AGE-DEPENDENT FECUNDITY AND THE DYNAMICS OF A DENSITY-DEPENDENT POPULATION-MODEL

The Ricker Stock-Recruitment (SR) relationship is one of the most comm on mathematical models used in fishery science. Without age-structure, this model is a first-order difference equation that shares with othe r and similar nonlinear models complicated behaviors, including chaoti c ones. As many animal populations have demographic characteristics th at differ with age, the importance of considering age-structure within population dynamics models may be critical. Introducing age-structure in the Ricker model considerably complicates the behavior of the popu lation dynamics due to a great sensitivity to life-history parameters. The goal of this study is to explore some of those behaviors. A discr ete self-regenerating and age-structured model, based on the Ricker SR relationship, is applied to small pelagic fish's species. As any synt hetic reproductive function is not defined, the classical Leslie matri x notation is not used. Consequently, the exploration of the dynamic b ehaviors of the model is performed by numerical simulations with assoc iated graphical tools (attractors and bifurcation diagrams). The main result of this study deals with the distribution among age classes of the ''reproductive potential per recruit.'' This notion includes three basic life-history parameters: the natural mortality rate, the vector of mean weight and the vector of relative degree of fecundity. We foc us on the effects of increasing the degrees of fecundity with age, in particular when it results in the uniformity of the reproductive poten tial's distribution among spawner's age classes. Thus, each adult age class brings the same contribution-in term of eggs laid-to the reprodu ctive process. Such variation in age-dispersion of the reproductive po tential of fish seems to have a dramatic power of stabilization on the population in the sense that chaotic behavior disappears. More numeri cal simulations are needed to explore the demographic consequences of age-dispersion of the reproductive potential, as recent trends in ecol ogy suggest that ecological stability may not be a necessary condition to characterize evolutionary stability.