Differential-Integral Equation Modeling the Dynamics of Populations with a Rank Structure

摘要

In order to illustrate the stabilizing potential of rank structures for the development of populations, a differential-integral equation (differentiation in time, integration over rank) modeling the dynamics of rank-structured (e.g., territorially or hierarchically organized) populations is proposed. After establishing existence and uniqueness of solutions, it is proved that, under biologically interpretable conditions, the population either dies out or tends towards a uniquely determined nonzero equilibrium state. Which of these alternatives actually occurs depends on the reproductive potential of the population and the permeability of the rank structure.