Statistical learning for species distribution models in ecological studies

We discuss species distribution models (SDM) for biodiversity studies in ecology. SDM plays an important role to estimate abundance of a species based on environmental variables that are closely related with the habitat of the species. The resultant habitat map indicates areas where the species is likely to live, hence it is essential for conservation planning and reserve selection. We especially focus on a Poisson point process and clarify relations with other statistical methods. Then we discuss a Poisson point process from a view point of information divergence, showing the Kullback-Leibler divergence of density functions reduces to the extended Kullback-Leibler divergence of intensity functions. This property enables us to extend the Poisson point process to that derived from other divergence such as $\beta$ and $\gamma$ divergences. Finally, we discuss integrated SDM and evaluate the estimating performance based on the Fisher information matrices.