毒素脉冲输入与种群脉冲出生切换阶段结构单种群动力学模型研究

本文研究了毒素脉冲输入与脉冲出生切换阶段结构单种群动力学模型.利用常微分方程及差分分析,获得了系统种群灭绝和持久生存的控制条件结果,为污染环境中的生物资源管理提供了可靠的管理策略.     

污染环境下具有时滞增长反应和脉冲输入的单种群模型分析

研究污染环境下具有时滞增长反应和脉冲输入的单种群动力学模型,利用脉冲微分系统讨论营养基和毒素的脉冲输入对单种群物种生长的影响,证明微生物在吸收毒素的情况下灭绝的周期解是全局吸引的,并获得系统持久的条件.研究结果为控制环境中毒素对种群生长的影响提供了理论依据.     

具有脉冲毒素投放和营养再生的恒化器模型

研究具有脉冲毒素投放和营养再生的恒化器模型.利用脉冲微分方程的比较定理和小扰动方法得到了边界周期解全局渐近稳定的充分条件,进而得到了系统持续生存的充分条件.结果表明毒素环境将会导致微生物种群的灭绝.     

污染环境下具有脉冲输入环境毒素的单种群模型的灭绝阈值研究

本文研究了污染环境下具脉冲输入环境毒素的单种群模型.利用乘子理论和小振幅扰动法,当脉冲周期小于一个临界值时,我们得到了种群灭绝周期解是全局渐近稳定的,同时我们还得到了种群持久的条件.从生物学的观点看,污染环境下保护物种的方法是控制环境毒素的排放周期或排放量.我们的结论为资源环境下的生物资源管理提供了策略基础.     

环境污染中具有脉冲效应的捕食系统动力学分析

针对环境问题日益严峻,考虑到种群密度制约项的影响,建立了环境污染中脉冲输入污染物,且具有HollingⅡ型的两种群捕食与被捕食系统的动力学模型.利用脉冲微分方程的积分均值法和比较定理,得到系统弱平均持续生存和种群灭绝的充分条件.理论可用来保护物种,尤其是濒临灭绝的物种,防止灭绝.     

一类污染环境下具有脉冲输入的竞争培养模型的定性分析

本文研究了污染环境下具有脉冲输入的竞争培养模型.利用乘子理论和小振幅扰动法,我们得到了种群灭绝周期解全局渐近稳定的充分条件,同时还得到了种群持久的条件.我们的结果表明环境污染能最终导致种群灭绝.     

具有功能反应的污染环境中的非自治捕食系统的生存与灭绝

研究了一类具有HollingII型功能反应且居于污染环境中的非自治捕食系统,考虑到资源存在及死亡个体体内毒素回归环境对种群密度的影响.运用比较定理及微分方程稳定性理论,得到了此系统持续生存和灭绝的充分条件.     

污染环境下毒素脉冲输入和心理效应对随机捕食-食饵系统的影响

文章研究了在污染环境下毒素脉冲输入和心理效应对随机捕食-食饵系统的影响.通过构造Lyapunov函数,证明了系统全局正解的存在性;利用随机微分方程比较定理得到系统平均持续生存与灭绝的充分条件;应用Has'minskii定理证明了系统至少存在一个非平凡的正周期解,并给出了数值模拟.     

污染环境中的非自治种群模型的生存分析

研究了环境污染对种群的长期影响.考虑到新生个体的出生对种群体内毒素的影响,以及死亡的种群个体将体内毒素带回环境,建立了一个非自治数学模型.主要运用比较定理得到了种群一致持续生存、弱持续生存以及绝灭的判据.     

带有性别比的两阶段尺度结构种群系统的行为分析

分析了一类带有性别比的两阶段尺度结构种群模型.利用特征线方法和比较原理证明了状态系统解的存在唯一性.借助上-下解技巧分别给出了目标种群灭绝和长期生存的条件.     

THE EFFECTS OF REDUCING MATING LIKELIHOOD ON POPULATION VIABILITY

Abstract The success a species may have invading a patch previously unoccupied is of considerable interest for pest managers and conservation ecologists. The purpose here is to present a mechanistic approach to analyze reproductive Allee effects appearing through the failure in the process of fertilization in a two‐sex population and observe how the survival in an invaded patch is affected. This is in contrast to the usually employed stochastic models with a deterministic skeleton that describe the presence of Allee effects. A Poisson–Ricker model, which includes stochastic demography and sex determination with females classified as successfully fertilized or not fertilized, is used. Numerical approximations to the probabilities of extinction and the mean time to extinction are presented, for fixed parameter values, suggesting how stochasticity in the mating process combined with random fluctuations in the male and female densities, at each generation, contribute to the risk of extinction of a population which started an invasion at a low density.     

Survival of branching random walks with absorption

We consider a branching random walk on R starting from x≥0 and with a killing barrier at 0. At each step, particles give birth to b children, which move independently. Particles that enter the negative half-line are killed. In the case of almost sure extinction, we find asymptotics for the survival probability at time n, when n tends to infinity.     

POPULATION EXTINCTION IN DETERMINISTICAND STOCHASTIC DISCRETE‐TIME EPIDEMIC MODELS WITH PERIODIC COEFFICIENTS WITH APPLICATIONS TO AMPHIBIAN POPULATIONS

ABSTRACT. Discrete‐time deterministic and stochastic epidemic models are formulated for the spread of disease in a structured host population. The models have applications to a fungal pathogen affecting amphibian populations. The host population is structured according to two developmental stages, juveniles and adults. The juvenile stage is a post‐metamorphic, nonreproductive stage, whereas the adult stage is reproductive. Each developmental stage is further subdivided according to disease status, either susceptible or infected. There is no recovery from disease. Each year is divided into a fixed number of periods, the first period represents a time of births and the remaining time periods there are no births, only survival within a stage, transition to another stage or transmission of infection. Conditions are derived for population extinction and for local stability of the disease‐free equilibrium and the endemic equilibrium. It is shown that high transmission rates can destabilize the disease‐free equilibrium and low survival probabilities can lead to population extinction. Numerical simulations illustrate the dynamics of the deterministic and stochastic models.     

The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment

Uncontrolled contribution of pollutant to the environment has led many species to extinction and several others are at the verge of extinction. This article deals with the dynamics of a single stage-structured population model with impulsive toxin input and time delays (including constant individual maturation time delay and pollution time delay) in a polluted environment, in which we assume that only the mature individuals are affected by pollutants. We obtain conditions for the global attractivity of the population-extinction periodic solution and the permanence of the population. We show that maturation time delay and impulsive toxin input can bring great effects on the dynamics of the system, and pollution time delay is harmless. Numerical simulations confirm our theoretical results.     

Effects of cannibalism on a basic stage structure

In this paper, we discuss the effects of cannibalism on a basic stage-structured population model for a single species. A threshold condition for extinction versus persistence is obtained, and numerical simulations of the population dynamics are presented. These simulations suggest that cannibalism has a stabilizing effect on the population, promoting equilibrium of the adult population level.     

USING RESERVES TO PROTECT FISH AND WILDLIFE SIMPLIFIED MODELING APPROACHES

ABSTRACT. This paper investigates theoretically to what extent a nature reserve may protect a uniformly distributed population of fish or wildlife against negative effects of harvesting. Two objectives of this protection are considered: avoidance of population extinction and maintenance of population, at or above a given precautionary population level. The pre‐reserve population is assumed to follow the logistic growth law and two models for post‐reserve population dynamics are formulated and discussed. For Model A by assumption the logistic growth law with a common carrying capacity is valid also for the post‐reserve population growth. In Model B, it is assumed that each sub‐population has its own carrying capacity proportionate to its distribution area. For both models, migration from the high‐density area to the low‐density area is proportional to the density difference. For both models there are two possible outcomes, either a unique globally stable equilibrium, or extinction. The latter may occur when the exploitation effort is above a threshold that is derived explicitly for both models. However, when the migration rate is less than the growth rate both models imply that the reserve can be chosen so that extinction cannot occur. For the opposite case, when migration is large compared to natural growth, a reserve as the only management tool cannot assure survival of the population, but the specific way it increases critical effort is discussed.     

The threshold between permanence and extinction for a stochastic Logistic model with regime switching

A stochastic logistic model under regime switching is proposed and investigated. Sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The threshold between weak persistence and extinction is obtained. Then we show that this threshold also is the threshold between stochastic permanence and extinction under a simple additional condition. The results show that firstly, the stationary probability distribution of the Markov chain plays a key role in determining the permanence and extinction of the population. Secondly, different types of environmental noises have different effects on the permanence and extinction of the population. Thirdly, the more the stochastic noises, the easier the population goes to extinction.     

A Reversible Nearest Particle System on the Homogeneous Tree

We introduce a modified contact process on the homogeneous tree. The modification is to the death rate: an occupied site becomes vacant at rate one if the number of occupied id neighbors is at most one. This modification leads to a growth model which is reversible, off the empty set, provided the initial set of occupied sites is connected. Reversibility admits tools for studying the survival properties of the system not available in a nonreversible situation. Four potential phases are considered: extinction, weak survival, strong survival, and complete convergence. The main result of this paper is that there is exactly one phase transition on the binary tree. Furthermore, the value of the birth parameter at which the phase transition occurs is explicitly computed In particulars survival and complete convergence hold if the birth parameter exceeds 1/4. Otherwise, the expected extinction time is finite.     

Stochastic modelling of the effect of environmental disturbance on the population dynamics

The dynamics of a population, with its growth characterised by two stages namely an initial non-reproductive stage of length ρ, resistant to the environmental fluctuations and a second susceptible stage adding continuously to the population is modelled. The environment alternates in its character being hostile and favourable.The favourable periods are independently and identically distributed random variables and during the constantharsh periods all the adults in the population are wiped out While the existing models tacitly assume the environmental period to be much smaller than the biological period ρ, our modelling enables us to consider the two periods to be of comparable scale. In such a case, apart from the various statistical characteristics of interest derived, we show that the average extinction time increases with increasing duration of the disturbance, a result which is counter-intutive.Numerical evaluation of the time for extinction for certain values of the parameters involved are made.     

The role of cooperation and parasites in non-linear replicator delayed extinctions

In the present work we study the role of cooperation and parasites on extinction delayed transitions for self-replicating species with catalytic activity. We first use a one-dimensional continuous equation to study the dynamics of both single autocatalytic replicator and symmetric two-member hypercycles, where two well-defined phases involving survival and extinction of replicators are shown to exist. Extinction dynamics is analyzed numerically and analytically and under both deterministic and stochastic scenarios. A ghost is also found for the single autocatalytic replicator and for the asymmetric hypercycle, with an extinction time delay following the square-root scaling law near bifurcation threshold. We find that the extinction delay is longer for the two-member hypercycle than for the single autocatalytic species, indicating that cooperation among replicators might involve to spend a longer time in the bottle-neck region of the ghost. The asymmetry of the network is shown to prolong the extinction time. We also show that an attached parasite decreases the time spent in the bottle-neck region of the ghost, thus accelerating extinction in these systems of replicators. Nevertheless the effect of the parasite is not so important when replicators catalytically cooperate, being the two-member hypercycle less sensitive to the parasite than the autocatalytic species. Here the hypercycle asymmetry can also significantly increase the delaying capacity. These features make the hypercycle to undergo a longer extinction delay, thus increasing the memory effect of the ghost. We finally explore the role of the ghost in fluctuating media, where the extinction delayed transition is shown to increase the survival probability of cooperating catalytic species.