的Hassell-Varley-Holling功能性反应的捕食者-食饵模型,得到了系统耗散性和持续生存的条件.     

具性别偏食的二种群捕食者-食饵系统模型

本文根据生态学实验现象研究了一类二种群捕食者－食饵系统,其中捕食者对食饵有性别偏食情形。建立了相应的数学模型,并对该模型的有关性状进行了分析。     

基于改进的SURF指数甄选海州湾鱼类群落的关键捕食者

关键捕食者在生态系统中对饵料生物的数量波动、丰富度和空间分布等都起到重要的调控作用。本研究基于在海州湾进行的5个航次的渔业资源底拖网调查资料及胃含物分析数据,通过对传统SURF指数进行改进,甄选海州湾鱼类群落中的关键捕食者。结果表明: 星康吉鳗、长蛇鲻、大泷六线鱼、小眼绿鳍鱼和小黄鱼为海州湾鱼类群落中的关键捕食者,这5种鱼类不但具有较高的连接数,还是多种生物的主要捕食者,在物种连接中具有较强的聚集效应,它们的数量波动会对生态系统能量流动和食物网结构产生较大的影响。通过本方法对关键捕食者进行甄选,不仅考虑了物种间的摄食比例,还将捕捞量及物种的资源量作为重要影响因素,与传统方法相比,具有较大的改进,为关键捕食者的甄选提供了一种新的方法。本研究还发现,物种之间的强相互作用在维护食物网的结构与功能中起着重要作用,加强对关键捕食者的保护,有利于维持生物群落的稳定性和物种多样性,在实施基于生态系统的管理时,要优先保护这些关键物种。星康吉鳗和小黄鱼作为重要的经济鱼种,承受的捕捞压力较高,尤其需要加强保护和管理。     

捕食者-食饵交错扩散模型的整体解

应用能量估计方法和Bootstrap技巧证明含有两类竞争的食饵种群和一类捕食者种群的三种群捕食者-食饵扩散模型在空间维数小于6时古典解的整体存在性.     

Cannibalism in an age-structured predator-prey system

Recently, Kohlmeier and Ebenhöh showed that cannibalism can stabilize population cycles in a Lotka-Volterra type predator-prey model. Population cycles in their model are due to the interaction between logistic population growth of the prey and a hyperbolic functional response. In this paper, we consider a predator-prey system where cyclic population fluctuations are due to the age structure in the predator species. It is shown that cannibalism is also a stabilizing mechanism when population oscillations are due to this age structure. We conclude that in predator-prey systems, cannibalism by predators can stabilize both externally generated (consumer-resource) as well as internally generated (agestructure) fluctuations.     

Food web dynamics in correlated and autocorrelated environments

The densities of populations in a community or food web vary as a consequence of both population interactions and environmental (e.g. weather) fluctuations. Populations often respond to the same kinds of environmental fluctuations, and therefore experience correlated environments. Furthermore, some environmental factors change slowly over time, thereby producing positive environmental autocorrelation. We show that the effects of environmental correlation and autocorrelation on the dynamics of the populations in a food web can be large and unintuitive, but can be understood by analyzing the eigenvectors of the community (system) matrix of interactions among populations. For example, environmental correlation and autocorrelation may either obscure or enhance the cyclic dynamics that generally characterize predator-prey interactions even when there is no direct effect of the environment on how species interact. Thus, understanding the population dynamics of species in a food web requires explicit attention to the correlation structure of environmental factors affecting all species.     

Persistence in fluctuating environments for interacting structured populations

Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and species coexistence. To understand these effects, we provide a general theory for coexistence of structured, interacting species living in a stochastic environment. The theory is applicable to nonlinear, multi species matrix models with stochastically varying parameters. The theory relies on long-term growth rates of species corresponding to the dominant Lyapunov exponents of random matrix products. Our coexistence criterion requires that a convex combination of these long-term growth rates is positive with probability one whenever one or more species are at low density. When this condition holds, the community is stochastically persistent: the fraction of time that a species density goes below \(\delta >0\) approaches zero as \(\delta \) approaches zero. Applications to predator-prey interactions in an autocorrelated environment, a stochastic LPA model, and spatial lottery models are provided. These applications demonstrate that positive autocorrelations in temporal fluctuations can disrupt predator-prey coexistence, fluctuations in log-fecundity can facilitate persistence in structured populations, and long-lived, relatively sedentary competing populations are likely to coexist in spatially and temporally heterogenous environments.     

Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation

Interplay between predator and prey is a complex process in ecosystems due to its nature. The population dynamics can be affected by many extrinsic and intrinsic factors. In this paper, we make an attempt to uncover the effects from environmental disturbances when populations are subject to habitat complexity and aggregation effect. We firstly propose a stochastic predator-prey model with habitat complexity and aggregation efficiency for prey. We then mathematically analyze the model, to demonstrate the existence, uniqueness and the stochastically ultimately boundedness of the global positive solution, and to establish sufficient conditions for the existence of ergodic stationary distribution of the solution. We also establish sufficient conditions under which either only predator population dies out or the entire predator-prey model becomes extinct. Our theoretical and numerical results indicate that: (1) the environmental noises are disadvantage for the survival of biological populations; (2) when the density of prey is greater than one, prey aggregation can heighten the capability of predator species to capture prey and reduce the effect of environmental fluctuations, while when the density of prey is less than one, the results are opposite; (3) habitat complexity is propitious to the survival of prey population and may seriously threaten the persistence of the predator population.     

Resonance of plankton communities with temperature fluctuations

The interplay between intrinsic population dynamics and environmental variation is still poorly understood. It is known, however, that even mild environmental noise may induce large fluctuations in population abundances. This is due to a resonance effect that occurs in communities on the edge of stability. Here, we use a simple predator-prey model to explore the sensitivity of plankton communities to stochastic environmental fluctuations. Our results show that the magnitude of resonance depends on the timescale of intrinsic population dynamics relative to the characteristic timescale of the environmental fluctuations. Predator-prey communities with an intrinsic tendency to oscillate at a period T are particularly responsive to red noise characterized by a timescale of τ = T/2π. We compare these theoretical predictions with the timescales of temperature fluctuations measured in lakes and oceans. This reveals that plankton communities will be highly sensitive to natural temperature fluctuations. More specifically, we demonstrate that the relatively fast temperature fluctuations in shallow lakes fall largely within the range to which rotifers and cladocerans are most sensitive, while marine copepods and krill will tend to resonate more strongly with the slower temperature variability of the open ocean.     

Analysis of seasonal fluctuations in the Lotka-Volterra model

A modification of the Lotka-Volterra model was proposed. The modification takes into account the factor of seasonal fluctuations in a "predator-prey" model. In this modification, interactions between species in summer are described by the Lotka-Volterra equations; in winter, individuals of both species extinct. This generalization makes the classic model unrough, which substantially extends the field of its application. The results of numerical simulation illustrate the statement formulated above.     

Phase locking, the Moran effect and distance decay of synchrony: experimental tests in a model system

Spatially separated populations of many species fluctuate synchronously. Synchrony typically decays with increasing interpopulation distance. Spatial synchrony, and its distance decay, might reflect distance decay of environmental synchrony (the Moran effect), and/or short-distance dispersal. However, short-distance dispersal can synchronize entire metapopulations if within-patch dynamics are cyclic, a phenomenon known as phase locking. We manipulated the presence/absence of short-distance dispersal and spatially decaying environmental synchrony and examined their separate and interactive effects on the synchrony of the protist prey species Tetrahymena pyriformis growing in spatial arrays of patches (laboratory microcosms). The protist predator Euplotes patella consumed Tetrahymena and generated predator-prey cycles. Dispersal increased prey synchrony uniformly over both short and long distances, and did so by entraining the phases of the predator-prey cycles. The Moran effect also increased prey synchrony, but only over short distances where environmental synchrony was strongest, and did so by increasing the synchrony of stochastic fluctuations superimposed on the predator-prey cycle. Our results provide the first experimental demonstration of distance decay of synchrony due to distance decay of the Moran effect. Distance decay of the Moran effect likely explains distance decay of synchrony in many natural systems. Our results also provide an experimental demonstration of long-distance phase locking, and explain why cyclic populations provide many of the most dramatic examples of long-distance spatial synchrony in nature.     

Relative nonlinearity and permanence

We modify the commonly used invasibility concept for coexistence of species to the stronger concept of uniform invasibility. For two-species discrete-time competition and predator-prey models, we use this concept to find broad easily checked sufficient conditions for the rigorous concept of permanent coexistence. With these results, permanent coexistence becomes a tractable concept for many discrete-time population models. To understand how these conditions apply to nonpoint attractors, we generalize the concept of relative nonlinearity and use it to show how population fluctuations affect the long-term low-density growth rate (“the invasion rate”) of a species when it is invading the system consisting of the other species (“the resident”) at a single-species attractor. The concept of relative nonlinearity defines circumstances when this invasion rate is increased or decreased by resident population fluctuations arising from a nonpoint attractor. The presence and sign of relative nonlinearity is easily checked in models of interacting species. When relative nonlinearity is zero or positive, fluctuations cannot decrease the invasion rate. It follows that permanence is then determined by invasibility of the resident’s fixed points. However, when relative nonlinearity is negative, invasibility, and hence permanent coexistence, can be undermined by resident population fluctuations. These results are illustrated with specific two-species competition and predator-prey models of generic forms.     

一类食饵种群中具有传染病的捕食-被捕食系统

对疾病仅在食饵种群传播的有比例依赖的捕食-被捕食系统的动力学进行了分析,给出了每个平衡点附近系统的性态,定义了决定疾病灭绝和成为地方病的阁值R_0．得出的结论是:在比例依赖的捕食-被捕食系统中,染病食饵种群可以充当一个生物控制量,以抑制种群的绝灭．     

What they didn't tell you about limit cycles

Summary The paper examines the numerous assumptions involved in theories of predator-prey limit cycles. Predatorprey theories should incorporate the environmental fluctuations appropriate to each specific case.