Improving Parameter Estimation for Integral Projection Models in Fluctuating Environments

Abstract

The matrix projection model (MPM) is one of the mainstream approaches for population and environmental dynamics in biological and ecological sciences. MPM is very popular in modern biological sciences mainly due to its simplicity and the ease in which results can be explained. The main basis of MPM is a discrete staged transition matrix. MPM then projects the current population into the next census. However, MPM forces continuous trait, such as drought index, length, or mass into discrete staged classes. Easterling proposed the integral projection model (IPM) to avoid this artificial breakpoints of a continuous trait. The application of IPMs is rapidly growing in forest and wildlife ecology and it started attracting statisticians only recently. While IPM has advantages over the MPM, existing IPM estimation techniques are sensitive to outliers or mixing of population traits. We propose a robust fitting approach for IPMs and we analyze how the gain in robustness in the continuous size variable affects the estimation of population growth rate using a simulation study. We demonstrate the benefits of the proposed approach by analyzing the population dynamics of African elephants (Loxodonta africa) in Amboseli National Park, Kenya, where drought is thought to influence the population dynamics. Furthermore, existing IPM fails to generate a fecundity kernel in the situation of incomplete reproduction information. We propose a permutation based model to overcome this situation and demonstrate the applicability using a real life dataset.