Nonlinearity in eigenvalue-perturbation curves of simulated population projection matrices

Sensitivity and elasticity analyses of population projection matrices (PPMs) are established tools in the analysis of structured populations, but they make a linear approximation of the usually nonlinear relationship between population growth and matrix elements. The evaluation of alternative population management interventions may be particularly vulnerable to error if the degree of nonlinearity depends on the element of the PPM that is targeted. The second self-derivative and the self-sensitivity of elasticity can be used to estimate the degree and sign of nonlinearity in sensitivity and elasticity analyses, respectively. Using simulated matrices, we demonstrate that the magnitude and sign of the second self-derivative and the self-sensitivity of elasticity vary systematically, according to the element of the PPM subject to perturbation. Population management prescriptions based on sensitivity and elasticity analysis should always be backed up by nonlinear analyses.