Searching and Learning in a Random Environment

Area concentrated search provides a means by which foragers may exploit heterogeneities in a resource following a simple rule of thumb which reacts to encounters with that resource by changing search speeds. A model with few parameters is presented. It permits an analysis of optimal searching rules in a random environment. We show that optimal search involves a set of conditional rules that reflect the “patchiness” of resource distribution. The optimal area concentrated search strategy is not only a matter of slowing down when encountering a resource, but may involve speeding up when encountering the resource in more uniform environments. The manner in which foragers accumulate information about a resource during searching is analysed as a trade-off between “identification” and “control” or exploration and exploitation. The value of a period of identification, i.e. a period of learning, is analysed in a fluctuating environment in which the state of the environment is samples from a given distribution following each new foraging bout. The value of learning during searching relates to stochasticity within a bout and variation between bouts. The value of information about the environment within a given foraging bout, and hence the likely value of learning is analysed by comparing optimal strategies with optimal generalist strategies. Information becomes increasingly valuable as resource distributions?!becomes more patchy. Foragers adopting conditional searching rules may manifest type three functional responses (sigmoidal functional response) through an apostatic (positive density dependent) effect. The significance of this response, and learning behaviour on population stability, is briefly discussed.