Advances in presence-only methods in ecology

Abstract

Species distribution models are useful tools for relating the locations of species in a given region to environmental factors. This thesis will focus on the modelling of presence-only data, in which information is available about where species are reported present but not where species are reported absent. The aims of this thesis are to use theoretical tools from statistics to improve modern presence-only methods of analysis. This thesis establishes that MAXENT, a popular method in ecology based on maximum entropy, is equivalent to Poisson point process modelling, a widely-used statistical method for analysing spatial point patterns only recently applied to species distribution modelling. This equivalence result significantly unifies the presence-only analysis literature and has important ramifications for MAXENT and point process models. Despite its good predictive performance, MAXENT has shortcomings in interpretation and implementation that can now be overcome. In particular, MAXENT users can inherit from point process models some well-developed tools for addressing model adequacy and the ability to model point interactions. MAXENT's use of a LASSO penalty is known to improve predictive performance. However, the default penalty chosen by MAXENT software is ad hoc. Another focus of this thesis is implementing LASSO for point process models, which has rarely been done previously. This thesis provides an asymptotic result for applying a LASSO penalty to point process models such that consistent estimates of model parameters and predictions can be achieved. A new consistent criterion for choosing the LASSO penalty ( MSI") is consequently developed as an alternative to the default MAXENT penalty which has better properties. MSI is found to be competitive with traditional methods of choosing the LASSO penalty and generally superior to the MAXENT penalty in a broad comparison using real and simulated species data. This extension of point process models regularised with a LASSO penalty ( PPM-LASSO") therefore represents a significant advance of current species distribution modelling methods by combining the statistical foundations of point process models and the strong predictive performance of MAXENT via LASSO penalisation. I have developed the freely-available ppmlasso package for R so that PPM-LASSO models may now be fitted by users.