Evolutionarily stable strategies for defensive switching

This paper concentrates on the study of ecological stability for guaranteeing evolutionarily stable strategies in a two-predator and one-prey model system. It is assumed that the prey has defensive switching property of predation-avoidance which can be characterized by two parameters: the relative alertness of the prey against a predator, u, and the intensity of defensive switching, n. Assuming that the system is encountered with another immigrant prey with altered defensive switching parameters one after another, the conditions of replacement of the former occupant prey by an immigrant are studied. It is shown that the system eventually attains the evolutionarily stable state such that no entry of an immigrant prey is possible. Unless some trade-off relation exists between u and n, the evolutionarily stable state is not unique, but it is given by a set of parameters {u, n} which form a curve designated "ESS line". Thus, it is seen that if a number of two-predator and one-prey systems are allowed to evolve independently, each system will reach a different state on the "ESS line". Finally, we discuss a strategy that leads to optimal (minimum) prey consumption by both predators in relation to the "ESS line".

[1]  J. Lawton,et al.  Enemy free space and the structure of ecological communities , 1984 .

[2]  Simon A. Levin,et al.  A More Functional Response to Predator-Prey Stability , 1977, The American Naturalist.

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

[4]  J. Endler.  A Predator’s View of Animal Color Patterns , 1978 .

[5]  A. H. Sadiyal,et al.  Coexistence of species in a defensive switching model. , 2003, Mathematical biosciences.

[6]  M Tansky,et al.  Switching effect in prey--predator system. , 1978, Journal of theoretical biology.

[7]  Thomas L. Vincent,et al.  The evolutionary response of systems to a changing environment , 1989 .

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

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

[10]  V. Křivan.  Ideal free distributions when resources undergo population dynamics. , 2003, Theoretical population biology.

[11]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[12]  D. H. Morse,et al.  Behavioral Mechanisms in Ecology , 1980 .

[13]  M. Hori,et al.  Frequency-Dependent Natural Selection in the Handedness of Scale-Eating Cichlid Fish , 1993, Science.

[14]  P. Abrams,et al.  The effect of adaptive anti-predator behavior on exploitative competition and mutualism between predators , 1993 .

[15]  M. Milinski,et al.  Influence of a predator on the optimal foraging behaviour of sticklebacks (Gasterosteus aculeatus L.) , 1978, Nature.

[16]  A. B. Roy,et al.  Global stability of prey-predator systems with predatory switching. , 1992, Bio Systems.

[17]  E. Brunswik.  Probability as a determiner of rat behavior. , 1939 .

[18]  W. Murdoch,et al.  Predation and Population Stability , 1975 .

[19]  D. Lendrem.  Predation risk and vigilance in the blue tit (Parus caeruleus) , 1983, Behavioral Ecology and Sociobiology.

[20]  A. B. Roy,et al.  On local(ly) ESS of a pair of prey-predator system with predatory switching. , 1998, Mathematical biosciences.

[21]  H. Matsuda.  Evolutionarily stable strategies for predator switching , 1985 .

[22]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[23]  B. Drossel,et al.  The influence of predator--prey population dynamics on the long-term evolution of food web structure. , 2000, Journal of theoretical biology.

[24]  W. Murdoch.  Switching in General Predators: Experiments on Predator Specificity and Stability of Prey Populations , 1969 .

[25]  Robert D. Holt,et al.  Optimal Foraging and the Form of the Predator Isocline , 1983, The American Naturalist.

[26]  M. Hori,et al.  Unstable Evolutionarily Stable Strategy and Oscillation: A Model of Lateral Asymmetry in Scale-Eating Cichlids , 1994, The American Naturalist.

[27]  C. Cosner,et al.  A comparison of foraging strategies in a patchy environment. , 1999, Mathematical biosciences.

[28]  M. Elgar,et al.  PREDATOR VIGILANCE AND GROUP SIZE IN MAMMALS AND BIRDS: A CRITICAL REVIEW OF THE EMPIRICAL EVIDENCE , 1989, Biological reviews of the Cambridge Philosophical Society.

[29]  E. Charnov,et al.  Ecological Implications of Resource Depression , 1976, The American Naturalist.

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

[31]  A. Sih.  STABILITY AND PREY BEHAVIOURAL RESPONSES TO PREDATOR DENSITY , 1979 .

[32]  P. Abrams.  Functional Responses of Optimal Foragers , 1982, The American Naturalist.