The Evolutionarily Stable Exploitation of a Renewing Resource

The evolutionary stable distribution of animals between two sources of food is considered. At one source (the “fixed” source), food is obtained at a fixed rate, regardless of the number of animals present and the time since the source was used. At the other source (the “renewing” source) the probability that an item of food is present depends on the time since the previous item was obtained. Animals may switch from the fixed source to the renewing source to see if an item is available and then return to the fixed source. This takes a total time τ. The evolutionarily stable distribution gives iu an ideal free distribution. This distribution depends on the number of animals as well as on the parameters of the two sources and the travel time τ. The rate on the renewing source is defined to be the probability of obtaining an item divided by τ. In contrast to most ideal free distributions, the rates on the two sources are not always equal, but they do tend to become equal as the number of animals becomes large.