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.     

斑块生境中具有捕食风险的动力系统模型及其数值模拟研究

从生物的捕食系统出发．提出了一种斑块生境中具有异质捕食风险的新机制．并构造了一个动力系统模型。在此模型之上,首先研究了扩散对系统稳定性的作用．并对系统进行了计算机模拟。研究发现：具有不同捕食风险的斑块生境之间的扩散(无论是只有食饵的扩散．还是食饵和捕食者共同的扩散)对整个捕食系统所起的作用主要取决于扩散的速率——只有在适中的扩散速率下系统才会稳定．如果扩散速率过快,则引起系统的强烈振荡。当只有食饵发生扩散时,参数f的值越小(f代表高捕食风险生境斑块体积占整个系统体积的比例)．系统越稳定。在捕食者与食饵同时扩散的时候．只有适中或较小的参数f才可以实现系统的长期稳定。其次研究了系统中种群空间平均平衡密度随扩散速率增加的变化趋势。模拟结果表明：系统中食饵种群的空间平均平衡密度随扩散速率增加而减小;捕食者种群平衡密度的变化趋势则取决于系统斑块之间的扩散形式：只有食饵发生扩散时．捕食者种群的空间平衡密度先保持不变．然后缓慢下降;捕食者与食饵同时扩散的时候．捕食者种群平衡密度呈上升趋势。上述结论是由空间异质的捕食风险所决定的．也就是一种下行控制力所限制的结果。综合以上两个结论．认为斑块之间的扩散形式决定了扩散对系统动态的作用和种群空间平均平衡密度对扩散速率增加的反应。     

种群行为对疾病空间传播动态的影响

依据基于个体的空间模拟模型,文章构建了食饵感染疾病的一类捕食-食饵系统,并从特征调节的食饵偏好、寄生导致的宿主繁殖率下降以及捕食者对食饵资源的转换等方面研究种群行为的改变对疾病空间传播动态与生物控制的影响。其中,文章采用了无标度网络、小世界网络、随机网络以及规则格子等四种空间网络结构来明确网络异质性对疾病空间动态的影响。模拟结果显示,特征调节的捕食种群对食饵偏好的改变以及对食饵资源的转换行为显著影响了疾病的流行与捕食者的数量。不同网络结构下,疾病的流行与捕食者的数量之间均呈现显著的负相关性,这也说明捕食者对疾病的生物控制有不可忽视的作用;而寄生调节的宿主生长率对疾病的传播和捕食者数量产生较为微弱的影响。另外,空间网络拓扑结构的异质性对疾病的流行率也产生显著影响,网络结构异质性的增加将不利于局部感染作用的发生,从而抑制疾病的空间传播。最后,斑块发生率的模拟结果揭示,虽然网络节点的度越高越有利于局部相互作用的发生,但是已感染食饵为了权衡感染与捕食风险的正负作用,其斑块发生率呈现先增加后减弱的趋势。总之,种群的行为与网络空间结构的异质性均可作为控制疾病传播的有效策略,具有一定的研究意义。     

一类捕食者与被捕食者模型的持久性与稳定性

研究了一类捕食者与被捕食者模型,该生态系统是一个食饵种群被一个捕食种群捕食.当给定参数满足一定条件下,利用比较原理和构造Lyapunov函数的方法,证明了系统的持久性和全局渐近稳定性,并讨论了正平衡点的渐近稳定性.     

具有反馈控制的Lotka-Volterra捕食-食饵系统研究

研究具有反馈控制的两种群Lotka-Volterra捕食系统平衡点的稳定性.通过构造适当的Lyapunov函数分别获得一组保证正平衡点和边界平衡点全局吸引的充分性条件.研究表明针对我们所采取的反馈控制策略,捕食者种群绝灭的风险加大,其可能的原因在于随着对食饵种群干扰力度的加大,捕食者种群将难以获得足够的食物,从而导致绝灭.     

捕食者-食饵交错扩散模型的整体解

应用能量估计方法和Bootstrap技巧证明含有两类竞争的食饵种群和一类捕食者种群的三种群捕食者-食饵扩散模型在空间维数小于6时古典解的整体存在性.     

一类具HOllingⅡ类功能性反应且存在两个极限环的捕食系统的定性分析

本文在文献[1]的基础上对具有HollingⅡ类功能性反应,且食饵、捕食者两种群均具有密度制约的食饵-捕食者生态系统（E）的定性结构进行了进一步的分析,得到（E）存在唯一正平衡点的充要条件,进而在此条件下,对（E）进行全面的定性分析,特别地证明了在一定条件下,系统（E）在其唯一正平衡点外围至少存在两个极限环。     

一类稀疏效应下具Ⅱ类功能反应生态系统的定性分析

本文对一类食饵种群在稀疏效应下具有HollingⅡ类功能性反应和常数存放率的食饵──捕食者系统进行定性分析,研究了系统平衡点的性态及全局稳定性,证明了系统极限环的存在唯一性,并解释了生态意义．     

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.     

一类被开发的HollingⅢ类功能反应模型的定性分析

本文研究了一类捕食种群、食饵种群同时具有收获率的HollingⅢ类功能反应生态系统,其中食饵种群具有非线性密度制约,捕食者无密度制约.应用微分方程定性理论讨论了系统的平衡点,分析了中心焦点的阶数以及稳定性,所给定参数满足一定条件时系统不存在极限环,最后根据细焦点的稳定性判断出极限环的存在性,并验证了极限环的惟一性.     

Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model

We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, when the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability.     

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.     

Impact of spatial heterogeneity on a predator-prey system dynamics

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.     

The Effect of Refuge on Dermestes ater (Coleoptera: Dermestidae) Predation on Musca domestica (Diptera: Muscidae): Refuge for Prey or the Predator?

It is believed that habitat heterogeneity can change the extent of predator-prey interactions. Therefore, in this study we examined the effect of habitat heterogeneity (characterized here as an addition of refuge) on D. ater predation on M. domestica. Predation of D. ater on M. domestica larvae was carried out in experimental habitats with and without refuge, and examined at different prey densities. The number of prey eaten by beetles over 24 h of predator-prey interaction was recorded, and we investigated the strength of interaction between prey and predator in both experimental habitats by determining predator functional response. The mean number of prey eaten by beetles in the presence of refuge was significantly higher than in the absence of refuge. Females had greater weight gains than males. Logistic regression analyses revealed the type II functional response for both experimental habitats, even though data did not fit well into the random predator model. Results suggest that the addition of refuge in fact enhanced predation, as prey consumption increased in the presence of refuge. Predators kept in the presence of refuge also consumed more prey at high prey densities. Thus, we concluded that the addition of refuge was an important component mediating D. ater-M. domestica population interactions. Refuge actually acted as a refuge for predators from prey, since prey behaviors detrimental to predators were reduced in this case.     

Predator-prey shell games: large-scale movement and its implications for decision-making by prey

Many classical models of food patch use under predation risk assume that predators impose patch-specific predation risks independent of prey behavior. These models predict that prey should leave a chosen patch only if and when the food depletes below some critical level. In nature, however, prey individuals may regularly move among food patches, even in the apparent absence of food depletion. We suggest that such prey movement is part of a predator-prey "shell game", in which predators attempt to learn prey location, and the prey attempt to be unpredictable in space. We investigate this shell game using an individual-based model that allows predators to update information about prey location, and permits prey to move with some random component among patches, but with reduced energy intake. Our results show the best prey strategy depends on what the predator does. A non-learning (randomly moving) predator favors non-moving prey – moving prey suffer higher starvation and predation. However, a learning predator favors prey movement. In general, the best prey strategy involves movement biased toward, but not completely committed to, the richer food patch. The strategy of prey movement remains beneficial even in combination with other anti-predator defenses, such as prey vigilance.     

Handling time promotes the coevolution of aggregation in predator-prey systems

Predators often have type II functional responses and live in environments where their life history traits as well as those of their prey vary from patch to patch. To understand how spatial heterogeneity and predator handling times influence the coevolution of patch preferences and ecological stability, we perform an ecological and evolutionary analysis of a Nicholson-Bailey type model. We prove that coevolutionarily stable prey and searching predators prefer patches that in isolation support higher prey and searching predator densities, respectively. Using this fact, we determine how environmental variation and predator handling times influence the spatial patterns of patch preferences, population abundances and per-capita predation rates. In particular, long predator handling times are shown to result in the coevolution of predator and prey aggregation. An analytic expression characterizing ecological stability of the coevolved populations is derived. This expression implies that contrary to traditional theoretical expectations, predator handling time can stabilize predator-prey interactions through its coevolutionary influence on patch preferences. These results are shown to have important implications for classical biological control.     

Piscivore efficiency and refuging prey: the importance of predator search mode

In predator-prey interactions, the efficiency of the predator is dependent on characteristics of both the predator and the prey, as well as the structure of the environment. In a field enclosure experiment, we tested the effects of a prey refuge on predator search mode, predator efficiency and prey behaviour. Replicated enclosures containing young of the year (0+) and 1-year-old (1+) perch were stocked with 3 differentially sized individuals of either of 2 piscivorous species, perch (Perca fluviatilis), pike (Esox lucius) or no piscivorous predators. Each enclosure contained an open predator area with three small vegetation patches, and a vegetated absolute refuge for the prey. We quantified the behaviour of the predators and the prey simultaneously, and at the end of the experiment the growth of the predators and the mortality and habitat use of the prey were estimated. The activity mode of both predator species was stationary. Perch stayed in pairs in the vegetation patches whereas pike remained solitary and occupied the corners of the enclosure. The largest pike individuals stayed closest to the prey refuge whereas the smallest individuals stayed farthest away from the prey refuge, indicating size-dependent interference among pike. Both size classes of prey showed stronger behavioural responses to pike than to perch with respect to refuge use, distance from refuge and distance to the nearest predator. Prey mortality was higher in the presence of pike than in the presence of perch. Predators decreased in body mass in all treatments, and perch showed a relatively stronger decrease in body mass than pike during the experiment. Growth differences of perch and pike, and mortality differences of prey caused by predation, can be explained by predator morphology, predator attack efficiency and social versus interference behaviour of the predators. These considerations suggest that pike are more efficient piscivores around prey refuges such as the littoral zones of lakes, whereas perch have previously been observed to be more efficient in open areas, such as in the pelagic zones of lakes.     

Effects of density-dependent migrations on stability of a two-patch predator-prey model

We consider a predator-prey model in a two-patch environment and assume that migration between patches is faster than prey growth, predator mortality and predator-prey interactions. Prey (resp. predator) migration rates are considered to be predator (resp. prey) density-dependent. Prey leave a patch at a migration rate proportional to the local predator density. Predators leave a patch at a migration rate inversely proportional to local prey population density. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. First, we show that for a large class of density-dependent migration rules for predators and prey there exists a unique and stable equilibrium for migration. Second, a numerical bifurcation analysis is presented. We show that bifurcation diagrams obtained from the complete and aggregated models are consistent with each other for reasonable values of the ratio between the two time scales, fast for migration and slow for local demography. Our results show that, under some particular conditions, the density dependence of migrations can generate a limit cycle. Also a co-dim two Bautin bifurcation point is observed in some range of migration parameters and this implies that bistability of an equilibrium and limit cycle is possible.     

Population dynamics of thrips prey and their mite predators in a refuge

Prey refuges are expected to affect population dynamics, but direct experimental tests of this hypothesis are scarce. Larvae of western flower thrips Frankliniella occidentalis use the web produced by spider mites as a refuge from predation by the predatory mite Neoseiulus cucumeris. Thrips incur a cost of using the refuge through reduced food quality within the web due to spider mite herbivory, resulting in a reduction of thrips developmental rate. These individual costs and benefits of refuge use were incorporated in a stage-structured predator-prey model developed for this system. The model predicted higher thrips numbers in presence than in absence of the refuge during the initial phase. A greenhouse experiment was carried out to test this prediction: the dynamics of thrips and their predators was followed on plants damaged by spider mites, either with or without web. Thrips densities in presence of predators were higher on plants with web than on unwebbed plants after 3 weeks. Experimental data fitted model predictions, indicating that individual-level measurements of refuge costs and benefits can be extrapolated to the level of interacting populations. Model-derived calculations of thrips population growth rate enable the estimation of the minimum predator density at which thrips benefit from using the web as a refuge. The model also predicted a minor effect of the refuge on the prey density at equilibrium, indicating that the effect of refuges on population dynamics hinges on the temporal scale considered.     

Dragonfly larvae and tadpole frog space use games in varied light conditions

Predators and prey often engage in a game where predators attemptto be in areas with higher prey densities and prey attempt tobe in areas with lower predator densities. A few models havepredicted the resulting distributions of predators and prey,but little empirical data exist to test these predictions andto examine how abiotic and biotic factors shape the distributions.Thus, we observed how Anax dragonfly nymphs and Pacific treefrog tadpoles (Pseudacris regilla) either together or separatelydistributed themselves in an arena with a high- and a low-preyresource patch. Trials were conducted in high- and low-lightconditions to manipulate predation risk and to view the effectsof this abiotic factor. Counter to the model predictions, wefound that predators were not more abundant in high-resource(HR) patches, and they thus did not force prey toward beinguniformly distributed. Using a model selection approach to assesswhat factors affected predator and prey patch-switching movement,we found that prey more often left patches that had more predatorspresent, but predators surprisingly more often left patcheswith more prey present. Light levels did not affect predationrisk; however, in the dark with the associated reduction invisual information predators preferred HR patches. This causeda lower coincidence of prey and predators in patches. Predatorsalso switched patches less often when they occupied the samepatch as the other predator. This suggests that predator distributions,and indirectly prey distributions, are affected by the riskof intraguild predation.