Parasitism and host patch selection: A model using aggregation methods (original) (raw)

Host Patch Selection Induced by Parasitism: Basic Reproduction Ratio R0 and Optimal Virulence

Theoretical Population Biology, 2002

The effects of parasites on the behavior of their hosts are well documented. For example, parasites may affect the habitat selection of the host individual. We used variables aggregation methods to investigate the way in which parasites affect the spatial pattern of susceptible hosts. We developed a simple epidemiological model, taking into account both the reproduction processes of hosts (density-dependent birth and death) and infection, considered separately on two different patches, and the migration of susceptible hosts between these two patches. We used the complete model of three equations to generate an aggregated model describing the dynamics of the combined susceptible and infected host populations. We obtained the basic reproduction ratio (R 0 ) from the aggregated model, and then studied the effect of the migratory behavior of susceptible hosts on the ability of the parasite to invade the system. We also used the basic reproduction ratio to investigate the evolution of parasite virulence in relation to the migration decisions of susceptible hosts. We found that host investment in avoidance of the infected patch leads to an increase in optimal virulence if host investment is costly. & 2002 Elsevier Science (USA)

Dynamic behavior of a parasite–host model with general incidence

Journal of Mathematical Analysis and Applications, 2007

In this paper, we consider the global dynamics of a microparasite model with more general incidences. For the model with the bilinear incidence, Ebert et al. [D. Ebert, M. Lipsitch, K.L. Mangin, The effect of parasites on host population density and extinction: Experimental epidemiology with Daphnia and six microparasites, American Naturalist 156 (2000) 459-477] observed that parasites can reduce host density, but the extinction of both host population and parasite population occurs only under stochastic perturbations. Hwang and Kuang [T.W. Hwang, Y. Kuang, Deterministic extinction effect of parasites on host populations, J. Math. Biol. 46 -30] studied the model with the standard incidence and found that the host population may be extinct in the absence of random disturbance. We consider more general incidences that characterize transitions from the bilinear incidence to the standard incidence to simulate behavior changes of populations from random mobility in a fixed area to the mobility with a fixed population density. Using the techniques of Xiao and Ruan [D. Xiao, S. Ruan, Global dynamics of a ratio-dependent predator-prey system, J. Math. Biol. 43 (2001) 268-290], it is shown that parasites can drive the host to extinction only by the standard incidence. The complete classifications of dynamical behaviors of the model are obtained by a qualitative analysis.

Density Dependence in Host-Parasitoid Models

The Journal of Animal Ecology, 1981

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Spatial synchrony in host–parasitoid models using aggregation of variables

Mathematical Biosciences, 2006

We consider a host-parasitoid system with individuals moving on a square grid of patches. We study the effects of increasing movement frequency of hosts and parasitoids on the spatial dynamics of the system. We show that there exists a threshold value of movement frequency above which spatial synchrony occurs and the dynamics of the system can be described by an aggregated model governing the total population densities on the grid. Numerical simulations show that this threshold value is usually small. This allows using the aggregated model to make valid predictions about global host-parasitoid spatial dynamics.

The role of heterogeneity on the spatiotemporal dynamics of host–parasite metapopulation

Ecological Modelling, 2004

Subpopulations of organisms in different habitat patches may differ from each other in biotic (e.g., inherent growth rate and interaction strength) and abiotic (e.g., climatic and landscape pattern) components. Such heterogeneity can influence the mode and extent of dispersal of individuals among these subpopulations, which, in turn, may regulate their spatiotemporal dynamics. We have modelled a homogeneous metapopulation of the interacting host and parasite system, with closed boundary and dispersal limited to nearest neighbours, using the spatially explicit coupled map lattice approach. We have studied the role of heterogeneity in terms of landscape fragmentation and demographic heterogeneity on the spatiotemporal dynamics. The homogeneous metapopulation shows spatiotemporally synchronous dynamics in the long-term, which is independent of the exact forms of the dispersal function considered commonly. The primary role of both types of heterogeneity is to resist evolution of spatiotemporal synchrony in the lattice, and the dynamics in the metapopulation remains asynchronous for a very long time. Spatiotemporal synchrony in species population may be detrimental to persistence and is a potential problem for conservation biologists. Thus, evolution and maintenance of ecological and demographic diversity in nature seem to aid in species persistence at a metapopulation level.

Host‐parasite population dynamics under combined frequency‐and density‐dependent transmission

2007

Many host-parasite models assume that transmission increases linearly with host population density ('densitydependent transmission'), but various alternative transmission functions have been proposed in an effort to capture the complexity of real biological systems. The most common alternative (usually applied to sexually transmitted parasites) assumes instead that the rate at which hosts contact one another is independent of population density, leading to 'frequency-dependent'transmission.

Behavioral stabilization of host-parasite population dynamics

Theoretical Population Biology, 1992

We demonstrate that individual behavior can stabilize classical (Nicholson-Bailey) host-parasite population dynamics. Our model assumes that hosts can be divided into at least two phenotypes and that parasites either do not attack one of the phenotypes or attack them facultatively. The former case corresponds to a behavioral refuge and it is known that other kinds of refuges lead to stability of population dynamics. Behavioral refuges can stabilize the population dynamics in the same way that spatial refuges do. When parasites attack hosts facultatively within the year, strange attractors may arise in the year-to-year population dynamics, in response to the nonlinear nature of the facultative response to the distribution of host densities. 0 1992 Academic Press. Inc.