Density independent fluctuations of population size

Abstract

Under constant environmental conditions, a population whose size remains bounded usually has some kind of density dependent regulation. The population size may approach a constant equilibrium level, undergo regular oscillations in size, or exhibit some more complex form of fluctuation depending on the particular type of density dependence. However, there is no guarantee that all populations remain within finite bounds or that density dependent factors predominate. Environmental conditions vary in time, and the organism involved may be sufftciently sensitive to environmental changes so that the population size is determined largely by extrinsic factors. Such factors could.lead to periodic local extinctions with subsequent increases due to propagules from the outside. The purpose of this paper is to investigate various aspects of the dynamics of a population for which density independent factors are predominant. While our theory cannot directly determine the relative importance of density dependent and density independent factors in natural populations (see Lack (1966, Appendix) for a summary of the controversy), it does lead to testable predictions for a large class of density independent factors. We will analyze a class of population growth laws which have explicitly determined autocorrelated environmental fluctuations, and we will find the moments of the persistence times and population sizes. We will also identify those features of environmental perturbations that are most important for the dynamics of a population controlled by such density independent factors. An important feature of our model is the re-establishing of local populations after local extinction. In natural systems, the population could 37 0040.5809/81/010037-21SO2.OOjO