A Hierarchical Bayesian Non-linear Spatio-temporal Model for the Spread of Invasive Species with Application to the Eurasian Collared-Dove

Abstract

Differential equation based advection-diffusion models have been used in atmospheric science to mimic complex processes such as weather and climate. Differential and partial-differential equations (PDE's) have become popular in biological and ecological fields as well. In many cases, these models are considered in a strictly deterministic framework even though many sources of uncertainty in the process, the model, and the measurements may exist. Many deterministic PDE models are well-equiped to represent the theoretical spread of organisms, but have no mechanism to account for the various sources of uncertainty related to the inadequacies of the model as well as the process itself and our knowledge of it. However, the use of a PDE within the framework of a hierarchical Bayesian model can provide a useful link between scientifically based deterministic models and statistical models that accurately portray variability (Wikle 2003). Specifically we model the spread of Eurasian Collared-Dove (ECD; Streptopelia decaocto) in the United States using a reaction-diffusion PDE (Fisher 1937, Skellam 1951) within a hierarchical model.