Pitfalls to avoid in nonlinear perturbation analysis of structured population models

Abstract

Despite the ubiquity of nonlinear functional relationships in nature we tend to characterize mechanisms in science using more tractable linear functions. In demographic modeling, transfer function analysis is used to calculate the nonlinear response of population growth rate to a theoretical perturbation of one or more matrix elements. This elegant approach is not yet popular in ecology. Inconveniently, using transfer function without care can produce erroneous results without warning. We used a large matrix projection model database to explore the potential pitfalls to be avoided in using transfer function analysis. We asked a fundamental population control question, what matrix element perturbation would be needed to reach a minimum goal of replacement population growth? We then tracked instances in which transfer function yields erroneous output and explored these cases in detail to measure how frequently it occurs. We developed a phylogenetically-corrected mixed effects logistic regression model in a Bayesian framework to test the effect of species traits and the identity of matrix elements on the probability that transfer function yields errors. We found in 16% of cases the transfer function