Reproductive Schedules in a Density Dependent

Recruitment Model

Jacques A. L. Silva

Instituto de Matematica

Universidade Federal do Rio Grande do Sul

Av. Bento Gon?calves, 9500

Caixa Postal 15091

90501-900 Porto Alegre, RS Brazil

E-mail : [email protected]

Abstract

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 the 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 it was found the explicit and implicit reproductive delays have a destabilizing effect while spreading the reproductive effort over larger intervals has a stabilizing effect.

1. Introduction

Mechanisms governing the dynamics of natural populations are usually interlaced each one trying to drive the system to a certain state. Sometimes these regulatory mechanisms can interact in a conflicting way. The system dynamics in this case is driven by a resultant of a sum of forces. In order to understand the dynamic behavior of the population is necessary to uncouple these forces and study the consequences in the system dynamics caused by variations in the magnitude of these driving forces. A further analysis is then required to measure the relative strength of each these mechanisms.

In this paper a study on the stability of a density dependent age structured population is done from the reproductive schedule point of view, that is, the shape of the