Sensitivity and elasticity of density-dependent population models

The sensitivity analysis of linear matrix population models is well-developed, but no comparable approach exists for the nonlinear models appropriate for density-dependent populations. This paper presents such an approach, using matrix differential calculus to obtain the derivatives of equilibria and cycles with respect to arbitrary demographic parameters. The method readily calculates the sensitivity and elasticity of the population vector or of weighted densities, ratios of age classes or stages, proportional structures or temporal means and variances calculated from the population vector. Examples are presented using data on flour beetles of the genus Tribolium. An attempt is made to extend the approach to the sensitivity of averages over strange attractors, but the resulting calculations fail to converge, apparently due to a positive Lyapunov exponent for the sensitivity equation.