Density Dependence and the Microtine Cycle I. A. Continuous Time Model with Delay due to Development

Abstract

A model incorporating time delayed density-dependent survival and reproductive rates is considered; in the model the lag corresponds to the time needed by a newly weaned female to develop into a mature female producing her own weanlings. It is demonstrated that such a model may explain the microtine cycle (both with respect to amplitude and period length), particularly if the time lag is large, if the density dependence mainly operates through reproduction (rather than through survival of adults), and if a (positive) density dependence operates in (ecological) survival. This prediction corresponds to observations of cyclic microtines suggesting that such species often are characterized by strongly density dependent rates, particularly with respect to reproduction. Some population dynamic consequences of dispersal through its effect on the ecological mortality (or disappearance) are discussed: It is suggested that high saturation (or non-adaptive) dispersal may stabilize population density; on the other hand, high pre-saturation (or adaptive) dispersal may destabilize the population density. If presaturation dispersal is more pronounced than saturation dispersal, then effective survival may increase with increased density.