Territorial Dynamics: Persistence in Territorial Species

Abstract

The widely studied and very controversial northern spotted owl, along with many other threatened and endangered species, exhibits territorial behavior. That is, adult pairs claim and defend a home range encompassing sufficient resources and of sufficient size to allow the pair to survive and reproduce successfully. Readers may be familiar with population models such as the logistic growth model, the Gompertz model, the Ricker model, and the Beverton-Holt model. These all capture the basic concept of limited growth (carrying capacity); however, they fail to exhibit some fundamental characteristics of the dynamics of territorial species. In particular, they do not exhibit a threshold in the density of suitable habitat below which the species is destined for extinction even if some suitable habitat is still available. In this paper, we develop a model first proposed by Lamberson and Carroll [1] for the dynamics of a territorial animal or bird population. It consists of a continu ous model for dispersal which distinguishes between adults?individuals who hold territories?and juveniles?those (nonterritorial) individuals that have not yet secured a home range. Here we think of birth not as the time of physical birth, but the time at which juveniles leave their natal territory and begin the search for their own home range. The model explicitly considers the cost of dispersal by including an ongoing rate of mortality due to pr?dation and starvation while animals search for a territory. We establish that there is a threshold for density of suitable habitat, below which the population must decrease to extinction and above which the population tends to a stable positive equilibrium size. Within populations of territorial animals we frequently find individuals that have not had the good fortune to secure a home range. These individuals, sometimes called floaters, usually occupy habitat of marginal quality and not suitable for attracting a mate. Usually, they eke out a secretive existence on the fringes of territories already claimed by other individuals. The dynamics of this floater population is important in understanding the overall behavior of the species, especially if the species is threat ened or endangered. In our model, the floaters are considered part of the population of juveniles since they have not yet secured a suitable territory. In this paper, we use a simple system of differential equations to describe the dy namics of a territorial species. The behavior of the system will be studied under both equilibrium and nonequilibrium conditions. For equilibrium conditions, we will es tablish: the fixed points, their stability, and the critical threshold in habitat density for persistence of the population.