Effects of prey refuges on a predator-prey model with a class of functional responses: the role of refuges.

In this paper, the effects of refuges used by prey on a predator-prey interaction with a class of functional responses are studied by using the analytical approach. The refuges are considered as two types: a constant proportion of prey and a fixed number of prey using refuges. We will evaluate the effects with regard to the local stability of the interior equilibrium point, the values of the equilibrium density and the long-term dynamics of the interacting populations. The results show that the effects of refuges used by prey increase the equilibrium density of prey population while decrease that of predators. It is also proved that the effects of refuges can stabilize the interior equilibrium point of the considered model, and destabilize it under a very restricted set of conditions which is disagreement with previous results in this field.

[1]  M. Hassell.  The dynamics of arthropod predator-prey systems. , 1979, Monographs in population biology.

[2]  C. S. Holling.  Some Characteristics of Simple Types of Predation and Parasitism , 1959, The Canadian Entomologist.

[3]  Andrew Sih,et al.  Prey refuges and predator prey stability , 1987 .

[4]  Rodrigo Ramos-Jiliberto,et al.  Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability , 2003 .

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

[6]  R. May,et al.  STABILITY IN INSECT HOST-PARASITE MODELS , 1973 .

[7]  H. I. Freedman.  Deterministic mathematical models in population ecology , 1982 .

[8]  Maurice W. Sabelis,et al.  Spider mites: their biology, natural enemies and control: vol. 1A , 1985 .

[9]  John B. Collings,et al.  Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge , 1995 .

[10]  G. Ruxton,et al.  Short Term Refuge Use and Stability of Predator-Prey Models , 1995 .

[11]  Michael E. Hochberg,et al.  Refuge evolution and the population dynamics of coupled host—parasitoid associations , 1995, Evolutionary Ecology.

[12]  T. K. Kar,et al.  Stability analysis of a prey–predator model incorporating a prey refuge , 2005 .

[13]  Vlastimil Kr ivan,et al.  Effects of Optimal Antipredator Behavior of Prey on Predator Prey Dynamics : The Role of Refuges , 1998 .

[14]  Li Zhong,et al.  Stability analysis of a prey-predator model with holling type III response function incorporating a prey refuge , 2006, Appl. Math. Comput..

[15]  S. Jørgensen.  Models in Ecology , 1975 .

[16]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

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