Opportunities for improved distribution modelling practice via a strict maximum likelihood interpretation of MaxEnt

Maximum entropy (MaxEnt) modelling, as implemented in the Maxent software, has rapidly become one of the most popular methods for distribution modelling. Originally, MaxEnt was described as a machine-learning method. More recently, it has been explained from principles of Bayesian estimation. MaxEnt offers numerous options (variants of the method) and settings (tuning of parameters) to the users. A widespread practice of accepting the Maxent software's default options and settings has been established, most likely because of ecologists' lack of familiarity with machine-learning and Bayesian statistical concepts and the ease by which the default models are obtained in Maxent. However, these defaults have been shown, in many cases, to be suboptimal and exploration of alternatives has repeatedly been called for. In this paper, we derive MaxEnt from strict maximum likelihood principles, and point out parallels between MaxEnt and standard modelling tools like generalised linear models (GLM). Furthermore, we describe several new options opened by this new derivation of MaxEnt, which may improve MaxEnt practice. The most important of these is the option for selecting variables by subset selection methods instead of the (1)-regularisation method, which currently is the Maxent software default. Other new options include: incorporation of new transformations of explanatory variables and user control of the transformation process; improved variable contribution measures and options for variation partitioning; and improved output prediction formats. The new options are exemplified for a data set for the plant species Scorzonera humilis in SE Norway, which was analysed by the standard MaxEnt procedure in a previously published paper. We recommend that thorough comparisons between the proposed alternative options and default procedures and variants thereof be carried out.