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IMA Journal of Mathematical Control and Information 2000 17(1):75-93; doi:10.1093/imamci/17.1.75
© 2000 by Institute of Mathematics and its Applications
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A spatial model of antipredator vigilance

C. J. PROCTOR{dagger} and M. BROOM{dagger}

Centre for Statistics and Stochastic Modelling, School of Mathematical Sciences, University of Sussex Falmer BN1 9QH UK

{dagger}The authors are also members of the Centre for the Study of Evolution at the University of Sussex (Email: C.J.Proctor{at}sussex.ac.uk and M.Broom{at}sussex.ac.uk)

Many species of animals have to perform two contradictozy tasks: feeding, and avoiding becoming food for others. A large number of theoretical and empirical studies have investigated the trade-off between feeding and antipredator vigilance, especially in birds. An important factor which has been neglected in these studies is that of the area occupied by the flock. If individuals feed close together, competition increases and feeding rates decrease. However, if individuals space themselves widely, then vigilance efficiency goes down and there is an increased predation risk. We develop a vigilance model which allows birds to control the area the flock occupies as well as their vigilance rate. The optimal strategy is found for the birds under a variety of environmental conditions. In particular the effect of each environmental parameter on this optimum is considered in turn. How the model can be adapted for different bird species is also investigated.

Keywords: foraging; predation; spatial model; strategy; vigilance.


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