2 Θ exp i ti − ti−1 −2

Coalescent models describe the distribution of ancestry in a population under some assumptions on the variation in the parameter Θ = 2Nν, with N the number of alleles in the population and ν the neutral mutation rate. The present document gives the likelihood function, and some computational details, for several models with Θ varying through time. These models are available in coalescentMCMC as R functions (see below). The general mathematical framework has been given by Griffiths & Tavaré [1]. If Θ is constant, the probability of observing the coalescent times t1,..., tn is: n∏ i