Behavioral choices based on patch selection: a model using aggregation methods.

The aim of this work is to study the influence of patch selection on the dynamics of a system describing the interactions between two populations, generically called 'population N' and 'population P'. Our model may be applied to prey-predator systems as well as to certain host-parasite or parasitoid systems. A situation in which population P affects the spatial distribution of population N is considered. We deal with a heterogeneous environment composed of two spatial patches: population P lives only in patch 1, while individuals belonging to population N migrate between patch 1 and patch 2, which may be a refuge. Therefore they are divided into two patch sub-populations and can migrate according to different migration laws. We make the assumption that the patch change is fast, whereas the growth and interaction processes are slower. We take advantage of the two time scales to perform aggregation methods in order to obtain a global model describing the time evolution of the total populations, at a slow time scale. At first, a migration law which is independent on population P density is considered. In this case the global model is equivalent to the local one, and under certain conditions, population P always gets extinct. Then, the same model, but in which individuals belonging to population N leave patch 1 proportionally to population P density, is studied. This particular behavioral choice leads to a dynamically richer global system, which favors stability and population coexistence. Finally, we study a third example corresponding to the addition of an aggregative behavior of population N on patch 1. This leads to a more complicated situation in which, according to initial conditions, the global system is described by two different aggregated models. Under certain conditions on parameters a stable limit cycle occurs, leading to periodic variations of the total population densities, as well as of the local densities on the spatial patches.

[1]  Anthony R. Ives,et al.  Antipredator Behavior and the Population Dynamics of Simple Predator-Prey Systems , 1987, The American Naturalist.

[2]  Pierre Auger,et al.  Complex ecological models with simple dynamics: From individuals to populations , 1994 .

[3]  Donald A. Dewsbury,et al.  Behavioral Ecology: Ecological Consequences of Adaptive Behavior. , 1986 .

[4]  B. Hart.  Behavioural defense against parasites: interaction with parasite invasiveness , 1994, Parasitology.

[5]  D. J. Hall,et al.  An Experimental Test of the Effects of Predation Risk on Habitat Use in Fish , 1983 .

[6]  H. Schwardt,et al.  Biological Studies of Horse Flies in New York , 1953 .

[7]  Pierre Auger,et al.  Parasitism and host patch selection: A model using aggregation methods , 1998 .

[8]  Craig Loehle,et al.  Social barriers to pathogen transmission in wild animal populations , 1995 .

[9]  Neil Fenichel.  Persistence and Smoothness of Invariant Manifolds for Flows , 1971 .

[10]  T. Caraco,et al.  Living in groups: is there an optimal group size? , 1984 .

[11]  C. Combes,et al.  Interactions Durables: Ecologie et Evolution du Parasitisme , 1997 .

[12]  Pierre Auger,et al.  Macroscopic Dynamic Effects of Migrations in Patchy Predator-prey Systems , 1997 .

[13]  J. McNair,et al.  The effects of refuges on predator-prey interactions: a reconsideration. , 1986, Theoretical population biology.

[14]  A. Ives,et al.  Continuous-Time Models of Host-Parasitoid Interactions , 1992, The American Naturalist.

[15]  M. Mooring,et al.  Animal Grouping for Protection From Parasites: Selfish Herd and Encounter-Dilution Effects , 1992 .

[16]  A Sih,et al.  Optimal behavior: can foragers balance two conflicting demands? , 1980, Science.

[17]  M. Basu,et al.  Neoglycosylated liposomes as efficient ligands for the evaluation of specific sugar receptors on macrophages in health and in experimental leishmaniasis , 1994, Parasitology.

[18]  F. Hoppensteadt.  Singular perturbations on the infinite interval , 1966 .

[19]  G. Gauze.  The struggle for existence, by G. F. Gause. , 1934 .

[20]  Pierre Auger,et al.  EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES , 1995 .

[21]  M. Mangel,et al.  Behavioral stabilization of host-parasite population dynamics , 1992 .

[22]  J. Krebs,et al.  Behavioural Ecology: An Evolutionary Approach , 1978 .

[23]  A. Sih.  Antipredator Responses and the Perception of Danger by Mosquito Larvae , 1986 .

[24]  M. Hassell,et al.  Environmental heterogeneity and the stability of host-parasitoid interactions , 1993 .

[25]  P Auger,et al.  Emergence of population growth models: fast migration and slow growth. , 1996, Journal of theoretical biology.

[26]  Robert Poulin,et al.  Risk of parasitism and microhabitat selection in juvenile sticklebacks , 1989 .

[27]  J. F. Guthrie,et al.  Schooling Habits of Injured and Parasitized Menhaden , 1974 .