Statistical Modeling of Distribution Patterns: A Markov Random Field Implementation and Its Application on Areas of...

A statistical framework to infer areas of endemism from geographic distributions is proposed. This novel method is based on hidden Markov random fields (HMRFs), a type of undirected graph model commonly used in computer vision. This framework assumes areas of endemism are the states of the hidden layer of the model, whereas taxon distributions are emitted values in the observed layer. Taxon distributions are associated to the observed layer through a clustering procedure based on the extent of overlap. Observations are emitted by the hidden layer according to a Gaussian distribution, whereas the joint distribution of the hidden layer follows a Potts model. State and parameter inference of the maximum a posteriori configuration is performed through a modified version of the expectation-maximization algorithm. The optimal number of areas of endemism in the data set is estimated through the pseudolikelihood information criterion, a model selection procedure that uses an approximation to likelihood. The performance of the new algorithm was assessed on simulated data, and compared with the most popular methods for delimitation of areas of endemism: biotic element analysis, parsimony analysis of endemism, and endemicity analysis. HMRFs efficiently recovered the true pattern across a wide range of uncertainty values. The performance was also examined on empirical data: South African weevils (Sciobius) and Central American ground beetles and funnel-web tarantulas (Carabidae and Dipluridae, respectively). HMRFs uncovered six areas of endemism from the weevil data set, whereas eight were estimated for the Central American arthropods (compared with 3-5 and 3-14 from the other methods, respectively).