一类具有退偿增长曲线的生物种群的捕获优化问题

本文研究一类具有延偿增长曲线的生物种群,讨论了该种群的动力学性质及捕获问题,确定了最优捕获努力量、相应的种群密度和最大可持续捕获量、讨论了开放条件下的生物资源的管理。     

具有阶段结构的自食单种群生长模型的稳定性及最有收获策略

本文讨论了一生中具有两个生长阶段－成年与未成年的种群模型,该模型收获成年种群并且成年种群食自身所产的卵,即模型为自食模型,得到了正平衡点全局渐近稳定的条件及收获成年种群的阈值和最优收获策略。     

具脉冲扩散效应的单种群动力学模型

讨论了两斑块间脉冲扩散的单种群动力学模型,利用离散动力系统频闪映射理论,得到了种群持续生存的充分条件．结论31,1~了现实的生物种群动力学性质,也丰富了脉冲微分方程理论．     

昆虫种群死亡过程的数字模拟

昆虫种群的死亡过程,是影响种群数量变动的一个重要因素。在正确地构造昆虫种群的生长发育模型,并使种群发育时间的理论分布拟合实际资料的同时,必需正确地考虑死亡个体在种群中对数量变动的作用,才有可能全面地表达种群的增长与消亡的数量动态。 有关模拟种群的死亡过程的讨论已发表很多,其中多数只讨论种群总的死亡率(如Pielou,1969)。也有过一些比较详细的结果,甚至可以逐天地根据昆虫存活的最长寿命以及     

一个生物种群非线性泛函微分方程模型整体解的聚集性

自然界的种群,如鱼类、鸟类和有蹄兽类有聚集成群的现象,研究种群的聚集性是生物数学中的一个有趣的课题．本文讨论了一个有关生物种群的非线性泛函微分方程模型整体解的聚集性和稳定性问题．     

生长季节和非生长季节交替出现的种群动态模型及环境变化的影响

有些生物的生长季节和非生长季节交替出现,本文建立了描述这种生物种群动态的方程,并研究了在环境稳定、随机波动、定向变化的情况下种群的变化方式,还讨论了种群的危害及濒危情况．生长季节延长时种群增大,有害生物的危害加重,濒危生物濒危程度减轻;生长季节缩短时种群减小,有害生物的危害减轻,濒危生物更加濒危或灭绝．     

野古草种群克隆的遗传变异和遗传结构

用酶电泳法和同工酶分析对东北松嫩草原西北部野古草种群克隆遗传变异性和种群遗传结构做了探讨。讨论了遗传多样性、地理距离和遗传距离之间的关系、大种群和小种群的遗传变异性和种群间的基因流 ;种群间 ,包括大种群和小种群间基因流、遗传和地理距离对遗传多样性的影响、昆虫和风传粉、种群籽苗的补充、遗传多样性的发生和保持 ,自交不亲和性和无性繁殖及体细胞突变     

污染与捕获对Logistic种群的影响

本文研究污染与捕获并存时Logistic种群的β生存问题．证明了种群若不永远β生存，则必在有限时间内绝灭．给出了种群β生存、β绝灭条件，并对临界情况作了讨论．     

山西云蒙山油松种群的年龄结构和动态特征

本文用样方法研究了山西云蒙山油松种群的年龄结构、存活曲线和数量动态规律,并且讨论了油松种群数量动态和群落演替的关系,结果表明:油松种群具有增长型和衰退型的动态特征,影响油松种群数量的内在机制主要是种内光资源的竞争。尽管大多数油松种群处于不断衰减状态,但其群落结构及性质在较长时期内将不会发生显著的变化。     

四川长寿湖两种越冬野鸭的考查报告

本文对长寿湖的绿头鸭Anas platyrnchos、斑嘴鸭A.poecilorhyncha的种群数量变动作了记载和分析,记录了它们的生殖腺的形态变化过程,并对近年来野鸭种群数量下降的原因作了讨论。     

Multiple mating and sperm displacement in a natural population of Drosophila melanogaster

Summary Mother-offspring data for alcohol dehydrogenase genotypes of a vineyard cellar population of D. melanogaster are best explained by a model that allows 21% of females in the population to mate twice with an 83% level of sperm displacement. A population model with multiple mating and sperm displacement is examined theoretically. A formula for the effective population size is derived under this model. Multiple mating increases the effective population size relative to single mating.     

On the accuracy of a diffusion approximation to a discrete state–space Markovian model of a population

The traditional Kolmogorov equations treat the size of a population as a discrete random variable. A model is introduced that extends these equations to incorporate environmental variability. Difficulties with this discrete model motivate approximating the population size as a continuous random variable through the use of diffusion processes. The set of cumulants for both the population size and the environmental factors affecting the population size characterize the population–environmental system. The evolution of this set, as predicted by the diffusion approximation, closely matches the corresponding predictions for the discrete model. It is also noted that the simulation estimates of the cumulants against which the predictions of the diffusion model are checked can vary considerably between simulations — despite averaging over a large number of simulation runs. The precision of the simulation estimates–both over time and with differing cumulant order–is discussed.     

Estimating the area under the ROC curve when transporting a prediction model to a target population

We propose methods for estimating the area under the receiver operating characteristic (ROC) curve (AUC) of a prediction model in a target population that differs from the source population that provided the data used for original model development. If covariates that are associated with model performance, as measured by the AUC, have a different distribution in the source and target populations, then AUC estimators that only use data from the source population will not reflect model performance in the target population. Here, we provide identification results for the AUC in the target population when outcome and covariate data are available from the sample of the source population, but only covariate data are available from the sample of the target population. In this setting, we propose three estimators for the AUC in the target population and show that they are consistent and asymptotically normal. We evaluate the finite-sample performance of the estimators using simulations and use them to estimate the AUC in a nationally representative target population from the National Health and Nutrition Examination Survey for a lung cancer risk prediction model developed using source population data from the National Lung Screening Trial.     

Patterns and processes of population dynamics with fluctuating habitat size: a case study of a marine copepod inhabiting tide pools

The logistic model is a fundamental population model often used as the basis for analyzing wildlife population dynamics. In the classic logistic model, however, population dynamics may be difficult to characterize if habitat size is temporally variable because population density can vary at a constant abundance, which results in variable strength of density‐dependent feedback for a given population size. To incorporate habitat size variability, we developed a general population model in which changes in population abundance, density, and habitat size are taken into account. From this model, we deduced several predictions for patterns and processes of population dynamics: 1) patterns of fluctuation in population abundance and density can diverge, with respect of their correlation and relative variability; and 2) along with density dependence, habitat size fluctuation can affect population growth with a time lag because changes in habitat size result in changes in population density. In order to test these predictions, we applied our model to population dynamics data of 36 populations of Tigriopus japonicus, a marine copepod inhabiting tide pools of variable sizes caused by weather processes. As expected, we found a significant difference in the fluctuation patterns of population abundance and density of T. japonicus populations with respect to the correlation between abundance and density and their relative variability, which correlates positively with the variability of habitat size. In addition, we found direct and lagged‐indirect effects of weather processes on population growth, which were associated with density dependence and impose regulatory forces on local and regional population dynamics. These results illustrate how changes in habitat size can have an impact on patterns and processes of wildlife population dynamics. We suggest that without knowledge of habitat size fluctuation, measures of population size and its variability as well as inferences about the processes of population dynamics may be misleading.     

On the accuracy of a diffusion approximation to a discrete state–space Markovian model of a population

The traditional Kolmogorov equations treat the size of a population as a discrete random variable. A model is introduced that extends these equations to incorporate environmental variability. Difficulties with this discrete model motivate approximating the population size as a continuous random variable through the use of diffusion processes. The set of cumulants for both the population size and the environmental factors affecting the population size characterize the population–environmental system. The evolution of this set, as predicted by the diffusion approximation, closely matches the corresponding predictions for the discrete model. It is also noted that the simulation estimates of the cumulants against which the predictions of the diffusion model are checked can vary considerably between simulations — despite averaging over a large number of simulation runs. The precision of the simulation estimates–both over time and with differing cumulant order–is discussed.     

Effects of a disease affecting a predator on the dynamics of a predator-prey system

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical “aggregation method” in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a “disease-free” or to a “disease-endemic” state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the “disease-free” equilibrium (DFE).     

Coevolutionary interactions between a haploid species and a diploid species

We investigate a general model describing coevolutionary interaction between a haploid population and a diploid population, each with two alleles at a single locus. Both species are allowed to evolve, with the fitness of the genotypes of each species assumed to depend linearly on the frequencies of the genotypes of the other species. We explore the resulting outcomes of these interactions, in particular determining the location of equilibria under various conditions. The coevolution here is much more complex than that between two haploid populations and allows for the possibility of two polymorphic equilibria. To allow for further analysis, we construct a semi-symmetric model. The variety of outcomes possible even in this second model provides support for the geographic mosaic theory of coevolution by suggesting the possibility of small local populations coevolving to very different outcomes, leading to a shifting geographic mosaic as neighboring populations interact with each other through migration.     

Optimal harvesting and stability for a two-species competitive system with stage structure

In this paper, we consider a stage-structured competitive population model with two life stages, immature and mature, with a mature population of harvesting. We obtain conditions for the existence of a globally asymptotically stable positive equilibrium and a threshold of harvesting for the mature population. The optimal harvesting of the mature population is also considered.     

一个污染环境中的单种群模型的动力学性质

以脉冲微分方程为基础建立了一个污染环境中在固定时刻对污染净化处理的单种群模型,详细研究了此模型的动力学性质,给出了种群灭绝和持续生存的充分条件.结果表明,当脉冲作用的周期小于某个阈值时,种群将持续生存;否则,种群将趋于灭绝.     

Density-dependence as a size-independent regulatory mechanism

The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.