Predators with two modes of searching: A mathematical model*

Hunting predators often change their mode of searching immediately after finding a prey: they increase their rate of turning, increase the width of their search path, or slow down their movement. This is known as “area concentrated search”. From a functional point of view, such a habit seems to make sense only if the distribution of the prey is clustered, and certain other conditions are fulfilled. This idea is explored by means of a mathematical model. Predators are represented as points moving along a line along which prey points are distributed in a clumped, but otherwise random, fashion. A distinction is made between Knowing Predators, who know the boundaries between areas with high expected prey density, and areas with low expected prey density; and Ignorant Predators, who don't know these boundaries. Boundaries may be neglected when clusters are very large; for Knowing Predators and Ignorant Predators with “infinitely large clusters” exact mathematical results are derived; for Ignorant Predators and finite clusters, Monte Carlo simulations provided useful insight. We explored the values of the parameters for which a two-modes searching behaviour is better than just one, and the optimal degree of area concentrated search for various parameter values. Area concentrated search may have two effects: it may increase the chance of capturing prey that are encountered, and it may increase the average amount of time spent in high density areas. The present model is an addition to mathematical foraging theory because now the case is considered where there are no sharp boundaries between prey patches and areas devoid of prey, whereas in current optimal foraging models such boundaries are assumed.