Analysis of nonlinear matrix equations for fish population dynamics

Abstract

P.H. Leslie's matrix model, which predicts population size of individual age classes in discrete time intervals, is examined. Leslie's original constant matrix, as well as the more general nonconstant matrix, to which density-dependence (compensation) has been added, are discussed. The properties of the matrix itself and the properties of the modeled population are presented for each type of model. A population is modeled with the probability of survival of the 0/sup th/ age class, p/sub 0/, assumed to be density dependent. The stability of this population, i.e., ability to maintain steady-state, is predicted. It is shown that a population modeled with p/sub 0/ depending only on the population size of age class 0 will always be stable. When p/sub 0/ depends on the populations of older age classes it is possible for the population to be unstable, depending on the specific functional relationship.