Dynamics of populations with nonoverlapping generations, continuous mortality, and discrete reproductive periods

Abstract

Simple nonlinear difference equations have been used to describe the growth of populations with nonoverlapping generations; these equations assume mortality and recruitment to be discrete and instantaneous. In reality, mortality is more or less continuous and recruitment is more or less continuous over discrete intervals of time. This information was incorporated into the discrete time form of the logistic equation and the closed form solution was obtained. The population growth rate depends on recruitment, mortality, duration of the lifespan, and timing of the reproductive period. Population stability depends on the population growth rate, and therefore, stability also depends on the above factors. A stable population occurs with high mortality and a relatively short reproductive period. Under certain conditions a relatively small decrease in mortality can cause the dynamical behavior of a population to change drastically.