Stability and return times of Leslie matrices with density-dependent survival: applications to fish populations☆

Abstract A Leslie matrix population model is used to predict the stability and times of return to equilibrium of fish populations following perturbations. The model is compensatory, having density dependence in the young-of-the-year (y-o-y) survival term. We first present conditions under which a unique equilibrium point exists for a population. Then, through stability analysis, we derive conditions that the y-o-y survival function must satisfy for stability to be assured. It is demonstrated that the dominant eigenvalue of the linearized Leslie matrix can be used to calculate, to good approximation, the time of return to equilibrium of the population following a perturbation. The return times of five model fish populations are compared over a range of assumed strengths of the compensatory mechanism. The model of the Hudson River striped bass population, in which the peak egg contribution occurs in age class 7, has a slower return time than that of an Atlantic menhaden population, where the peak egg contribution is in age class 2.

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