A statistical-reaction–diffusion approach for analyzing expansion processes

Abstract

In this article, we propose a method for analyzing the spatial variations in the range expansion of the pine processionary moth (PPM), an invasive species in France. Based on binary measurements – the presence or absence of PPM nests – the proposed method allows us to infer the local effect of the environment on PPM population expansion. This effect is estimated at each position x using a parameter F(x) that corresponds to the local PPM fitness. The data type and the two stage PPM life cycle make estimating this parameter difficult. To overcome these difficulties we adopt a mechanistic-statistical approach that combines a statistical model for the observation process with a hierarchical,reaction–diffusion based mechanistic model for the expansion process. Bayesian inference of the parameter F(x) reveals that PPM fitness is spatially heterogeneous and highlights the existence of large regions associated with lower fitness. The factors underlying this lower fitness are yet to be determined.