© 1998 by Institute of Mathematics and its Applications
Modelling responses in vigilance rates to arrivals to and departures from a group of foragers
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Centre for Statistics and Stochastic Modelling, School of Mathematical Sciences, University of Sussex Falmer, Brighton BN1 9QH, UK
Division of Environmental and Evolutionary Biology, University of Glasgow Glasgow G12 8QQ, UK
Email: G.Ruxton{at}bio.gkLac.uk
Feeding birds must balance food gathering against predation risk. Group foraging is generally considered as a strategy for optimizing this trade-off. Previous modelling studies assumed that group sizes were static and that all group members are informed of an imminent predator attack if one of them detects it. These models implicitly assumed that birds could estimate group size, and adopt a fixed rate of anti-predator vigilance scanning. Recent empirical results suggest that group sizes are generally dynamic rather than static and the group members are often unaware of another's detection of imminent attack. It has also been observed that vigilance rates are not static but change after the arrival or departure of another. Here, we present a model which allows feeding-group size (and individuals' vigilance rates) to vary dynamically, and investigate the implications which this has for the optimum trade-off between foraging and avoiding predation. We find that newly arrived birds should generally be the most vigilant and that vigilance rates should decrease after the arrival of another into the feeding group but increase after a departure. Vigilance rates should increase as the cost of predator attack increases or if the reward rate from foraging decreases. Vigilance should increase if predator attacks are more common but decrease if predators require a longer time undetected to approach the feeding group. In common with many experimental studies, we observe that vigilance rates decrease as the average number of birds feeding together increases. Hence, the main conclusion of previous works (that foraging in groups is an effective strategy for balancing the conflicting pressures of foraging and avoiding predation) is obtained by our model, despite relaxing several previously used assumptions. Finally, we discuss some of the open questions related to group vigilance and how extensions to our modelling framework might be used to address these.
Keywords: co-operation; flocking; foraging; game theory; predation; strategy