Territoriality in Variable Environments: A Simple Model

Abstract

A territory owner is likely to find itself in a variable (stochastic) environment rather than a static (deterministic) environment. Current models of optimal territoriality, however, do not directly address this fact. The model that I develop in this paper, which treats prey density and intruder pressure as random variables rather than constants, indicates that some territorial strategies suggested by current models may do poorly in terms of the probability of starvation. The deterministic energy maximizer strategy, however, may often lead to a rough approximation of that territory size which minimizes the probability of starvation. Qualitative predictions derived from the stochastic approach and its current, deterministic analogues, such as an inverse relationship between prey density and territory size, are often in agreement. The prediction that a nonbreeding territory owner will spend much of its time inactive and defend excess, uneaten food is unique to the stochastic approach, and it appears to be supported by much of the evidence available in the current literature.