带有年龄结构的捕食者-食饵模型研究

研究带有年龄结构的捕食者-食饵模型的渐近行为.本文所研究的模型假定捕食者从幼年阶段到成年阶段的转变率依赖于幼年种群的密度,还假定幼年捕食者捕食食饵.本文最终给出了有年龄结构的捕食者-食饵模型的捕食者持久和灭绝的若干条件.     

一类捕食者具有阶段结构的捕食系统的全局稳定性分析

本文建立了一类捕食者具有阶段结构的捕食系统,计算得到了不存在食饵种群时捕食者种群模型和食饵种群存在时捕食系统的平衡点,并证明了平衡点的存在性.分析和比较了两个模型平衡点的全局稳定性,最终确定了决定模型全局稳定性的捕食者种群基本再生数、食饵灭绝与否的捕食率阈值以及捕食存在时食饵种群的净增长率.     

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.     

食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。     

具Holling第Ⅱ类功能性反应的捕食者--食饵系统的定性分析

考虑捕食者无密度制约,食饵具有非线性密度制约的第二类Holling功能性反应捕食者－食饵系统。对该系统给出了完整的定性分析,证明了该系统至多有一个极限环,存在极限环的充要条件是平衡点不稳定。     

一类基于比率的离散捕食者-食饵系统的持续生存

讨论了一类基于比率的离散捕食者．食饵系统,给出持续生存的充分条件,结果表明当捕食者的死亡率相当小同时食饵的内禀增长率相对较大的时候,种群会长期共存．     

一个具有寄生虫病感染和恢复的捕食模型(英文)

本文假设感染的食饵有恢复率和对捕食者有收获,研究了一个对部分食饵和全部捕食者具有寄生虫病感染的捕食模型.用定性理论证明了边界和正平衡点的稳定性.结论表明恢复率和收获率对正平衡点的稳定性有影响.     

一类具有阶段结构和脉冲效应的捕食者-食饵模型的动力学分析

研究了一个捕食者具有阶段结构,食饵具有脉冲效应和时滞的捕食者-食饵模型.利用离散动力系统的频闪映射,我们获得了捕食者-灭绝的周期解同时给出了该周期解全局吸引的充分条件.利用时滞脉冲微分方程的理论,得到了系统持续生存的充分条件.     

一类具有非单调增长率和功能反应的捕食者-食饵系统的定性分析

考虑一类食饵密度具有非单调增长率,捕食者具有功能性反应的捕食者一食饵系统。得到系统在第一象限内正平衡点的区域稳定的条件和极限环存在唯一的条件,完整地讨论了系统(1)的拓扑结构。     

一类食饵具有常数投放率系统的恢复率

在现实的生态系统中,特别当捕食者的密度大或捕食能力强时,人们常采用食饵补充的方式来控制捕食者和食饵种群数量的稳定,以达到生态平衡．本文在Chisholm,R．A．和Filotas,E．研究的捕食-食饵模型基础上,定义了食饵具有常数投放率的捕食系统,讨论了此系统的恢复率与食饵最大容量之间的关系以及投放率对恢复率和预警长度的影响．最后通过算例分析了递减的恢复率作为系统转移的指示器与投放率与食饵最大容量的关系,说明食饵的投放率可增强预警效果．     

Evolutionary and plastic rescue in multitrophic model communities

Under changing environmental conditions, intraspecific variation can potentially rescue populations from extinction. There are two principal sources of variation that may ultimately lead to population rescue: genetic diversity and phenotypic plasticity. We compared the potential for evolutionary rescue (through genetic diversity) and plastic rescue (through phenotypic plasticity) by analysing their differential ability to produce dynamical stability and persistence in model food webs. We also evaluated how rescue is affected by the trophic location of variation. We tested the following hypotheses: (i) plastic communities are more likely to exhibit stability and persistence than communities in which genetic diversity provides the same range of traits. (ii) Variation at the lowest trophic level promotes stability and persistence more than variation at higher levels. (iii) Communities with variation at two levels have greater probabilities of stability and persistence than communities with variation at only one level. We found that (i) plasticity promotes stability and persistence more than genetic diversity; (ii) variation at the second highest trophic level promotes stability and persistence more than variation at the autotroph level; and (iii) more than variation at two trophic levels. Our study shows that proper evaluation of the rescue potential of intraspecific variation critically depends on its origin and trophic location.     

Global stability, local stability and permanence in model food webs

The dynamical theory of food webs has been based typically on local stability analysis. The relevance of local stability to food web properties has been questioned because local stability holds only in the immediate vicinity of the equilibrium and provides no information about the size of the basin of attraction. Local stability does not guarantee persistence of food webs in stochastic environments. Moreover, local stability excludes more complex dynamics such as periodic and chaotic behaviors, which may allow persistence. Global stability and permanence could be better criteria of community persistence. Our simulation analysis suggests that these three stability measures are qualitatively consistent in that all three predict decreasing stability with increasing complexity. Some new predictions on how stability depends on food web configurations are generated here: a consumer-victim link has a smaller effect on the probabilities of stability, as measured by all three stability criteria, than a pair of recipient-controlled and donor-controlled links; a recipient-controlled link has a larger effect on the probabilities of local stability and permanence than a donor-controlled link, while they have the same effect on the probability of global stability; food webs with equal proportions of donor-controlled and recipient-controlled links are less stable than those with different proportions.     

Stability of interstitial crustacean communities in an isolated alluvial aquifer

The temporal stability of interstitial crustacean communities was investigated in relation to environmental variability in a perched aquifer, characterized by limited connection with surface waters. The author hypothesized that strong physico-chemical stability would enhance persistence and affect dominance patterns for groundwater fauna. Fifteen wells were sampled four times over a two-year period in order to assess the global stability of ground waters and to evaluate temporal changes in species assemblages. For each station, environmental patterns displayed only minor changes, while between-site differences were much larger. At the scale of the aquifer, strong temporal stability was found for groundwater physical and chemical variables. Interstitial crustaceans displayed diverse assemblages dominated by cyclopoid taxa. High persistence characterized community composition and structure (species relative abundance patterns, species richness, Shannon's diversity index) over the study period. Most well faunas were dominated numerically by a single species, whether micro- or macrocrustacean assemblages were considered. Faunal persistence observed in the aquifer was greater than that reported in many surface waters and was probably related to the strong environmental stability.     

Directional persistence of EGF-induced cell migration is associated with stabilization of lamellipodial protrusions

Migrating cells can sustain a relatively constant direction of lamellipodial protrusion and locomotion over timescales ranging from minutes to hours. However, individual waves of lamellipodial extension occur over much shorter characteristic times. Little understanding exists regarding how cells might integrate biophysical processes across these disparate timescales to control the directional persistence of locomotion. We address this issue by examining the effects of epidermal growth factor (EGF) stimulation on long-timescale directional persistence and short-timescale lamellipodial dynamics of EGF receptor-transfected Chinese hamster ovary cells migrating on fibronectin-coated substrata. Addition of EGF increased persistence, with the magnitude of increase correlating with fibronectin coating concentration. Kymographic analysis of EGF-stimulated lamellipodial dynamics revealed that the temporal stability of lamellipodial protrusions similarly increased with fibronectin concentration. A soluble RGD peptide competitor reduced both the persistence of long-timescale cell paths and the stability of short-timescale membrane protrusions, indicating that cell-substratum adhesion concomitantly influences lamellipodial dynamics and directional persistence. These results reveal the importance of adhesion strength in regulating the directional motility of cells and suggest that the short-timescale kinetics of adhesion complex formation may play a key role in modulating directional persistence over much longer timescales.     

具有时滞和避难所的捕食者-两共存食饵模型

研究了一类具有时滞和避难所的捕食-被捕食模型的一致持久性和全局稳定性.利用比较原理讨论了模型的一致持久性,运用Lyapunov函数方法得到了模型全局渐近稳定的充分条件.     

On the generality of stability-complexity relationships in Lotka-Volterra ecosystems

Understanding how complexity persists in nature is a long-standing goal of ecologists. In theoretical ecology, local stability is a widely used measure of ecosystem persistence and has made a major contribution to the ecosystem stability-complexity debate over the last few decades. However, permanence is coming to be regarded as a more satisfactory definition of ecosystem persistence and has relatively recently become available as a tool for assessing the global stability of Lotka-Volterra communities. Here we document positive relationships between permanence and Lotka-Volterra food web complexity and report a positive correlation between the probability of local stability and permanence. We investigate further the frequency of discrepancy (attributed to fragile systems that are locally stable but not permanent or locally unstable systems that are permanent and have cyclic or chaotic dynamics), associate non-permanence with the local stability or instability of equilibria on the boundary of the state-space, and investigate how these vary with aspects of ecosystem complexity. We find that locally stable interior equilibria tend to have all locally unstable boundary equilibria. Since a locally stable boundary is inconsistent with permanent dynamics, this can explain the observed positive correlation between local interior stability and permanence. Our key finding is that, at least in Lotka-Volterra model ecosystems, local stability may be a better measure of persistence than previously thought.     

Synchronisation and stability in river metapopulation networks

Spatial structure in landscapes impacts population stability. Two linked components of stability have large consequences for persistence: first, statistical stability as the lack of temporal fluctuations; second, synchronisation as an aspect of dynamic stability, which erodes metapopulation rescue effects. Here, we determine the influence of river network structure on the stability of riverine metapopulations. We introduce an approach that converts river networks to metapopulation networks, and analytically show how fluctuation magnitude is influenced by interaction structure. We show that river metapopulation complexity (in terms of branching prevalence) has nonlinear dampening effects on population fluctuations, and can also buffer against synchronisation. We conclude by showing that river transects generally increase synchronisation, while the spatial scale of interaction has nonlinear effects on synchronised dynamics. Our results indicate that this dual stability – conferred by fluctuation and synchronisation dampening – emerges from interaction structure in rivers, and this may strongly influence the persistence of river metapopulations.     

Temporal patterns in the stability, persistence and condition of stream macroinvertebrate communities: relationships with catchment land-use and regional climate

1. A spatially‐extensive data set of stream macroinvertebrate communities from 49 northern New Zealand sites sampled over a 10‐year period was analysed to assess relationships between the environment (catchment land‐cover, landscape position and regional‐scale weather patterns), and (i) community persistence and stability based on the constancy of species occurrence (presence–absence) and abundance (per cent composition), respectively and (ii) the temporal variability of various community condition metrics. 2. No significant relationship was evident between community stability or persistence within sites and a gradient of increasing land‐use stress (LUS) based on types of upstream land‐cover, with interannual mean similarities at all sites falling within the standard deviations recorded at long‐term reference sites. In contrast, condition metrics were inversely related to LUS. Land‐use appeared to be a key factor influencing community composition among sites whereas climate influenced stability and persistence within sites. 3. Three response trajectories of community variability to increasing LUS were distinguished based on the coefficient of variation of mean interannual similarities, such that (i) persistence and stability appeared to be more variable at developed sites with low LUS and at sites with high stress relative to the variability experienced naturally, but similar to the natural range at intermediate levels of stress (‘sinusoidal response’); (ii) variability in Ephemeroptera, Plecoptera and Trichoptera metrics increased at low‐to‐moderate stress and then accelerated rapidly at highly developed sites (‘stepped‐exponential response’) and (iii) variability in a pollution tolerance metric increased rapidly and then maintained a similar level of variability along the remaining stress gradient (‘plateau response’). 4. The results of this study have implications for biomonitoring approaches that assume high temporal persistence and stability of communities to define site impairment. Misclassifications caused by interannual variability could lead to misinterpretation of site condition, if conclusions are based on single annual surveys. Temporal variability in stability and persistence may help distinguish low levels of impairment where a predominantly healthy fauna experiences increased environmental fluctuations.     

多种群阶段结构竞争系统的周期解与概周期解

研究具有阶段结构的多种群竞争系统,得到该系统一致持久,正周期解全局渐近稳定及概周期解的存在性与一致渐近稳定性的充分条件。     

Stability properties of 2-species models of mutualism: Simulation studies

Summary Most previous analyses of the stability properties of models of mutualism have emphasized the destabilizing effects of mutualism. However, these analyses can be shown to be based upon inappropriate assumptions, or to be applicable only for special cases of mutualism. In this paper three basic 2-species models of mutualism are presented and their six combinations are analyzed by computer simulation for their return time stability and persistence stability. Four out of six models show greater return time stability than an appropriate model without mutualism, and all models show higher persistence stability than the model without mutualism. It is argued that real biological systems can be related to the qualitative structure of each of the basic models of mutualism, and that therefore none of the basic models or their stability properties can be eliminated a priori as being inappropriate. The conclusion follows that while some kinds of mutualistic interactions may be relatively unstable, other mutualisms, probably representing the majority of cases, can be considered to be relatively stable. The limitations of these models and analyses are considered.