Stage duration distributions in matrix population models

Abstract

Matrix population models are a standard tool for studying stage-structured populations, but they are not flexible in describing stage duration distributions. This studydescribes a method for modeling various such distributions in matrix models. Themethod uses a mixture of two negative binomial distributions (parametrized using amaximum likelihood method) to approximate a target (true) distribution. To examinethe performance of the method, populations consisting of two life stages (juvenileand adult) were considered. The juvenile duration distribution followed a gamma distribution, lognormal distribution, or zero-truncated (over-dispersed) Poisson distribution, each of which represents a target distribution to be approximated by a mixturedistribution. The true population growth rate based on a target distribution was obtained using an individual-based model, and the extent to which matrix models canapproximate the target dynamics was examined. The results show that the methodgenerally works well for the examined target distributions, but is prone to biasedpredictions under some conditions. In addition, the method works uniformly betterthan an existing method whose performance was also examined for comparison.Other details regarding parameter estimation and model development are alsodiscussed.