This proposal seeks support for the principal investigator to learn mathematical techniques and collaborate with mathematicians at the University of British Columbia. Its scientific goal is to determine how feeding behaviors which change adaptively with time affect the population dynamics of species interacting in a food web. Previous work by the P.I. have shown that, when individuals of a species adjust their foraging behavior in relation to food availability and the risk of predation, interactions between species are changed greatly. This situation produces indirect affects between species that have no direct feeding relationship, and can completely reverse the effects of predator-prey interactions. These previous models have assumed that time does not affect the optimal feeding behavior directly. Time does not have a role in almost every natural system to which these results apply. It is therefore essential to extend the food web results with models with time dependent foraging strategies. Behavioral ecologists, including two mathematicians at the University of British Columbia have done considerable work determining the nature of time-dependent strategies when there are discrete alternative feeding behaviors. The P. I. will collaborate in extending these results to situations in which foraging is defined by a continuous variable, such a percent of time spent feeding. The continuous strategies will then be incorporated into food-web models to determine the applicability of conclusions from previous time- dependent models.
