Parameter-varying partial differential equation to model the global change impacts on wildlife populations

Accurate models of wildlife population dynamics are needed to assess the causes of global biodiversity decline. In this paper, new parameter-varying PDE models are proposed with an original methodology for parametric estimation from ecological data. The model structure makes it possible to introduce the environmental heterogeneity which can characterize global changes. Particular attention was paid to the implementation of the identification procedure: true parametric sensitivity functions in the optimization algorithm, a Galerkin method with a proper orthogonal decomposition for the PDE solution and a pre-estimate to initialize the iterative procedure. The tools are validated on simulation data and then applied to a real application modelling the impact of climate change and agricultural intensification on the population of a passerine bird.