Convergence of the mean and variance of size for a stochastic population model
We have proved that the dynamical system of variability for the stochastic body size in a population, given by \textit{R. B. Deriso} and \textit{A. M. Parma} [Can. J. Fish. Aquat. Sci. 45, 1054-1068 (1988)], possesses a unique and globally stable fixed point in the considered case. This result excludes the existence of limit cycles or chaos for the mean and variance asymptotic body size of individuals in the population under the action of considered evolutionary forces. Moreover, numerical studies have shown rapid convergence to equilibrium, usually in fewer than 20 iterations. On the other hand, the study presented in this article can be extended to a general case of correlated characters using mathematical techniques developed previously by us [Convergence de la variabilité de caractères génétiques quantitatifs. Ph.D. thesis, Dep. Math. Stat. Univ. Montreal (1994)].
scientific article; zbMATH DE number 955253
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