Clines in the presence of asymmetric migration

If a population, which consists of individuals having genetic variation at one locus, with two alleles A and a, evolves under the influence of migration and selection, gradients in the distribution of alleles may arise. We consider the effect of asymmetry in the migration and spatial dependence of the selection process, upon the emergence and stability of such gradients.     

修正Camassa-Holm方程尖峰孤波解的稳定性

通过对具有哈密顿结构的修正Camassa-Holm方程的三个守恒量进行先验估计,算子谱分析,讨论了尖峰孤波解的稳定性取决于d″（c）的符号,并且给出d″（c）的具体表达式.借此给出修正Camassa-Holm方程的尖峰孤波解的稳定性与速度c有关,即c〉0,孤波解稳定,c〈0,孤波解不稳定;推广了[2]中相应的结论.     

Juvenile versus adult competition

A general class of age-structured models based upon the McKendrick/von Foerster equations are used to study intraspecific competition between juveniles and adults. Criteria for the existence and stability of equilibria are obtained and the dependence of equilibrium stability (i.e. equilibrium resilience) on competition coefficients is analyzed for low inherent net reproductive numbers. The results are applied to the question of whether juvenile vs. adult intraspecific competition is stabilizing or destabilizing. Two types of competition are studied. The first, involving suppressed adult fertility due to competition from juveniles, was found to be destabilizing in that equilibrium levels are lowered and equilibrium resilience weakened by increased competition. The second, involving increased juvenile mortality due to competition from adults, was found to be considerably more complicated. While equilibrium levels were again reduced by increased competition, equilibrium resilience can either be weakened or strengthened. A criterion for determining the effects on resilience is derived and several examples are given to illustrate various possibilities in this case.The author gratefully acknowledges the support of the Applied Mathematics Division and the Population Biology/Ecology Division of the National Science Foundation under NSF grant No. DMS-8902508Research supported by the Department of Energy under contracts W-7405-ENG-36 and KC-07-01-01     

Cyclic competition of three species in the time periodic and diffusive case

We consider a semilinear reaction diffusion system with time periodic coefficients. The system models the competitive interaction of three species, which inhabit a bounded domain. We make assumptions that may be loosely stated (cyclically for i {1, 2, 3}) as: Species i outcompetes species i + 1 in the absence of species i + 2. Under those assumptions we prove the existence of a time periodic solution, which is strictly positive in each of its three components. Moreover, we obtain a new result on the nonexistence of positive time-periodic solutions and the extinction of one species for the related two-species subsystem. Our discussion includes a situation, known as cyclic competition in the autonomous ODE-case, in a more general framework that includes temporal and spatial heterogeneity.     

Evidence for large-scale effects of competition: niche displacement in Canada lynx and bobcat

Determining the patterns, causes and consequences of character displacement is central to our understanding of competition in ecological communities. However, the majority of competition research has occurred over small spatial extents or focused on fine-scale differences in morphology or behaviour. The effects of competition on broad-scale distribution and niche characteristics of species remain poorly understood but critically important. Using range-wide species distribution models, we evaluated whether Canada lynx (Lynx canadensis) or bobcat (Lynx rufus) were displaced in regions of sympatry. Consistent with our prediction, we found that lynx niches were less similar to those of bobcat in areas of sympatry versus allopatry, with a stronger reliance on snow cover driving lynx niche divergence in the sympatric zone. By contrast, bobcat increased niche breadth in zones of sympatry, and bobcat niches were equally similar to those of lynx in zones of sympatry and allopatry. These findings suggest that competitively disadvantaged species avoid competition at large scales by restricting their niche to highly suitable conditions, while superior competitors expand the diversity of environments used. Our results indicate that competition can manifest within climatic niche space across species’ ranges, highlighting the importance of biotic interactions occurring at large spatial scales on niche dynamics.     

甘油生物歧化非线性动力系统的平衡点及其稳定性分析

针对甘油生物歧化为1,3-丙二醇过程的酶催化动力系统,利用符号化实根隔离法求解系统的平衡点,验证了系统的多稳态现象,利用微分方程稳定性理论,分析了平衡点的稳定性,并结合数值结果讨论了系统的多态现象．本文的结果可为微生物发酵甘油生产1,3-丙二醇的实验优化参数设计提供参考．     

具有种群Logistic增长的SIR模型的稳定性和Hopf分支

基于种群Logistic增长假设,本文构建了一个三维非线性发生率的SIR模型.首先探讨了该模型平衡点的稳定性,然后应用中心流形投影法得到了系统在非平凡平衡点附近产生超临界分支,并给出了数值模拟.     

具有非线性平均增长率的离散Logistic方程的稳定性和振动性

考虑具非线性平均增长率的Ｌｏｇｉｓｔｉｃ方程 这里ｒ,ａ,ｂ都是正常数,本文证明了方程（１）的一切解关于 ｋ振动的充要条件是 ｋｒ（ａ＋２ｂｋ）＞１,其中ｋ是方程（１）的唯一的正平衡解。同时获得了方程（１）的正平衡解ｋ是渐近稳定与全局渐近稳定的充分条件．     

一类具有时滞的传染病模型的稳定性分析

研究了一类具有时滞的传染病生物模型．首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式．     

A nonlinear ergodic theorem for discrete systems

A theorem concerning the asymptotic behavior of a general class of systems of difference equations is proven. This theorem guarantees the existence of a stable normalized distribution vector, and enables the constructing of a scalar limiting equation for an aggregate variable. This theory is illustrated using an example from population dynamics, a nonlinear size-structured model of competition for a dynamically modeled limiting resource.Supported in the Program in Applied Mathematics at the University of Arizona by the Applied Mathematics and Population Biology/Ecology Divisions of the National Science Foundation under grant No. DMS-8902508. Supported at Cornell University by the US Army Research Office through the Mathematical Sciences Institute, Contract DAAL03-91-C-0027, and by the National Science Foundation through the Biometrics Unit, grant No. DEB-9253570; This work comprises part of the author's dissertation at the University of Arizona, directed by J. M. Cushing     

The form of sexual selection arising from male-male competition depends on the presence of females in the social environment

Sexual selection arises from social interactions, and if social environments vary so too should sexual selection. For example, male-male competition often occurs either in the presence or in the absence of females, and such changes in the social environment could affect the form and strength of sexual selection. Here we examine how the presence of a female influences selection arising from male-male competition in a leaf-footed cactus bug, Narnia femorata, which has a resource defence mating system. Males compete for territories on cacti because females lay eggs on the cactus plants. Females are not always present when this competition first occurs; however, the presence or absence of the female matters. We found that both the form and strength of selection on male traits, those traits that influenced success in intrasexual competition, depended on the social context. When a female was not present, male size and the area of the sexually dimorphic hind legs was only marginally important to winning a contest. However, males with larger overall size and leg area were more likely to win in the presence of a female. There was also positive quadratic selection on these traits when a female was present with both the largest and the smallest males winning. The implication is unexpected alternative strategies when females are present. Our results support the notion that sexual selection should be studied under all relevant social contexts.     

Stability of a Ricker-type competition model and the competitive exclusion principle

Our main objective is to study a Ricker-type competition model of two species. We give a complete analysis of stability and bifurcation and determine the centre manifolds, as well as stable and unstable manifolds. It is shown that the autonomous Ricker competition model exhibits subcritical bifurcation, bubbles, period-doubling bifurcation, but no Neimark–Sacker bifurcations. We exhibit the region in the parameter space where the competition exclusion principle applies.     

Probiotic‐mediated competition,exclusion and displacement in biofilm formation by food‐borne pathogens

The objective of this study was to examine the inhibitory effect of probiotic strains on pathogenic biofilm formation in terms of competition, exclusion and displacement. Probiotic strains (Lactobacillus acidophilus KACC 12419, Lact. casei KACC 12413, Lact. paracasei KACC 12427 and Lact. rhamnosus KACC 11953) and pathogens (Salmonella Typhimurium KCCM 40253 and Listeria monocytogenes KACC 12671) were used to evaluate the auto‐aggregation, hydrophobicity and biofilm formation inhibition. The highest auto‐aggregation abilities were observed in Lact. rhamnosus (17·5%), Lact. casei (17·2%) and Lact. acidophilus (15·1%). Salm. Typhimurium had the highest affinity to xylene, showing the hydrophobicity of 53·7%. The numbers of L. monocytogenes biofilm cells during the competition, exclusion and displacement assays were effectively reduced by more than 3 log when co‐cultured with Lact. paracasei and Lact. rhamnosus. The results suggest that probiotic strains can be used as alternative way to effectively reduce the biofilm formation in pathogenic bacteria through competition, exclusion and displacement.

Significance and Impact of the Study

This study provides new insight into biofilm control strategy based on probiotic approach. Probiotic strains effectively inhibited the biofilm formation of Listeria monocytogenes through the mechanisms of competition, exclusion and displacement. These findings contribute to better understand the probiotic‐mediated competition, exclusion and displacement in biofilm formation by pathogens.     

Spite and the scale of competition

In recent years there has been a large body of theoretical work examining how local competition can reduce and even remove selection for altruism between relatives. However, it is less well appreciated that local competition favours selection for spite, the relatively neglected ugly sister of altruism. Here, we use extensions of social evolution theory that were formulated to deal with the consequences for altruism of competition between social partners, to illustrate several points on the evolution of spite. Specifically, we show that: (i) the conditions for the evolution of spite are less restrictive than previously assumed; (ii) previous models which have demonstrated selection for spite often implicitly assumed local competition; (iii) the scale of competition must be allowed for when distinguishing different forms of spite (Hamiltonian vs. Wilsonian); (iv) local competition can enhance the spread of spiteful greenbeards; and (v) the theory makes testable predictions for how the extent of spite should vary dependent upon population structure and average relatedness.     

Species coexistence under resource competition with intraspecific and interspecific direct competition in a chemostat

Competition theory has developed separately for direct competition and for exploitative competition. However, the combined effects of the two types of competition on species coexistence remain unclear. To examine how intraspecific and interspecific direct competition contributes to the coexistence of species competing for a single resource, we constructed a chemostat-type resource competition model. With general functions for intraspecific and interspecific direct competition, we derived necessary and sufficient conditions (except for a critical case that rarely occurs in a biological sense) that determine the number of stably coexisting species. From these conditions, we found that the number of coexisting species is determined just by the invasibility of each species into subcommunities with a smaller number of species. In addition, using a combination of rigorous mathematical theory and a simple graphical method, we can demonstrate how the stronger intraspecific direct competition facilitates species invasion, leading to a larger number of coexisting species.     

Community-wide character displacement in the presence of clines: a test of Holarctic weasel guilds

1. Competition is thought to be a major influence on community assembly, ecology and evolution; presence of competitors may cause divergence in traits related to resource use (character displacement). 2. Such traits, however, often vary clinally, and this phenomenon may be independent of the presence or absence of competing species. 3. The presence of such clines can either obscure the effects of competition, or create an impression that competition is operating when, in fact, it is not. 4. We corrected for clinal variation while testing for character displacement in two well-studied weasel (Mustela) guilds, in the Nearctic and the west Palaearctic. 5. Without accounting for clines, our results agreed with previous studies suggesting character displacement in these guilds. 6. However, when we corrected for clines, predictions of competition theory were not met - and often we obtained evidence for character convergence in sympatry. 7. This may suggest that the nature of the resource base may be more important than interspecific competition in shaping morphology and size in these carnivores. 8. Our results highlight the need to account for geographic variation when studying character displacement and cast some doubt on prevailing ideas regarding the effect of competition on morphological evolution.     

Sperm competition mechanisms in birds: models and data

This study presents three models to explain the mechanism oflast male sperm precedence in birds. Because passive loss ofsperm from the female reproductive tract occurs, all modelsincorporate this process. The three models are passive spermloss alone, stratification with passive sperm loss, and displacementwith passive sperm loss. With two inseminations containing thesame number of sperm, the models make the following predictions.For passive sperm loss alone, (1) differential paternity ispositively and linearly related to the time interval betweeninseminations, (2) with a slope that is equal to rate of lossof sperm from the female reproductive tract, (3) with an interceptthat is the same as the differential fertilizing capacity betweenthe semen of the two inseminations, and (4) the ratio of offspringfrom two inseminations remains constant over time. For stratification,(1) the relationship between differential paternity and theinterval between inseminations is nonlinear and exhibits a "brokenstick" pattern, with a substantial first-insemination precedencefor short intervals, and (2) the proportion of offspring fatheredby the first insemination increases over time. For displacement,the relationship between differential paternity and the intervalbetween inseminations is nonlinear and also exhibits a "brokenstick" pattern, but in contrast to the stratification model,sperm from the last insemination have precedence. Data fromthree experimental studies of the domestic fowl and one forthe turkey provide the opportunity to test these models, albeitto different extents. The data from all studies are consistentwith the passive sperm-loss model, except that one aspect ofone data set provided ambiguous support for stratification.None of the data provided any support for the displacement model.