C. Lepage et P. Cury, AGE-DEPENDENT FECUNDITY AND THE DYNAMICS OF A DENSITY-DEPENDENT POPULATION-MODEL, Mathematical and computer modelling, 21(6), 1995, pp. 13-26
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.