THE IMPACT OF ENVIRONMENTAL VARIATION ON DEMOGRAPHIC CONVERGENCE OF LESLIE MATRIX POPULATION-MODELS - AN ASSESSMENT USING LYAPUNOV CHARACTERISTIC EXPONENTS

In a constant environment, the rate of convergence of a density-indepe ndent Leslie matrix model to stable age distribution is determined by the damping ratio (the ratio of the absolute magnitudes of the first a nd second eigenvalues of the projection matrix). In a stochastic envir onment, the difference between the first two Lyapunov exponents is kno wn to be analogous to the logarithm of the damping ratio, but there ha s been no systematic investigation of the consequences of enviromnenta l variation on convergence rates. In this study, the Lyapunov spec tru m has been calculated for a wide variety of density-independent projec tion matrices subject to random variations in vital rates. This allows the impact of these random variations on convergence rates to be asse ssed. For rapidly convergent life histories, stochastic variation lead s to a decrease in convergence rate. For life histories which are slow to converge, stochastic variation speeds up convergence. These effect s are, however, relatively minor, and the value of the damping ratio f or the mean matrix is a good predictor of the damping ratio in a stoch astic environment. Consequently, when only an approximate indication o f convergence rates is needed, the damping ratio for the mean projecti on matrix gives a very good guide. Detailed calculations of the Lyapun ov spectrum would only be necessary to make comparisons between simila r life histories or if very precise information on convergence rates w ere needed. (C) 1996 Academic Press, Inc.