Dynamic models for bird population—A parameter-varying partial differential equation identification approach

Abstract

In order to study the global decline of biodiversity, accurate models of animal population dynamics are required. In this paper, this challenging problem of biodiversity decline analysis is tackled by modelling the dynamics of bird populations. More specifically, a new data-driven modelling of bird population dynamics is suggested which resorts to a parameter-varying partial differential equation (PDE) model, the Galerkin method and the proper orthogonal decomposition. The parameter-varying formulation allows us to introduce in models prior information such as temperatures or landscape patterns. Hence, such models can be used to study the impact on biodiversity of the global warming or the agricultural intensification, for instance. In order to deal with the specific conditions of ecological applications, a specific attention is paid to the initialization as well as the implementation of an iterative identification procedure based on 3D partial moments and a Levenberg–Marquardt algorithm. These tools are tested on the data-driven modelling of the population of European Stonechat Saxicola torquatus, a European common bird species, by using data from the national French Breeding Bird Survey and the CORINE Land Cover. The perspectives are to model specific community of birds in order to evaluate the effect of global changes in population trends and to develop tools to help decision makers take into account biodiversity goals into public policies.