Supporting Information The

coalescent model The coalescent is a stochastic model for the genealogical tree of a sample of n sequences. It has become a standard tool in population genetics, and it is frequently used for simulating genomic data (see e.g. [9, 7]). The coalescent model provides an approximation of the genealogy of a sample containing n genes, for a large class of models in populations genetics for which the population size is constant [3]. A coalescent event occurs when two lineages find a common ancestor. In a sample of n ≥ 3 sequences, the first coales-cence event corresponds to the first time when a pair of sequences finds a common ancestor. After the first coalescence event, the two sequences that coalesced are replaced by their common ancestor so that the initial sample of n sequences is represented by n − 1 ancestral sequences. The second coa-lescence event corresponds to the first time when a pair of sequences, chosen among the n − 1 ancestral sequences, coalesces. This process is repeated un-til a unique common ancestor is found. In the coalescent, time is measured backward and in units of N generations where N is the diploid population size. This rescaling of time means that one unit of time corresponds to N generations. The inter-coalescence times Yj, 2 ≤ j ≤ n, measure the amount of time during which the sample has j ancestors. These times form indepen-dent random variables distributed according to the exponential distribution of rate j(j − 1)/2, for 2 ≤ j ≤ n, and their joint distribution can then be computed as a product distribution. In varying population size models, the joint distribution of the Yj’s is no longer a product of exponential distributions. A description of the distri-bution of the inter-coalescence times, Yj, in a population whose size evolves deterministically, is given in [1]. For a large class of deterministic demo-graphic models, Griffiths and Tavare ́ [1] showed that, for 2 ≤ j ≤ n, we have P(Yj> t|Yn +...+ Yj+1 = s) = ex