Reproductive schedules in a density-dependent recruitment model

Understanding the mechanisms that regulate stability and oscillatory behavior requires isolated studies of each of the mechanisms so that their effects can be recognized and measured when they are coupled in a system. The role of the shape of the reproductive schedule, including its time lag, in determining stability properties in an age-structured density-dependent recruitment continuous model is investigated. The results are independent of the strength of the density dependence. Under the assumption of rather simple reproductive schedules, explicit and implicit reproductive delays were found to have a destabilizing effect, whereas spreading the reproductive effort over larger intervals has a stabilizing effect. Moreover, the stability is determined solely by the interplay of the reproductive effort and by the ratio between the standard deviation of the maternity distribution and the mean age of reproduction. This ratio has a stabilizing effect.