A stochastic model of an isolated population with seasonal breeding and self-limitation

We consider a stochastic model of an isolated population in which individuals can have offspring only at fixed times, have a random positive lifetime, and can perish due to self-limitation. Breeding of individuals is described by the general Cramp–Mode–Jagers branching process, and self-limitation by the pure death process. We obtain conditions for the almost sure retrogressive evolution of the population considered. We use the Monte Carlo method to justify the conditions indicated in the nonlinear case.