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1.
Parasites are an integral part of virtually all food webs and species communities. Here we consider the invasion of a resident predator-prey system by an infectious disease with frequency-dependent transmission spreading within the predator population. We derive biologically plausible and insightful quantities (demographic and epizootiological reproduction numbers) that allow us to completely determine community composition. Successful disease invasion can have two contrary effects in driving its host population to extinction or in stabilizing predator-prey cycles. Our findings contradict predictions from previous models suggesting a destabilizing effect of parasites. We show that predator infection counteracts the paradox of enrichment. In turn, parasite removal from food webs can have catastrophic effects. We discuss the implications for biological control and resource management on more than one trophic level. 相似文献
2.
We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-prey model. We assume that the defense is of all-or-nothing type but that the probability for a prey individual to express the defended phenotype increases gradually with predator density. Compared to a defense that is independent of predation risk, an inducible defense facilitates persistence of the predator-prey system. In particular, inducibility reduces the minimal strength of the defense required for persistence. It also promotes stability by damping predator-prey cycles, but there are exceptions to this result: first, a strong inducible defense leads to the existence of multiple equilibria, and sometimes, to the destruction of stable equilibria. Second, a fast increase in the proportion of defended prey can create predator-prey cycles as the result of an over-compensating negative feedback. Non-equilibrium dynamics of the model are extremely complex. 相似文献
3.
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
4.
Deterministic extinction effect of parasites on host populations 总被引:2,自引:0,他引:2
Experimental studies have shown that parasites can reduce host density and even drive host population to extinction. Conventional
mathematical models for parasite-host interactions, while can address the host density reduction scenario, fail to explain
such deterministic extinction phenomena. In order to understand the parasite induced host extinction, Ebert et al. (2000)
formulated a plausible but ad hoc epidemiological microparasite model and its stochastic variation. The deterministic model,
resembles a simple SI type model, predicts the existence of a globally attractive positive steady state. Their simulation
of the stochastic model indicates that extinction of host is a likely outcome in some parameter regions. A careful examination
of their ad hoc model suggests an alternative and plausible model assumption. With this modification, we show that the revised
parasite-host model can exhibit the observed parasite induced host extinction. This finding strengthens and complements that
of Ebert et al. (2000), since all continuous models are likely break down when all population densities are small. This extinction
dynamics resembles that of ratio-dependent predator-prey models. We report here a complete global study of the revised parasite-host
model. Biological implications and limitations of our findings are also presented.
Received: 30 October 2001 / Revised version: 11 February 2002 / Published online: 17 October 2002
Work is partially supported by NSF grant DMS-0077790
Mathematics Subject Classification (2000): 34C25, 34C35, 92D25.
Keywords or phrases: Microparasite model – Ratio-dependent predator-prey model – Host extinction – Global stability – Biological control 相似文献
5.
A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically. 相似文献
6.
Pierre Auger 《Journal of theoretical biology》2009,258(3):344-351
We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical “aggregation method” in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a “disease-free” or to a “disease-endemic” state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the “disease-free” equilibrium (DFE). 相似文献
7.
In this paper, we analyze a laissez-faire predator-prey model and a Leslie-type predator-prey model with type I functional responses. We study the stability of the equilibrium where the predator and prey coexist by both performing a linearized stability analysis and by constructing a Lyapunov function. For the Leslie-type model, we use a generalized Jacobian to determine how eigenvalues jump at the corner of the functional response. We show, numerically, that our two models can both possess two limit cycles that surround a stable equilibrium and that these cycles arise through global cyclic-fold bifurcations. The Leslie-type model may also exhibit super-critical and discontinuous Hopf bifurcations. We then present and analyze a new functional response, built around the arctangent, that smoothes the sharp corner in a type I functional response. For this new functional response, both models undergo Hopf, cyclic-fold, and Bautin bifurcations. We use our analyses to characterize predator-prey systems that may exhibit bistability. 相似文献
8.
J P Laplante 《Journal of theoretical biology》1979,81(1):29-45
We present and study a specific example of emergence of an inhomogeneous steady state distribution in a non- Lotka—Volterra predator-prey model. With the aid of a linear and a non-linear bifurcation analysis, the dependence of this distribution on species mobilities as well as other important model parameters is discussed. It is seen that the behaviour of the resulting colonies of species seems to correctly mimic some of the features of real predator-prey systems. 相似文献
9.
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
10.
Mainul Haque Joydev Chattopadhyay 《生物数学学报》2007,22(1):13-24
对疾病仅在食饵种群传播的有比例依赖的捕食-被捕食系统的动力学进行了分析,给出了每个平衡点附近系统的性态,定义了决定疾病灭绝和成为地方病的阁值R_0.得出的结论是:在比例依赖的捕食-被捕食系统中,染病食饵种群可以充当一个生物控制量,以抑制种群的绝灭. 相似文献
11.
DIANE P. BARTON 《Austral ecology》1997,22(3):316-324
Abstract The impact of introducing animals into an established ecosystem can be directly observed through predator-prey and competition interactions. The impact of animals via more obscure relationships, such as the host-parasite relationship, are generally not considered. The cane toad Bufo marinus (Linnaeus) was introduced to Australia in 1935. Despite intensive research into many aspects of the biology of the toad, there has been no systematic survey of the parasite fauna of B. marinus in Australia. It is unknown exactly what parasites the toad may have introduced to Australia and also the range of parasites that may have adapted to the toad from native fauna since its introduction. The provisional conclusion from this review is that all the helminth parasites so far recorded from B. marmus in Australia have been acquired from local hosts. The interaction of toads and nativa fauna via their parasites remains unknown. 相似文献
12.
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
13.
Haque M 《Mathematical biosciences》2011,234(1):1-16
The present investigation accounts for the influence of intra-specific competition among predators in the original Beddington-DeAngelis predator-prey model. We offer a detailed mathematical analysis of the model to describe some of the significant results that may be expected to arise from the interplay of deterministic and stochastic biological phenomena and processes. In particular, stability (local and global) and bifurcation (Saddle-node, Transcritical, Hopf-Andronov, Bogdanov-Takens) analysis of this model are conducted. Corresponding results from previous well known predator-prey models are compared with the current findings. Nevertheless, we also allow this model in stochastic environment with the influences of both, uncorrelated “white” noise and correlated “coloured” noise. This showing that competition among the predator population is beneficial for a number of predator-prey models by keeping them stable around its positive interior equilibrium (i.e. when both populations co-exist), under environmental stochasticity. Comparisons of these findings with the results of some earlier related investigations allow the general conclusion that predator intra-species competition benefits the predator-prey system under both deterministic and stochastic environments. Finally, an extended discussion of the ecological implications of the analytical and numerical results concludes the paper. 相似文献
14.
Connectance and parasite diet breadth in flea-mammal webs 总被引:1,自引:0,他引:1
The number of links in webs of species interactions, which lies at the heart of the biodiversity-stability debate, has given rise to controversy during the last 20 yr. Studies exploring these web properties have mainly focused on symmetric webs where each species can potentially feed on any other species; asymmetric webs such as host-parasite webs, where one set of species feed on another set of species, have been overlooked. However, food webs are incomplete without parasites and the study of parasite-host sub-web properties deserves attention. Here, using a large database involving 33 regional interaction webs between mammals and their flea parasites, we found a negative relationship between species richness and host-parasite connectance. We suggest that some phylogenetic constraints on flea diet may explain our observed patterns because we found that parasite diet breadth, measured as host taxonomic diversity, was invariant along our host richness gradient. We found that the slope of the logarithmic relationship between the number of realized links and species richness is lower than slope values reported for food webs. We suggest that connectance may not respond to increasing species richness as rapidly in host-parasite webs as in predator-prey food webs due to stronger coevolutionary requirements. 相似文献
15.
16.
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
17.
Luděk Berec 《Bulletin of mathematical biology》2010,72(1):94-121
Whereas impacts of predator interference on predator-prey dynamics have received considerable attention, the “inverse” process—foraging
facilitation among predators—have not been explored yet. Here we show, via mathematical models, that impacts of foraging facilitation
on predator-prey dynamics depend on the way this process is modeled. In particular, foraging facilitation destabilizes predator-prey
dynamics when it affects the encounter rate between predators and prey. By contrast, it might have a stabilizing effect if
the predator handling time of prey is affected. Foraging facilitation is an Allee effect mechanism among predators and we
show that for many parameters, it gives rise to a demographic Allee effect or a critical predator density in need to be crossed
for predators to persist. We explore also the effects of predator interference, to make the picture “symmetric” and complete.
Predator interference is shown to stabilize predator-prey dynamics once its strength is not too high, and thus corroborates
results of others. On the other hand, there is a wide range of model parameters for which predator interference gives rise
to three co-occurring co-existence equilibria. Such a multi-equilibrial regime is rather robust as we observe it for all the
functional response types we explore. This is a previously unreported phenomenon which we show cannot occur for the Beddington–DeAngelis
functional response. An interesting topic for future research thus might be to seek for general conditions on predator functional
responses that would produce multiple co-existence equilibria in a predator-prey model. 相似文献
18.
具有稀疏效应的Predator-Prey模型的分支问题 总被引:4,自引:0,他引:4
讨论了具有稀疏效应的捕食-食饵模型的分支问题,并利用Hopf分支理论和分界线环分支理论,得到了有多个极限环的结果。 相似文献
19.
The bifurcations of a periodically forced predator-prey model (the chemostat model), with a prey feeding on a limiting nutrient,
are numerically detected with a continuation technique. Eight bifurcation diagrams are produced (one for each parameter in
the model) and shown to be topologically equivalent. These diagrams are also equivalent to those of the most commonly used
predator-prey model (the Rosenzweig-McArthur model). Thus, all basic modes of behavior of the two main predator-prey models
can be explained by means of a single bifurcation diagram. 相似文献
20.
We investigate the emergence of spatio-temporal patterns in ecological systems. In particular, we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predator-prey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 Turing-Takens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns, are observed. 相似文献