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.

翻译：我们讨论了生态学中用于生物多样性研究的物种分布模型（SDM）。SDM在基于与物种栖息地密切相关的环境变量估计物种丰富度方面发挥着重要作用。由此生成的栖息地图指示了物种可能生活的区域，因此对保护规划和保护区选择至关重要。我们特别关注泊松点过程，并阐明其与其他统计方法的关系。然后，我们从信息散度的角度探讨泊松点过程，揭示了密度函数的Kullback-Leibler散度可简化为强度函数的扩展Kullback-Leibler散度。这一特性使我们能够将泊松点过程推广为源自其他散度（如$\beta$和$\gamma$散度）的形式。最后，我们讨论了集成SDM，并基于Fisher信息矩阵评估了其估计性能。