A general population growth model with density dependence

Abstract

A model for the growth of a population with p+ q+ r age groups in which there is competition for limited resources is considered. The steady-state solution is obtained and its stability is discussed. The existence of a time-invariant structure in which the ratios of the populations of the various age groups do not change with time is established under very general conditions, and its relation with the steady-state solution is discussed. The conditions under which we can treat the population as homogeneous with a common birth rate, a common death rate and a common inhibiting constant are also discussed.