具有抑制剂的恒化器竞争模型的分析（英文）

考虑了具有抑制剂的两种群竞争一种微生物的恒化器模型,其中吸收函数和功能反应函数都是营养的一般单调递增函数,并且一种微生物能够分泌一种对另一种微生物起致命影响的抑制剂.利用常微分方程定性理论,首先得到了平衡点的存在条件和局部渐进稳定性;然后讨论了全局渐进稳定性,以及极限环和Hopf分支的存在性.     

一类具Holling Ⅲ型功能反应的捕食者-食饵模型的定性分析

研究一类具Holling Ⅲ型功能反应的捕食者一食饵模型．应用定性分析和Hopf分支理论,得到了一个正平衡点的全局稳定性、三个正平衡点的局部稳定性和极限环的存在性的充分条件,使用MATLAB软件。本文给出了三个例子来模拟这些结论。     

Stable long-period cycling and complex dynamics in a single-locus fertility model with genomic imprinting

Although long-period population size cycles and chaotic fluctuations in abundance are common in ecological models, such dynamics are uncommon in simple population-genetic models where convergence to a fixed equilibrium is most typical. When genotype-frequency cycling does occur, it is most often due to frequency-dependent selection that results from individual or species interactions. In this paper, we demonstrate that fertility selection and genomic imprinting are sufficient to generate a Hopf bifurcation and complex genotype-frequency cycling in a single-locus population-genetic model. Previous studies have shown that on its own, fertility selection can yield stable two-cycles but not long-period cycling characteristic of a Hopf bifurcation. Genomic imprinting, a molecular mechanism by which the expression of an allele depends on the sex of the donating parent, allows fitness matrices to be nonsymmetric, and this additional flexibility is crucial to the complex dynamics we observe in this fertility selection model. Additionally, we find under certain conditions that stable oscillations and a stable equilibrium point can coexist. These dynamics are characteristic of a Chenciner (generalized Hopf) bifurcation. We believe this model to be the simplest population-genetic model with such dynamics.     

Dynamic models of infectious diseases as regulators of population sizes

Five SIRS epidemiological models for populations of varying size are considered. The incidences of infection are given by mass action terms involving the number of infectives and either the number of susceptibles or the fraction of the population which is susceptible. When the population dynamics are immigration and deaths, thresholds are found which determine whether the disease dies out or approaches an endemic equilibrium. When the population dynamics are unbalanced births and deaths proportional to the population size, thresholds are found which determine whether the disease dies out or remains endemic and whether the population declines to zero, remains finite or grows exponentially. In these models the persistence of the disease and disease-related deaths can reduce the asymptotic population size or change the asymptotic behavior from exponential growth to exponential decay or approach to an equilibrium population size.Research supported by Centers for Disease Control contract 200-87-0515. Support services provided at the University of Iowa Center for Advanced Studies     

Ecological public goods games: cooperation and bifurcation

The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.     

Density dependence at some time and place?

There appears to be widespread acceptance that for a population to persist, some demographic parameter must be density dependent at some place or time. In this paper, we question the veracity and heuristic value of treating this statement as a general principle of ecology. We also point out that some processes that have recently been defined as density dependent are, in fact, not. Taken in its original sense, density dependence implies a change in demographic rates based on biological (generally negative) feedback. Situations exist, however, in which demographic rates change in relation to density without negative biological feedback. For example, per capita recruitment in marine populations will decrease as local population size increases even as absolute numbers of arriving larvae do not change. The failure to separate these density-related processes from true density-dependent processes affects our understanding of population regulation and of the way in which the natural world functions. Furthermore, focusing solely on density-dependent processes and their role in population regulation neglects to address numerous density-independent processes like disturbance and climatic variation that may have important impacts in determining population size. Received: 20 January 1999 / Accepted: 12 January 2000     

不同干扰荒漠生境中子午沙鼠的繁殖及种群动态特征

子午沙鼠(Merionesmeridianus)广泛分布于我国西北部地区,是荒漠啮齿动物群落的优势鼠种。种群繁殖特征是动物生活史参数中的一个重要组成部分,是种群数量补充的重要来源,而干扰是影响繁殖特征的重要因素。本研究于2012~2014年,在位于蒙古阿拉善左旗南部典型荒漠的野外实验区,设置禁牧、开垦、过牧、轮牧4种不同干扰样地,使用铗日法对实验样地子午沙鼠相对数量及繁殖特征进行调查。4种不同干扰生境中的子午沙鼠种群数量具有显著差异,禁牧过牧轮牧开垦;雌雄性比在轮牧生境中最高,开垦生境次之,禁牧生境最低;4种干扰生境中,轮牧样地子午沙鼠雌鼠怀孕率显著高于禁牧、过牧和开垦样地;雄鼠的睾丸下降率在过牧干扰样地显著高于其他3种干扰方式样地,轮牧样地雄鼠睾丸下降率最低;雌鼠平均胎仔数在4种干扰生境间无显著性差异;轮牧干扰样地繁殖指数显著高于其他3种干扰方式样地;繁殖指数、怀孕率及睾丸下降率对密度的反馈作用最为明显,但在不同的干扰生境中其反馈特征有差异。综上,子午沙鼠在轮牧生境中各繁殖特征指数最高,繁殖能力最强,种群密度相对较高,更适合其生存,其密度制约效应表现最为明显。     

Population growth and habitat distribution in cyclic small rodents: to expand or to change?

Habitat selection determined by intraspecific interactions (social behaviour), being either free or despotic, should result in the largest densities in the most favourable habitat at least in late increase and decline phases of cyclic populations. Habitat distribution determined by interspecific effects such as herbivore-plant or predator-prey interactions may result in higher densities in inferior habitats at late peaks and/or declines due to overgrazing of preferred habitats, or invasion of such habitats by specialist predators. An examination of the distributions of the rodent species Clethrionomys glareolus and Microtus agrestis during a population cycle on forest clearcuts at Grimsö, south-central Sweden, demonstrated clear changes towards less preferred habitats during the decline phase, particularly in M. agrestis. Intraspecific competition could be excluded as a cause since the numbers of both species declined simultaneously. There was no sign of overgrazing, while weasels, Mustela nivalis, invaded the preferred M. agrestis habitat during peak–decline. Predation thus appears more important for the local occurrence at early decline, rather than territoriality or other social behaviour. It is concluded that distributions in various habitats do not always reveal any primary habitat selection but, rather, habitat-dependent survival.     

Do nomadic avian predators synchronize population fluctuations of small mammals? a field experiment

Three-to-five-year population oscillations of northern small rodents are usually synchronous over hundreds of square kilometers. This regional synchrony could be due to similarity in climatic factors, or due to nomadic predators reducing the patches of high prey density close to the average density of a larger area. We estimated avian predator and small rodent densities in 4–5 predator reduction and 4–5 control areas (c. 3 km² each) during 1989–1992 in western Finland. We studied whether nomadic avian predators concentrate at high prey density areas, and whether this decreases spatial variation in prey density. The yearly mean number of avian predator breeding territories was 0.2–1.0 in reduction areas and 3.0–8.2 in control areas. Hunting birds of prey concentrated in high prey density areas after their breeding season (August), but not necessarily during the breeding season (April to June), when they were constrained to hunt in vicinity of the nest. The experimental reduction of breeding avian predators increased variation in prey density among areas but not within areas. The difference in variation between raptor reduction and control areas was largest in the late breeding season of birds of prey, and decreased rapidly after the breeding season. These results appeared to support the hypothesis that the geographic synchrony of population cycles in small mammals may be driven by nomadic predators concentrating in high prey density areas. Predation and climatic factors apparently are complementary, rather than exclusive, factors in contributing to the synchrony.     

Effect of predator density dependent dispersal of prey on stability of a predator-prey system

This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system.     

Friends and strangers: a test of the Charnov-Finerty Hypothesis

Summary We tested the hypothesis that populations composed of unrelated animals should perform worse than those composed of related animals by setting up two moderatedly dense field populations in adjacent enclosures: one was composed of related females and one of unrelated females; both had unrelated males. The survival and reproductive success of a number of litters located by spooling were determined. Final population size, pregnancy success, number of young recruited per pregnancy, and survival were similar in both populations. Thus, differences in relatedness produced no differences in demography. We conclude that the Charnov-Finerty Hypothesis in unlikely to be an explanation for microtine population fluctuations.     

Density, climate and varying return points: an analysis of long-term population fluctuations in the threatened European tree frog

Experimental research has identified many putative agents of amphibian decline, yet the population-level consequences of these agents remain unknown, owing to lack of information on compensatory density dependence in natural populations. Here, we investigate the relative importance of intrinsic (density-dependent) and extrinsic (climatic) factors impacting the dynamics of a tree frog (Hyla arborea) population over 22 years. A combination of log-linear density dependence and rainfall (with a 2-year time lag corresponding to development time) explain 75% of the variance in the rate of increase. Such fluctuations around a variable return point might be responsible for the seemingly erratic demography and disequilibrium dynamics of many amphibian populations.     

Positive solutions of an elliptic system arising from a model in evolutionary ecology

We give sufficient and almost necessary conditions for the existence of positive solutions to an elliptic system satisfying various Dirichlet boundary conditions. The elliptic system consists of the steady-state equations of a parabolic system used to model the growth and spread of a particular gene and population living in a bounded region. The model takes into account the fact that the fitness of the individuals in the population may depend on the population size. Some non-existence results are also included.Research partially supported by NSF grant no. DMS-8801968     

Which conditions promote negative density dependent selection on prey aggregations?

Negative density dependent selection on individuals in prey aggregations (negative DDS, the preferential selection by predators of spatially isolated prey) is assumed to contribute in many cases to the evolution and maintenance of aggregation. Both positive and negative DDS on prey groups have been documented in nature but there is no existing framework to predict when each of these forms of natural selection is most likely. By exploiting the tendency of artificial neural networks to exhibit consumer-like emergent behaviours, I isolate at least two environmental factors impinging on the consumer organism that may determine which form of density dependent natural selection is shown: the distribution of prey group size attacked by the predator and the spatial conformation (dispersed or compacted) of the prey group. Numerous forms of DDS on artificial prey (positive, negative, and non-DDS) are displayed through different combinations of these factors. I discuss in detail how the predictions of the model may be tested by empiricists in order to assess the usefulness of the framework presented. I stress the importance of understanding DDS on prey groups given the recent emergence of these systems as test beds for ideas on biological self-organisation.     

关于具时滞的捕食-被捕食系统的稳定性与Hopf分支

研究了一类具时滞的捕食—被捕食系统正平衡解的稳定性和Hopf分支的存在性,即以转化率l为参数,得到存在一列l_k(k=0,1,2…),使当l∈(0,l_0)时正平衡解是渐近稳定的;当l>l_0时,正平衡解是不稳定的,而每一个l_k都是该系统的Hopf分支值,改进了一些已知的工作。     

一类时滞神经网络模型的稳定性与全局Hopf分支

研究了一类由两个神经元构成的时滞神经网络模型的稳定性和局部Hopf分支,并结合一般泛函微分方程的全局Hopf分支定理,利用度理论研究了全局Hopf分支的存在性．