EFFECTS OF DELAY, TRUNCATIONS AND DENSITY DEPENDENCE IN REPRODUCTION SCHEDULES ON STABILITY OF NONLINEAR LESLIE MATRIX MODELS

Understanding effects of hypotheses about reproductive influences, rep roductive schedules and the model mechanisms that lead to a loss of st ability in a structured model population might provide information abo ut the dynamics of natural population. To demonstrate characteristics of a discrete time, nonlinear, age structured population model, the tr ansition from stability to instability is investigated. Questions abou t the stability, oscillations and delay processes within the model fra mework are posed. The relevant processes include delay of reproduction and truncation of lifetime, reproductive classes, and density depende nt effects. We find that the effects of delaying reproduction is not s tabilizing, but that the reproductive delay is a mechanism that acts t o simplify the system dynamics. Density dependence in the reproduction schedule tends to lead to oscillations of large ''period'' and toward s more unstable dynamics. The methods allow us to establish a conjectu re of Levin and Goodyear about the form of the stability in discrete L eslie matrix models.