共查询到20条相似文献,搜索用时 31 毫秒
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In this paper we present a deterministic, discrete-time model for a two-patch predator-prey metapopulation. We study optimal
harvesting for the metapopulation using dynamic programming. Some rules are established as generalizations of rules for a
single-species metapopulation harvesting theory. We also establish rules to harvest relatively more (or less) vulnerable prey
subpopulations and more (or less) efficient predator subpopulations. 相似文献
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Allochthonous resources can be found in many foodwebs and can influence both the structure and stability of an ecosystem. In order to better understand the role of how allochthonous resources are transferred as quarry from one predator-prey system to another, we propose a predator-prey-quarry-resource-scavenger (PPQRS) model, which is an extension of an existing model for quarry-resource-scavenger (a predator-prey-subsidy (PPS) model). Instead of taking the allochthonous resource input rate as a constant, as has been done in previous theoretical work, we explicitly incorporated the underlying predator-prey relation responsible for the input of quarry. The most profound differences between PPS and PPQRS system are found when the predator-prey system has limit cycles, resulting in a periodic rather than constant influx of quarry (the allochthonous resource) into the scavenger-resource interactions. This suggests that the way in which allochthonous resources are input into a predator-prey system can have a strong influence over the population dynamics. In order to understand the role of seasonality, we incorporated non-autonomous terms and showed that these terms can either stabilize or destabilize the dynamics, depending on the parameter regime. We also considered the influence of spatial motion (via diffusion) by constructing a continuum partial differential equation (PDE) model over space. We determine when such spatial dynamics essentially give the same information as the ordinary differential equation (ODE) system, versus other cases where there are strong spatial differences (such as spatial pattern formation) in the populations. In situations where increasing the carrying capacity in the ODE model drives the amplitude of the oscillations up, we found that a large carrying capacity in the PDE model results in a very small variation in average population size, showing that spatial diffusion is stabilizing for the PPQRS model. 相似文献
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Eric Renshaw 《Journal of theoretical biology》1982,94(2):355-365
A spatial predator-prey process is constructed in which predators and their prey may migrate between distinct neighbouring sites. We examine the consequence of introducing a sudden influx of predators into a previously predator-free environment, obtaining expressions for both the velocity and waveform of predator propagation. A general solution is then derived for predator-prey behaviour when a system previously in equilibrium is perturbed. All the techniques developed are potentially of general application. 相似文献
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讨论了具时滞与分段常数变量的捕食-食饵生态模型的稳定性及Neimark-Sacker分支;通过计算得到连续模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件;以食饵的内禀增长率为分支参数,运用分支理论和中心流形定理分析了Neimark-Sacker分支的存在性与稳定性条件;通过举例和数值模拟验证了理论的正确性。 相似文献
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Fred Brauer 《Theoretical population biology》1979,15(2):268-273
Under minimal assumptions, we establish boundedness of every solution of a predator-prey system with constant rate harvesting or stocking of either or both species. This leads to an extension of the classical Kolmogorov theorem on asymptotic behavior of solutions of predator-prey systems. 相似文献
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In this paper we derive some results to ensure the global stability of a predator-prey system. The results cover most of the models which have been proposed in the ecological literature for predator-prey systems. The first result is very geometric and it is very easy to check from the graph of prey and predator isoclines. The second one is purely algebraic, however, it covers the defects of the first one especially in dealing with Holling's type-3 functional response in some sense. We also discuss the global stability of Kolmogorov's model. Some examples are presented in the discussion section.Works partially supported by the National Science Council of the Republic of China 相似文献
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Predator-prey models with delay and prey harvesting 总被引:1,自引:0,他引:1
It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating
time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying
the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey
models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium
to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium
if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and
then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical
conclusions.
Received: 1 March 2000 / Revised version: 7 September 2000 /?Published online: 21 August 2001 相似文献
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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. 相似文献
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Teruhiko Marutani 《Reviews in Fish Biology and Fisheries》2008,18(2):133-141
Ecosystem-based fishery management (EBFM) is a new direction for fishery management, essentially reversing the order of management
priorities to start with the ecosystem rather than the target species. This concept of management is a direct extension of
the concept of a holistic approach incorporating interspecific interactions and physical environmental influences. However,
because of the limited understanding of the complexity of marine ecosystems, few fisheries are actually managed on a multispecies
basis. Even now, in order to specify a practical fishing policy we need a single-species model and utilize it by partially
taking account of the effects of other factors mentioned above on the target species biomass. In fact, it is contended that
in systems with moderate amounts of data, EBFM could be characterized by effective single-species management with the addition
of precautionary set-asides for unknown ecosystem components. Hence, it is still necessary to examine a single-species model
so as to clarify the extent of its applicability. The model investigated in this paper is what is called the dynamic pool
model, which was proposed by C.W. Clark in the mid-1970s as a dynamic optimization of the classic Beverton and Holt static
model for a fishery, in an attempt to make the process of growth and aging inherent in each of the creature resources reflect
directly into the economic process. This dynamic model has been applied to a wide variety of commercial fish species. However,
the applications have been largely confined to computer simulations using the discrete-time stand-by of the original Clark
continuous-time model. This situation is caused mainly by the complexity of the mathematical structure of the Clark model.
In this paper, we first specify the material related to the complexity. Subsequently, we provide a rigorous proof for the
long-standing conjecture due to Clark concerning the optimal path or harvesting schedule. In addition, two derivative cases
are examined: one is the case in which a year-class of fish leaves a given fishing sea area permanently before its natural
biomass peaks, the other is the case in which the escapement of a year-class is required to be more than a given minimum level. 相似文献
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建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移,且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度,可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明,在一定条件下,存在唯一的正平衡点,并且此平衡点全局稳定。进一步,捕食者的数量随着食饵庇护所数量增加而降低;在一定条件下,食饵的数量随着食饵庇护所数量增加先增加后降低,在足够强的庇护所强度下,两物种出现灭绝。对比以往研究,利用显式含有和隐含空间庇护所的数学模型所得结论不一致,这意味着在研究庇护所对捕食系统种群动态影响时,空间结构可能起着重要作用。 相似文献
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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. 相似文献
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We study a nonhierarchical tritrophic system, whose predator-prey interactions are described by the rock-paper-scissors game rules. In our stochastic simulations, individuals may move strategically towards the direction with more conspecifics to form clumps instead of moving aimlessly on the lattice. Considering that the conditioning to move gregariously depends on the organism's physical and cognitive abilities, we introduce a maximum distance an individual can perceive the environment and a minimum conditioning level to perform the gregarious movement. We investigate the pattern formation and compute the average size of the single-species spatial domains emerging from the grouping behaviour. The results reveal that the defence tactic reduces the predation risk significantly, being more profitable if individuals perceive further distances, thus creating bigger groups. Our outcomes show that the species with more conditioned organisms dominate the cyclic spatial game, controlling most of the territory. On the other hand, the species with fewer individuals ready to perform aggregation strategy gives its predator the chance to fill the more significant fraction of the grid. The spatial interactions assumed in our numerical experiments constitute a data set that may help biologists and data scientists understand how local interactions influence ecosystem dynamics. 相似文献
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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. 相似文献
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Spatial heterogeneity (patchiness) in certain predator-prey situations has been observed even though their environment appears homogeneous. As a model mechanism to explain this patchiness phenomenon we propose a predator-prey interaction system with diffusive effects. We show that when the diffusion of the prey is small compared with that of the predator the non-linearity which we call a hump effect in the prey interaction, is a key mechanism for the system to exhibit, asymptotically in time, stable heterogeneity in a bounded domain with zero flux boundary conditions. The model can reasonably be applied to certain terrestrial plant-herbivore systems. 相似文献
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Ecologists studying consumer-resource interactions in advection-dominated systems such as streams and rivers frequently seek to link the results of small-scale experiments with larger-scale patterns of distribution and abundance. Accomplishing this goal requires determining the characteristic scale, termed the response length, at which there is a shift from local dynamics dominated by advective dispersal to larger-scale dynamics dominated by births and deaths. Here, we model the dynamics of consumer-resource systems in a spatially variable, advective environment and show how consumer-resource interactions alter the response length relative to its single-species value. For one case involving a grazer that emigrates in response to high predator density, we quantify the changes using published data from small-scale experiments on aquatic invertebrates. Using Fourier analysis, we describe the responses of advection-dominated consumer-resource systems to spatially extended environmental variability in a way that involves explicit consideration of the response length. The patterns we derive for different consumer-resource systems exhibit important similarities in how component populations respond to spatial environmental variability affecting dispersal as opposed to demographic parameters. 相似文献