Lotka-Volterra自治竞争系统的共存与绝灭

研究了一类自治n种群Lotka-Volterra竞争系统．建立了一部分种群绝灭，另一部分种群持续生存新的判别准则，推广了已知相关结果．     

一类时滞非自治Lotka-Volterra竞争系统的灭绝性

讨论一类具有离散时滞和连续分布时滞的Lotka-Volterra系统,通过构造Lyapunov函数并引入上下平均的概念,将[3]和[6]的方法结合在一起,得到比[6]种群灭绝条件弱的充分条件,同时把文献[3]的结果推广到了时滞非自治系统上.     

非自治Lotka-Volterra型捕食扩散系统中有害时滞对该系统持久性的影响

研究了时滞对一类非自治Lotka-Volterra型捕食扩散系统的影响,该系统由n个斑块组成,食饵种群可以在斑块间迁移,而摘食者限制在某一个斑块不能扩散．我们假设密度制约项系数并不总是严格正的．通过运用比较定理及时滞泛函微分方程的基本原理,分两种情况表明了在一定条件下系统是一致持久的．两种情况的结果表明时滞的引入和变化即可能是“有害”,也可能是”无害”．进一步还说明了系统在一致持久性的条件下至少存在一个正周期解．这些结果是对已知的非自治Lotka-Volterra系统的一些结果的推广与改进．     

一类离散Lotka-Volterra系统的灭绝和稳定性（英文）

考虑了一类受有毒物质影响的两物种非自治离散Lotka-Volterra系统.在平均增长率意义下,得到了其中一种物种灭绝的充分条件,证明了另外一种物种的稳定性.     

三种群竞争系统的持久性

本文研究了三种群非自治周期Lotka-Volterra竞争系统的持久性,得到了正周期解的存在性和平衡振荡的条件。     

非自治具有Ⅱ类功能反应的竞争捕食系统的周期解

用迭合度理论研究n个食饵种群m个捕食者种群的非自治具有Ⅱ类功能反应的竞争捕食周期系统,给出了用系数函数在一个周期内的平均值判断系统存在周期解的充分性条件．     

基于多时滞Lotka-Volterra型捕食链模型的概周期解

本文研究了一类基于多时滞Lotka-Volterra型非自治三种群捕食链模型,首先,利用微分方程比较原理得到了系统持久生存的充分条件;其次,通过构造一个合理的Lyapunov函数,得到了系统存在唯一的全局吸引的正的概周期解的充分条件;最后,运用matlab数学软件进行数值模拟验证了理论分析的可行性.     

研究脉冲竞争系统周期解新的单调迭代方法(英文)

文章研究了一类正常细胞和癌细胞相互作用的竞争系统周期解的存在性.数学模型包括竞争型的Lotka-Volterra方程组与描述周期性化疗的脉冲条件.文章建立了一类新的单调迭代方法,该方法是构造性的,周期解可以由一个线性迭代过程得到,每一步迭代只需求解一个脉冲微分方程初值问题.文章获得了系统至少存在一个严格正的周期解的充分条件.     

基于反馈控制离散Lotka-Volterra竞争模型的持续生存和稳定性

针对一类具有偏离自变量的离散Lotka-Volterra竞争模型,考虑到不可避免的外界扰动,通过引入反馈控制,基于一定的分析技巧得到该系统持久性与全局稳定性的充分条件.生态意义上表明:在外界扰动下,具有偏离自变量的离散Lotka-Volterra竞争模型仍能持续生存并保持全局稳定发展.     

具有无限时滞和扩散项的非自治竞争系统的正周期解(英文)

研究了一类具有无限时滞和扩散项的非自治竞争系统,利用重合度的廷拓定理,得到了该系统正周期解存在的充分性条件.     

Aggregation and species coexistence of ectoparasites of marine fishes.

Interspecific interaction may lead to species exclusion but there are several ways in which species can coexist. One way is by reducing the overall intensity of competition via aggregated utilisation of fragmented resources. Known as the 'aggregation model of coexistence', this system assumes saturation and an equilibrium number of species per community. In this study we tested the effects of interspecific aggregation on the level of intraspecific aggregation among ectoparasites of marine fishes (36 communities of gill and head ectoparasite species). If parasite species are distributed in a way that interspecific aggregation is reduced relative to intraspecific aggregation then species coexistence is facilitated. We found a positive relationship between parasite species richness and fish body size, controlling for host phylogeny. A positive relationship between infracommunity species richness and total parasite species richness was also found, providing no evidence for saturation. This result supports the view that infracommunities of parasites are not saturated by local parasite residents. The observed lack of saturation implies that we are far from a full exploitation of the fish resource by parasites. Ectoparasites were aggregated at both population and species levels. However, only half of the ectoparasite communities were dominated by negative interspecific aggregation. We found that infracommunity parasite species richness was positively correlated with the level of intraspecific aggregation versus interspecific aggregation. This means that intraspecific aggregation increases compared with interspecific aggregation when total parasite species richness increases, controlling fish size and phylogeny. This supports one assumption of the 'aggregation model of coexistence', which predicts that interspecific interactions are reduced relative to intraspecific interactions, facilitating species coexistence.     

Aggregation, intraguild interactions and the coexistence of competitors on small ephemeral patches

It is well established that intraspecific aggregation has the potential to promote coexistence in communities of species competing for patchy ephemeral resources. We developed a simulation model to explore the influence of aggregation on coexistence in such communities when an important assumption of previous studies – that interspecific interactions have only negative effects on the species involved – is relaxed. The model describes a community of competing insect larvae in which an interaction that is equivalent to intraguild predation (IGP) can occur, and is unusual in that it considers species exploiting very small resource patches (carrying capacity=1). Model simulations show that, in the absence of any intraspecific aggregation, variation between species in the way that resource heterogeneity affects survival increases the likelihood of species coexistence. Simulations also show that intraspecific aggregation of the dominant competitor's eggs across resource patches can promote coexistence by reducing the importance of interspecific competition relative to that of intraspecific competition. Crucially, however, this effect is altered if one competitor indulges in IGP. In general, coexistence is only possible when the species that is capable of IGP is less effective at exploiting the shared resource than its competitor. Because it reduces the relative importance of interspecific interactions, intraspecific aggregation of the eggs of a species that is the victim of IGP actually reduces the likelihood of coexistence in parts of parameter space in which the persistence of the other species is dependent on its ability to exploit its competitor. Since resource heterogeneity, intraspecific aggregation and IGP are all common phenomena, these findings shed light on mechanisms that are likely to influence diversity in communities exploiting patchy resources.     

Interspecific competition in perennial sedentary organisms: An individual-based model

We investigated a mathematical model of the dynamics of the ecological system consisting of two competing perennial species, each of which leads a sedentary life. It is an individual-based model, in which the growth of each individual is described. The rate of this growth is weakened by competition from neighboring individuals. The strength of the competitors' influence depends on their size and distance to them. The conditions, in which the competitive exclusion of one of the competitors and the coexistence of both competitors take place are provided. The influence of the parameters responsible for the strength of competition, the degree of competitive asymmetry, and consideration of the importance of specific elements of the spatial structure of this ecological system on the results of the competition were analyzed. Both species co-exist when they are equal competitors. Permanent coexistence is possible only when interspecific competition is weaker than intraspecific. When interspecific competition is stronger, the coexistence of equal interspecific competitors is random. Both species have equal probability of extinction. If species are not equal competitors, the stronger one wins. This result can be modified by different strengths of intraspecific competition. The weaker interspecific competitor can permanently coexist with stronger one, when its individuals suffer stronger intraspecific competition.     

Persistence in food webs—I Lotka-Volterra food chains

Persistence-extinction in simple food chains modelled by Lotka-Volterra dynamics is governed by a single parameter which depends upon the interspecific interaction coefficients, the intraspecific interaction coefficients, and the length of the food chain. In persistent systems with nonzero carrying capacity, two new features predominate. Trophic level influence factors relate persistence on different trophic levels and determine, in conjunction with the persistence parameter, the magnitude of persistence. Equilibrium component ordering, which results in persistent systems, mandates once again that systems need to be studied on the complete ecosystem level; static field measurements reflect species location in the food chain, the total length of the food chain and assume characteristics according to these factors.     

Integrating spatial structure and interspecific and intraspecific plant–soil feedback effects and responses into community structure

Plant–soil feedbacks have important effects on plant communities, but most theory has been derived from experiments on intraspecific plant–soil feedbacks. Much less is known about how interspecific plant–soil feedbacks affect coexistence and plant communities, due in part to experimental and analytical challenges. Here, we propose a framework for evaluating plant–soil feedbacks among multiple interacting species that incorporates 1) the average effect each species has on conspecific and heterospecific neighbors via how they modify soil biota, 2) the average response of each species to the soil modifications made by neighboring species, and 3) intraspecific feedback. We refer to this as the ‘effect–response–intraspecific’ (ERI) model. We used individual‐based models to evaluate the relative importance of intraspecific and interspecific soil feedback in determining species abundance ranks in simulated plant communities. To compare the heuristic value of the ERI model to that of an established model in which effects and responses to soil feedback are not explicitly recognized, we evaluated a ‘full‐factorial’ model in which soil feedbacks among five plant species were measured and then explicitly modeled. The ERI model indicated that the response to interspecific plant–soil feedbacks was the key factor for species’ abundance rank without spatial structure. In contrast, interspecific plant–soil feedback had no impact on species abundance with spatial structure, and intraspecific feedback became dominant. Thus, our models predict that the relative importance of intraspecific and interspecific feedbacks changes as a function of the degree of spatial structure in a system. Overall, the ERI model provides a novel and tractable framework for evaluating complex multi‐species plant–soil feedbacks.     

Patterns in intraspecific interaction strengths and the stability of food webs

A common approach to analyse stability of biological communities is to calculate the interaction strength matrix. Problematic in this approach is defining intraspecific interaction strengths, represented by diagonal elements in the matrix, due to a lack of empirical data for these strengths. Theoretical studies have shown that an overall increase in these strengths enhances stability. However, the way in which the pattern in intraspecific interaction strengths, i.e. the variation in these strengths between species, influences stability has received little attention. We constructed interaction strength matrices for 11 real soil food webs in which four patterns for intraspecific interaction strengths were chosen, based on the ecological literature. These patterns included strengths that were (1) similar for all species, (2) trophic level dependent, (3) biomass dependent, or (4) death rate dependent. These four patterns were analysed for their influence on (1) ranking food webs by their stability and (2) the response in stability to variation of single interspecific interaction strengths. The first analysis showed that ranking the 11 food webs by their stability was not strongly influenced by the choice of diagonal pattern. In contrast, the second analysis showed that the response of food web stability to variation in single interspecific interaction strengths was sensitive to the choice of diagonal pattern. Notably, stability could increase using one pattern and decrease using another. This result asks for deliberate approaches to choose diagonal element values in order to make predictions on how particular species, interactions, or other food web parameters affect food web stability.     

Biodiversity and the Lotka-Volterra theory of species interactions: open systems and the distribution of logarithmic densities

Theoretical interest in the distributions of species abundances observed in ecological communities has focused recently on the results of models that assume all species are identical in their interactions with one another, and rely upon immigration and speciation to promote coexistence. Here we examine a one-trophic level system with generalized species interactions, including species-specific intraspecific and interspecific interaction strengths, and density-independent immigration from a regional species pool. Comparisons between results from numerical integrations and an approximate analytic calculation for random communities demonstrate good agreement, and both approaches yield abundance distributions of nearly arbitrary shape, including bimodality for intermediate immigration rates.     

Comparing phylogenetic signal in intraspecific and interspecific body size datasets

Phylogenetic comparative methods have become a standard statistical approach for analysing interspecific data, under the assumption that traits of species are more similar than expected by chance (i.e. phylogenetic signal is present). Here I test for phylogenetic signal in intraspecific body size datasets to evaluate whether intraspecific datasets may require phylogenetic analysis. I also compare amounts of phylogenetic signal in intraspecific and interspecific body size datasets. Some intraspecific body size datasets contain significant phylogenetic signal. Detection of significant phylogenetic signal was dependant upon the number of populations (n) and the amount of phylogenetic signal (K) for a given dataset. Amounts of phylogenetic signal do not differ between intraspecific and interspecific datasets. Further, relationships between significance of phylogenetic signal and sample size and amount of phylogenetic signal are similar for intraspecific and interspecific datasets. Thus, intraspecific body size datasets are similar to interspecific body size datasets with respect to phylogenetic signal. Whether these results are general for all characters requires further study.     

The anatomy of the interspecific abundance–range size relationship for the British avifauna: II. Temporal dynamics

In a companion paper, we started an examination of the anatomy of the interspecific relationship between local abundance and geographical range size in the British avifauna by analysing its spatial dynamics. Here, we use the same data to extend this study to a consideration of the temporal dynamics of the relationship. Most species of British breeding bird show a positive intraspecific abundance–range size relationship through time: i.e. in years when a species is locally more abundant it also occupies a higher proportion of census sites. However, the majority of such relationships are not statistically significant, and other relationships that are statistically significant are negative. Therefore, intraspecific abundance–range size relationships do not simply mirror the relationship across species. Where they do arise, positive relationships are more likely to be associated with positive intraspecific relationships between range size and maximum rather than minimum abundance. The interspecific abundance–range size relationship is remarkably consistent across years, and is always significantly positive. The relationships for woodland and farmland census sites show correlated variation, so that in years when the linear regression slope and coefficient of determination are high across species on farmland plots, they also tend to be high across species on woodland plots. Common species tend to be common on both farmland and woodland plots, and tend to be common in all years. Likewise, rare species tend to be rare in all habitats and years. This concordance means that the positive interspecific abundance–range size relationship can be viewed as occurring largely independently of intraspecific relationships. It follows from the above that developing an understanding of intraspecific abundance–range size relationships may be of only limited value in ascertaining the determinants of positive interspecific abundance–range size relationships. We conclude that for interspecific relationships, it will be important to know why some species are consistently common and others rare, whereas for intraspecific relationships it will be important to understand the dynamic links between local abundances across sites.     

Competition and coexistence in plant communities: intraspecific competition is stronger than interspecific competition

Theory predicts that intraspecific competition should be stronger than interspecific competition for any pair of stably coexisting species, yet previous literature reviews found little support for this pattern. We screened over 5400 publications and identified 39 studies that quantified phenomenological intraspecific and interspecific interactions in terrestrial plant communities. Of the 67% of species pairs in which both intra‐ and interspecific effects were negative (competitive), intraspecific competition was, on average, four to five‐fold stronger than interspecific competition. Of the remaining pairs, 93% featured intraspecific competition and interspecific facilitation, a situation that stabilises coexistence. The difference between intra‐ and interspecific effects tended to be larger in observational than experimental data sets, in field than greenhouse studies, and in studies that quantified population growth over the full life cycle rather than single fitness components. Our results imply that processes promoting stable coexistence at local scales are common and consequential across terrestrial plant communities.