污染环境中Leslie系统的生存分析

研究环境污染对Ｌｅｓｌｉｅ资源－消费者系统中消费者种群的长期影响,给出了种群弱持续生存和绝灭的条件,在一定条件下得到了阈值．     

污染环境下单种群模型生存阈值

本论文研究了污染环境下毒素对单种群生存的影响。在环境容纳量较小的假设下建立了生物种群模型,在该模型中不但考虑了环境毒素浓度对生物个体生存的影响,还考虑了生物个体从食物链中吸收的毒素对其影响。通过研究得到种群一致持续生存和若平均持续生存的充分条件,同时得到种群持续生存依赖于模型参数和生物个体体内毒素净化率的某些充分条件．     

Leslie系统在污染环境下有关生存问题的分析

研究了在污染环境中毒素对Leslie资源-消费者系统中消费者种群的长期影响,给出了种群弱持续生存和灭绝的条件．     

毒素对种群生存的影响

本文总结了近年来我们关于污染环境中毒素对种群生存影响这一重要课题的研究成果,利用我们提出的积分均值法,给出了新的持续生存概念,对一些模型得到了种群持续生存与绝灭的阈值,我们的工作是从单个种群到ｎ维食物链,从简化模型到未简化模型、从无限时间到有限时间逐步展开的;另外,我们还讨论了一些模型解的稳定性与吸收域。     

二维Lotka-Volterra竞争系统的β持续生存与β绝灭

利用极限理论与延拓方法研究了二维Lotka-Volterra竞争务统在有限时间内的持续生存与绝灭问题,即β持续生存与β绝灭问题.给出了种群β持续生存与β绝灭的一些充分条件.所得结论表明:种群的β持续生存和β绝灭与种群的初始数量有关.在一定条件下,只要控制种群的初始数量在一定范围内,即可保证两种群永远β持续生存.     

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．     

具有毒素影响的二维Kolmogorov模型的持续生存和绝灭

研究了具有毒素影响的二维Kolmogorov模型,给出了该系统持续生存与绝灭的充分条件.     

环境污染中三维时变Volterra捕食-被捕食系统的持续生存

对环境容量很大且被污染的三种群时变系统进行了研究,给出了三维时变Ｖｏｌｔｅｒｒａ捕食－被捕食系统弱平均持续生存与绝灭的充分条件。     

体内毒素浓度不相同的三维时变Volterra系统的持续生存

在环境容量很大且被污染的情形下,对体内毒素浓度不相同的三种群时变Volterra系统进行了研究,并给出了三维时变Volterra捕食系统弱平均持续生存与灭绝的条件。     

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．     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

Viability analysis of endangered crayfish populations

The noble crayfish Astacus astacus L. is a threatened freshwater invertebrate. Many of the remaining populations are isolated and there is considerable concern that diseases and the increased frequency of flooding events may drive these remnant populations to extinction. We performed a population viability analysis for a typical isolated noble crayfish population. We quantified the extinction risk by the mean time to extinction within 1000 years for several scenarios (flooding events, restocking of adults). For a set of parameters derived from field estimates, we estimated the mean time to extinction to be 240 years. However, the median was only 80 years. Multiple sensitivity analysis by logistic regression revealed that spawning probability, juvenile and adult mortality were the important parameters for the survival of the population. The mean time to extinction decreased with increasing frequency of floodings. This is alarming, considering the magnitude of the effect and the expectation of an increasing number of floodings with global warming. Restocking, however, was found to have only a minor effect on the mean time to extinction. Overall, our simulations suggested that for the long-term and self-sustaining survival of the noble crayfish, particularly where they remain isolated, we have to improve the extent and quality of habitats. Nevertheless, additional measures are necessary, especially the removal of dispersal barriers to allow some exchange of individuals between populations. However, this also calls for a control of invasive crayfish species.     

Considering threats to population viability of the endangered Korean long-tailed goral (Naemorhedus caudatus) using VORTEX

Population viability analysis (PVA) has frequently been used in conservation biology to predict extinction rates for threatened or endangered species. In this study, we used VORTEX to model Korean long-tailed goral (Naemorhedus caudatus) using previously collected ecological data. We focused on modelling population extinction, mean population size and heterozygosity. The minimum viable population size was found to be at least 50 gorals for 100 years, regardless of carrying capacity. However, populations with fewer than 50 gorals could not remain successful in the model. Inbreeding depression, catastrophes and supplementation also affected patterns of population extinction, mean population size and heterozygosity. Supplementation with new individuals had the strongest effect on extinction, mean population size and heterozygosity, followed by initial population size, inbreeding, catastrophes and carrying capacity. These results suggest that a supplementation by extra goral individuals from goral proliferation facilities would be the most helpful means for the restoration programme. More Korean goral-specific information regarding demographic and habitat parameters is needed for further PVA of the species.     

Theory for designing nature reserves for single species

We examine the question of the optimal number of reserves that should be established to maximize the persistence of a species. We assume that the mean time to extinction of a single population increases as a power of the habitat area, that there is a certain amount of habitat to be reserved, and that the aim is to determine how this habitat is most efficiently divided. The optimal configuration depends on whether the management objective is to maximize the mean time to extinction or minimize the risk of extinction. When maximizing the mean time to extinction, the optimal number of independent reserves does not depend on the amount of available habitat for the reserve system. In contrast, the risk of extinction is minimized when individual reserves are equal to the optimal patch size, making the optimal number of reserves linearly proportional to the amount of available habitat. A model that includes dispersal and correlation in the incidence of extinction demonstrates the importance of considering the relative rate at which these two factors decrease with distance between reserves. A small number of reserves is optimal when the mean time to extinction increases rapidly with habitat area or when risks of extinction are high.     

Evolutionary stability for large populations

We present a revision of Maynard Smith's evolutionary stability criteria for populations which are very large (though technically finite) and of unknown size. We call this the large population ESS, as distinct from Maynard Smith's infinite population ESS and Schaffer's finite population ESS. Building on Schaffer's finite population model, we define the large population ESS as a strategy which cannot be invaded by any finite number of mutants, as long as the population size is sufficiently large. The large population ESS is not equivalent to the infinite population ESS: we give examples of games in which a large population ESS exists but an infinite population ESS does not, and vice versa. Our main contribution is a simple set of two criteria for a large population ESS, which are similar (but not identical) to those originally proposed by Maynard Smith for infinite populations.     

Extinction risk of a meta-population: aggregation approach

Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.     

Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle

Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.     

Sex ratio variance and the maintenance of environmental sex determination

Although variation in population sex ratios is predicted to increase the extinction rate of clades with environmental sex determination (ESD), ESD is still seen in a wide array of natural systems. It is unclear how this common sex-determining system has persisted despite this inherent disadvantage associated with ESD. We use simulation modelling to examine the effect of the sex ratio variance caused by ESD on population colonization and establishment. We find that an accelerating function of establishment success on initial population sex ratio favours a system that produces variance in sex ratios over one that consistently produces even sex ratios. This sex ratio variance causes ESD to be favoured over genetic sex determination, even when the mean global sex ratio under both sex-determining systems is the same. Data from ESD populations suggest that the increase in population establishment can more than offset the increased risk of extinction associated with temporal fluctuations in the sex ratio. These findings demonstrate that selection in natural systems can favour increased variance in a trait, irrespective of the mean trait value. Our results indicate that sex ratio variation may provide an advantage to species with ESD, and may help explain the widespread existence of this sex-determining system.     

扩散对污染斑块上Smith种群生存的影响

通过建立两斑块的单种群扩散系统,主要研究扩散对其中受污染的斑块上种群生存的影响．文中所考虑的是污染斑块上外界毒素的输入量存在极限值的情形,得到如下结论：无扩散时,若此极限值超过某一定值,则污染斑块上的种群趋于灭绝;扩散存在且两斑块上种群的扩散系数满足一定的条件时,则可使该系统的种群永久生存或灭绝．