Age dependent fecundity and the dynamics of a density-dependent population model

Abstract

The Ricker Stock-Recruitment (SR) relationship is one of the most common mathematical models used in fishery science. Without age-structure, this model is a first-order difference equation that shares with other and similar nonlinear models complicated behaviors, including chaotic ones. As many animal populations have demographic characteristics that 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 population dynamics due to a great sensitivity to life-history parameters. The goal of this study is to explore some of those behaviors. A discrete self-regenerating and age-structured model, based on the Ricker SR relationship, is applied to small pelagic fish's species. As any synthetic reproductive function is not defined, the classical Leslie matrix notation is not used. Consequently, the exploration of the dynamic behaviors of the model is performed by numerical simulations with associated 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 focus on the effects of increasing the degrees of fecundity with age, in particular when it results in the uniformity of the reproductive potential's distribution among spawner's age classes. Thus, each adult age class brings the same contribution—in term of eggs laid—to the reproductive process. Such variation in age-dispersion of the reproductive potential of fish seems to have a dramatic power of stabilization on the population in the sense that chaotic behavior disappears. More numerical simulations are needed to explore the demographic consequences of age-dispersion of the reproductive potential, as recent trends in ecology suggest that ecological stability may not be a necessary condition to characterize evolutionary stability.