A mathematical framework for optimal foraging of herbivores.

The aim of this paper is to study a model of optimal foraging of herbivores (with special reference to ungulates) assuming that food distribution is arbitrary. Usually the analysis of foraging of herbivores in the framework of optimal foraging theory is based on the assumption of a patchy food distribution. We relax this assumption and we construct more realistic models. The main constraint of our model is the total amount of food which the animal may eat and the currency is the total foraging time. We represent total foraging time as a variational expression depending on food eaten and the length of the path. We prove that there exists a threshold lambda for food acquisition. More explicitly, it exists a positive real number lambda such that, at any point x of the path, the animal either eats till the density of food is decreased to the value lambda or, if the density of food at x is less than lambda, there it does not eat. We discuss the results and emphasize some biologically important relationships among model parameters and variables. Finally,we try to give a sound biological interpretation of our results.