一类具阶段结构的捕食者-食饵模型的渐进性质

研究了一类具阶段结构的捕食者-食饵模型的渐近性质．文中假设由幼年阶段转化为成年阶段的转化率依赖于幼年个体数量．建立了捕食种群一致持续生存与绝灭的条件．证明了稳定的周期解的存在性．     

具有年龄结构的食蚜蝇-蚜虫捕食模型

现有的具有年龄结构的捕食-食饵模型总是假设只有成年捕食者捕食猎物,这与实际情况不符。建立了一个幼年捕食者捕食食饵的具有年龄结构的食蚜蝇-蚜虫模型,应用微分方程定性理论,讨论了系统平衡点及其稳定性:其中平衡点E1(0,0,0)为不稳定的;满足一定条件时,边界平衡点E2(K,0,0)及正平衡点E3(x*,y1*,y2*)为局部渐近稳定的;且应用一致持续生存理论得到了系统永久持续生存的条件,为有害生物综合治理提供了理论依据。     

一类具有阶段结构和脉冲效应的捕食者-食饵模型的动力学分析

研究了一个捕食者具有阶段结构,食饵具有脉冲效应和时滞的捕食者-食饵模型.利用离散动力系统的频闪映射,我们获得了捕食者-灭绝的周期解同时给出了该周期解全局吸引的充分条件.利用时滞脉冲微分方程的理论,得到了系统持续生存的充分条件.     

食饵染病的非自治生态-流行病模型的分析

研究了一类疾病仅在食饵中传播的非自治捕食者-食饵模型.文中假定捕食者受密度制约影响,在捕食时具有甄别能力而只捕食健康的食饵,且具有HollingⅢ类功效函数;对于食饵,将其分为食饵易感者和食饵染病者两类,模型假定疾病发生率为非线性的,且考虑到了环境对食饵种群的容纳量.文中运用Barbalat引理、比较原理等稳定性理论的相关方法,找到了系统的正向不变集,证明了模型解的最终有界性;通过理论分析,分别得到了两种群持续生存、周期解的存在性以及周期解全局渐进稳定的相关条件;最后,通过MATLAB数值模拟,验证了有关结论.     

脉冲捕获捕食者与食饵具阶段结构的捕食-食饵模型

研究脉冲捕获捕食者与食饵具阶段结构的捕食-食饵模型.利用频闪映射理论,得到食饵灭绝的周期解是全局吸引的;运用时滞脉冲微分方程理论,证明了此系统是持久的.本文的结论为生态保护提供了可靠的策略依据.     

一类捕食者具有阶段结构的捕食系统的全局稳定性分析

本文建立了一类捕食者具有阶段结构的捕食系统,计算得到了不存在食饵种群时捕食者种群模型和食饵种群存在时捕食系统的平衡点,并证明了平衡点的存在性.分析和比较了两个模型平衡点的全局稳定性,最终确定了决定模型全局稳定性的捕食者种群基本再生数、食饵灭绝与否的捕食率阈值以及捕食存在时食饵种群的净增长率.     

一类带一般功能反应的病原体捕食者-食饵模型中避难所的影响

本文讨论一类SIP型捕食者-食饵-病原体扩散模型,其中捕食者带有一般的功能反应函数.我们主要研究该模型中避难所与扩散的作用.首先通过线性化方法和Lypunov方法分别讨论非负常数平衡解的局部和全局渐近稳定性,然后给出交错扩散导致Turing不稳定的一个充分条件,最后,作为一个应用,我们研究一类带HollingⅡ型功能反应项的捕食者-食饵模型.     

高维“食饵—捕食者”模型周期解的存在性

一、引言文献对“Ⅱ类功能反应模型”进行了详细、完整的分析,给出了存在周期解的充分条件.但是在自然界中,就某一生态环境而言,往往同时存在上千种,甚至上万种“食饵-捕食者”系统,在食饵和捕食者之间都存在竞争关系.考虑到这些因素,本文将考虑更一般的高维“食饵-捕食者”模型.     

一类具有三个阶段结构的扩散捕食系统研究

讨论了一类捕食者具有三个阶段结构和Beddington型功能性反应,食饵可以在两个斑块间扩散的非自治捕食者-食饵系统.运用Liapunov函数方法,得到了该系统一致持续生存的充分条件.对于该模型的周期系统,讨论了存在唯一、全局渐近稳定的周期解的条件.     

具收获与脉冲的时滞捕食模型研究

研究了与生物资源管理相关的食饵具脉冲扰动与成年捕食者具连续收获的阶段结构时滞捕食-食饵模型.利用离散动力系统的频闪映射和脉冲时滞微分方程理论,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.结论为现实的可再生生物资源管理提供了可靠的策略依据.     

Multiple periodic solutions of a delayed predator–prey model with non-monotonic functional response and stage structure

The paper studies a periodic and delayed predator–prey system with non-monotonic functional responses and stage structure. In the system, both the predator and prey are divided into immature individuals and mature individuals by two fixed ages. It is assumed that the immature predators cannot attack preys, and the case of the mature predators attacking the immature preys is also ignored. Based on Mawhin's coincidence degree, sufficient conditions are obtained for the existence of two positive periodic solutions of the system. An example is presented to illustrate the feasibility of the main results.     

Dynamics of stage-structure predator-prey systems under density-dependent effect and mortality

We develop a four dimensional predator-prey system in continuous time with stage-structure for both the communities. The reproduction rate of the prey and the transition rate for the predator, in our model, are assumed to be density-dependent. The stability results for the coexisting equilibrium are obtained by making use of Routh–Hurwitz criteria. Because of the density-dependent effects, numerical simulations are applied in complex situations. We observe that increasing values of the coefficients linked with density-dependent term promote the stability of the coexisting steady state. Our main focus is to understand the variation of stocks when mortality rates on different stage classes are increased. We verified that stable stock on mature predator increases with its increasing mortality rate in three different modeling frameworks. However, no such positive effect on the biomass of the immature predator occurs when immature predators are removed, culled or harvested. Therefore, we could conclude that the appearance of hydra effect on many unstructured predator-prey models is due to the mortality of the mature predator only. No hydra effect is also detected when mature prey is removed in several situations we discussed. Overall, the obtained results are new and could be interesting contribution in theoretical ecology.     

不同性别和年龄的大仓鼠对黄鼬气味的反应

将雌性成体和雌雄亚成体大仓鼠 (Cricetulustriton)长期 (4周 )暴露给过量的黄鼬 (Mustelasibirica)肛腺分泌物 ,观察其行为和生理状态的变化 ,并通过与我们以前有关黄鼬气味对成年雄鼠影响的研究结果进行比较 ,表明黄鼬气味对不同性别和不同年龄大仓鼠的胁迫效应和生殖抑制存在差异。发现黄鼬气味对雌性大仓鼠的影响较雄性小 ,对亚成体的影响较成体小 ,这与雌性和未成年动物对各种胁迫因素的反应更敏感的普遍现象相反。在成年鼠中 ,雌雄鼠的攻击行为都受到黄鼬气味的抑制 ;但天敌气味使雌性的胁腺膨大 ,对胁腺标记和肾上腺大小无影响 ;成年雄鼠的肾上腺膨大 ,胁腺萎缩 ,标记减少。在亚成体中 ,除了雄性胁腺受到抑制(与成年雄鼠相同 )外 ,雌雄鼠的肾上腺和雌性的胁腺未受影响。亚成体实验鼠的体重都比对照组低 ,但成年鼠的体重未受影响。另外 ,与以往对其它鼠类的研究结果一致 ,天敌气味并不影响成年鼠的生殖器官 ,却抑制了未成年雄鼠的附睾和未成年雌鼠的子宫。这些差异可能和生理基础的性二态以及可能面临的被捕食风险大小有关     

Intraspecific competition in immature Amblyseius fallacis,Amblyseius andersoni,Typhlodromus occidentalis and Typhlodromus pyri (Acari: Phytoseiidae)

Intraspecific competition in immature Amblyseius fallacis, Amblyseius andersoni, Typhlodromus occidentalis and Typhlodromus pyri was examined in the laboratory using small cages at five different predator densities (two, four, eight, 16 and 32) in the absence and presence of prey 100 eggs of two-spotted spider mite, Tetranychus urticae (Koch), at 25 ± 1°C, 80% RH and 16L:8D photoperiod. In the absence of spider mite prey, some individuals of immature phytoseiids showed increased development and surival with increasing predator densities up to certain limits, but none survived to the adult stage, except for a single male each of A. andersoni and A. fallacis who completed development by cannibalizing on conspecifics at a density of 32 predators per cage. In the absence of spider mite prey, the mean immature survival time was independent of the initial predator density, but the variance of survival time increased with predator density. In the presence of prey, the proportion of immatures surviving to adulthood generally decreased with initial predator density and dropped sharply to almost none at the predator density of 32 for A. fallacis, eight for A. andersoni, 16 for T. occidentalis and four for T. pyri. The number of prey consumed per predator during the first day generally decreased with predator density in all four species, as prey available per predator decreased and the competition for food increased with predator density. Our data indicate that scramble competition is operating in these four species. Although cannibalism was occasionally observed, especially after the exhaustion of prey and in the generalist predators such as A. andersoni, the immatures of these phytoseiids were less influenced by the interference of conspecifics than by the increasing difficulty of finding food at high predator densities. The implications of this study for understanding phytoseiid population dynamics and their use in biological control are discussed.     

Mathematical analysis of a delayed stage-structured predator–prey model with impulsive diffusion between two predators territories

In most models of population dynamics, diffusion between two patches is assumed to be either continuous or discrete, but in reality, many species diffuse only during a single period, and diffusion often occurs in regular pulses. Further, in forest habitats, the highest-level predator species are restricted to a specific territory, but prey can impulsively move between territories. Therefore, in this paper, we consider a delayed stage-structured predator–prey model with impulsively diffusive prey between two patches; in the model, patches represent the territories of two different predator populations. Here, we analytically obtain the global attractivity condition of predator-extinction periodic solutions for the system by using the concepts of Hui and Chen (2005); a numerical simulation is also included to illustrate this result. Further, we establish permanence conditions for the coexistence of the species using the theory of impulsive delayed differential equations. Finally, we explore the possibilities of the permanence of the system by using the growth rates of immature predators and the impulse period as critical parameters, and we also obtain the parameters’ threshold limits using numerical experimentation.     

Invest conflicts of adult predators

Parental care is incorporated into a prey-predator model in which immature predators are taken care of by their parents. It is assumed that adult predators confront the problem to stay home to protect offspring or to go out to forage. The global dynamics of the mathematical model is analyzed by means of analytical methods and numerical simulations. Conditions for the extinction of predator populations are established and the manners in which predators become extinct are revealed. Bifurcation analysis shows that the model admits changes from the extinction of predators to stable coexistence at a positive equilibrium point, and then to stage-structure induced oscillations. It is shown that optimal invest of adult predators can be achieved.     

带有阶段结构的时滞捕食-被捕食动力系统的全局稳定性和最优收获量

讨论捕食和被捕食动力系统时,把生物种群分为幼年和成年两个阶段,仅成年有捕食能力。还考虑了种群相互作用中不可避免的时滞和密度制约作用,以及在捕食一被捕食模型中更切合实际的“比率依赖”理论。通过对系统的分析和构造李雅普诺夫函数,分别得出在适当条件下系统非负平衡位置的局部稳定性和全局稳定性。并研究了成熟种群的最优收获量。     

Impact of temperature and prey density on the predacious capacity and behaviour of Stethorus punctillum Weise

Temperature had various effects on the predacious efficacy of immature and mature stages of the coccinellid predator, Stethorus punctillum on the two-spotted spider mite, Tetranychus urticae. In the case of immature stages, food consumption at the lowest tested temperature (15°C) was significantly higher than that at higher temperatures (25 and 35°C). On the contrary, positive correlation between food consumption and temperature was evaluated in the case of adult predator. Regarding predator responses to different prey density, a high positive correlation between food consumption and prey density was evaluated among 4^th instar larvae of the predator, followed by adult predator, while younger instars did not show reasonable increases with increasing prey densities. These results confirm that larval and adult stages of S. punctillum exhibit “Type II” functional response. In conclusion, the 4^th instar larvae and adult predator are the most preferable stages in winter and summer crops to control T. urticae, respectively.     

Dynamical Adaptation of Parental Care

Two models are proposed to simulate population growth of species with mature stage and immature stage in which there are parental cares for immature. It is assumed that the protection of mature to their immature reduces mortality of immature at the cost of reduction of reproduction. Dynamical adaptation of parental care is incorporated into the models, one of which is described with the proportional transition rate from immature to mature (ODE model) and the other one is described with a transition rate from immature to mature according to a fixed age (DDE model). For the ODE model, it is shown that the adaptation of parental care enlarges the possibility of species survival in the sense that population is permanent under the influences of the adaptation, but becomes extinct in the absence of adaptation. It is proved that the outcome of the adaptation makes the population in an optimal state. It is also observed that there are parental care switches, from noncare strategy to care strategy, as the natural death rate of immature individuals increases. The analysis of the DDE model indicates that the adaptation also enlarges the opportunity of population persistence, but the stage delay has the tendency to hinder the movement of population evolution to the optimal state. It is found that the loss rate of immature in the absence of parental care can induce different patterns to disturb the adaptation of population to optimal state. However, it is shown that the adaptation of parental care approaches to the optimal state when parental care is required for the survival of the population, for example, when the loss rate of immature or competition among mature increases or the fecundity decreases. The research was supported by Heiwa–Nakajima Fund and National Science Fund of China (No. 10571143). The research was partly supported by the Sasakawa Scientific Research Grant from The Japan Science Society. The research was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.