The Owl's Odyssey:
A Continuous Model for the Dispersal of Territorial Species

ROLAND H. LAMBERSON, JOSEPH E. CARROLL

Department of Mathematics
Humboldt State University
Arcata, CA 95521

Abstract:

In this paper, a composite model is developed that consists of a continuous model for dispersal set within a difference equation model for the life history of territorial species. Two dispersal models are considered: one that assumes that suitable habitat is uniformly or randomly distrbuted throughout the range of the population, and one that assumes that home ranges are concentarated in clusters of suitable habitat. These models explicitly consider the cost of dispersal by including ongoing rates of morality due to predation and starvation while individuals search for territory. The cluster model also differentiates between mortality within and outside of clusters. An analysis of the difference equation model demonstrates a threshold for density of suitable habitat below which the population must decrease to extinction, and above which the population tends monotonically to a stable positive equilibrium size. In addition, it is established that the equilibrium size of the population can be increased by consolidating the reserves of suitable habitat into larger clusters.


Society for Industrial Mathematics Vol 53 : pages 205-218( February 1993)
Received by the editors September 30, 1991; accepted for publication February 24 1992


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