Stage duration distributions in matrix population models

Authored by Toshinori Okuyama

Date Published: 2018

DOI: 10.1002/ece3.4279

Sponsors: Ministry of Science and Technology of Taiwan

Platforms: R

Model Documentation: Other Narrative Flow charts Mathematical description

Model Code URLs: https://www-ncbi-nlm-nih-gov.ezproxy1.lib.asu.edu/pmc/articles/PMC6144974/#ece34279-sup-0001

Abstract

Matrix population models are a standard tool for studying stage-structured populations, but they are not flexible in describing stage duration distributions. This study describes a method for modeling various such distributions in matrix models. The method uses a mixture of two negative binomial distributions (parametrized using a maximum likelihood method) to approximate a target (true) distribution. To examine the performance of the method, populations consisting of two life stages (juvenile and 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 mixture distribution. The true population growth rate based on a target distribution was obtained using an individual-based model, and the extent to which matrix models can approximate the target dynamics was examined. The results show that the method generally works well for the examined target distributions, but is prone to biased predictions under some conditions. In addition, the method works uniformly better than an existing method whose performance was also examined for comparison. Other details regarding parameter estimation and model development are also discussed.

Tags

Stage-structured models time Costs Size Reproduction Individual variation Maximum likelihood Mixture distributions Stage duration