Phylogeography by Diffusion on a Sphere

Techniques for reconstructing geographical history along a phylogeny can answer many interesting question about the geographical origins of species. Bayesian models based on the assumption that taxa move through a diffusion process have found many applications. However, these methods rely on diffusion processes on a plane, and do not take the spherical nature of our planet in account. This makes it hard to perform analysis that cover the whole world, or do not take in account the distortions caused by projections like the Mercator projection. In this paper, we introduce a Bayesian phylogeographical method based on diffusion on a sphere. When the area where taxa are sampled from is small, a sphere can be approximated by a plane and the model results in the same inferences as with models using diffusion on a plane. For taxa samples from the whole world, we obtain substantial differences. We present an efficient algorithm for performing inference in an Markov Chain Monte Carlo (MCMC) algorithm, and show applications to small and large samples areas. Availability: The method is implemented in the GEO SPHERE package in BEAST 2, which is open source licensed under LGPL.