Understanding the geographic distributions of species is a fundamental problem in ecology. Many different statistical methods for modelling species distributions exist, but the most popular method is currently the machine learning algorithm Maxent. Despite its popularity, Maxent lacks the diagnostic tools available to more mature statistical models. In this thesis, we introduce leverage, influence, and residual methods for Maxent. We do so by applying recent results demonstrating the equivalence of Maxent and Poisson point process models. These results allow us to take methods from linear model theory and spatial statistics and adapt them to fit the Maxent framework. The result is a set of diagnostic methods for the critical evaluation of Maxent models. We illustrate these methods by applying them to Maxent models of the distributions of two ant species of the genus Trachymyrmex.