Phylogenetic comparative methods correct for the shared evolutionary history among a set of non-independent organisms by modeling the sampled continuous trait as arising from a stochastic process along the branches of a phylogenetic tree. Beyond the Brownian motion, several processes have been proposed in the literature, either Gaussian, in which case efficient algorithms relying on the Kalman filter are available to compute the likelihood; or based on more general Lévy processes, that can model a realistic evolution with jumps, but that are computationally intensive. We propose to use a Cauchy process, for which we derive a recursive algorithm to compute the likelihood in a polynomial time. The Cauchy process is a pure jump process, that can be used to model viral geographical diffusion as well as ecological trait evolution on various time scales.

Joint work with Gilles Didier. Reference: https://doi.org/10.1093/sysbio/syad053