Determining Best Practice for the Spatial Poisson Process in Species Distribution Modelling

Poisson processes have become a prominent tool in species distribution modelling when analysing citizen science data based on presence records. This study examines four distinct statistical approaches, each of which utilises a different approximation to fit a Poisson point process. These include two Poisson regressions with either uniform weights or the more elaborate Berman-Turner device, as well as two logistic regressions, namely the infinitely weighted logistic regression method and Baddeleys logistic regression developed in the context of spatial Gibbs processes. This last method has not been considered in depth in the context of Poisson point processes in the previous literature. A comprehensive comparison has been conducted on the performance of these four approaches using both simulated and actual presence data sets. When the number of dummy points is sufficiently large, all approaches converge, with the Berman-Turner device demonstrating the most consistent performance. A Poisson process model was developed to accurately predict the distribution of Arctotheca calendula, an invasive weed in Australia that does not appear to have been the subject of any species niche modelling analysis in the existing literature. Our findings are valuable for ecologists and other non-statistical experts who wish to implement the best practices for predicting species distribution using Poisson point processes.