Age-size structure in populations with quiescence

Abstract

An analysis is given of a mathematical model for the continuous age-size distribution of a population that has both normal (growing and reproducing) and quiescent individuals. Individuals can transit back and forth from one state to the other. The theory of positive operator semigroups is used to show that under general assumptions about individual behavior the age-size distribution of the population converges to a stable distribution. The features of the model are illustrated by several examples. The examples are designed to minimize technicalities, yet still reveal the interesting stability phenomena that occur when structure is combined with quiescence. For these examples the extinction or asynchronous exponential growth of the population is analyzed in terms of the parameters effecting transition between the normal and quiescent states. The continuous model is compared with an analogous discrete model.