Combining multiple data sources in species distribution models while accounting for spatial dependence and overfitting with combined penalised likelihood maximisation

O_LIThe increase in availability of species data sets means that approaches to species distribution modelling that incorporate multiple data sets are in greater demand. Recent methodological developments in this area have led to combined likelihood approaches, in which a log-likelihood comprised of the sum of the log-likelihood components of each data source is maximised. Often, these approaches make use of at least one presence-only data set and use the log-likelihood of an inhomogeneous Poisson point process model in the combined likelihood construction. While these advancements have been shown to improve predictive performance, they do not currently address challenges in presence-only modelling such as checking and correcting for violations of the independence assumption of a Poisson point process model or more general challenges in species distribution modelling such as overfitting.\nC_LIO_LIIn this paper, we present an extension of the combined likelihood frame-work which accommodates alternative presence-only likelihoods in the presence of spatial dependence as well as lasso-type penalties to account for potential overfitting. We compare the proposed combined penalised likelihood approach to the standard combined likelihood approach via simulation and apply the method to modelling the distribution of the Eurasian lynx in the Jura Mountains in eastern France.\nC_LIO_LIThe simulations show that the proposed combined penalised likelihood approach has better predictive performance than the standard approach when spatial dependence is present in the data. The lynx analysis shows that the predicted maps vary significantly between the model fitted with the proposed combined penalised approach accounting for spatial dependence and the model fitted with the standard combined likelihood.\nC_LIO_LIThis work highlights the benefits of careful consideration of the presence-only components of the combined likelihood formulation, and allows greater flexibility and ability to accommodate real datasets.\nC_LI