CoalHMMs (32, 33, 57) exploit the Markov approximation to the sequential coalescent process (58). These models can be constructed to capture various demographic scenarios in the ancestry of a set of sampled chromosomes. We have constructed a new model to infer parameters relevant for chromosomes from an admixed population and one or two populations related to the donor populations of the admixture event. Denote the populations in the model A, B, and C, where C is descended from the admixed population and A and B are related to the two donor populations. Parameters of the model include divergence times between all pairs of populations and the admixture proportions for the admixed population.

Kinda admixture. We first consider the most probable graph with a single admixture event. As an example, we consider P. kindae as the admixed population, C. We have two choices for population A, P. cynocephalus and P. ursinus, and two choices for population B, P. hamadryas and P. papio. With these choices, since each of the populations considered for A and B has two samples, we could choose independent chromosomes to compare for replication of results. With these species, we can estimate the time parameters for specific evolutionary events: (i) the north-south clade split, (ii) the split between hamadryas/papio and the species that hybridized to become P. kindae, (iii) the cynocephalus/ursinus split, (iv) the split between ursinus and the other species that hybridized to become P. kindae, and (v) the time of the admixture that formed P. kindae. Not all of these time points can be estimated by all triplets of species, but all can be estimated from at least two sets of species triplets, giving us four independent estimates.

Simulation test of goodness of fit and debiasing estimates. To examine which parameters are likely to be biased, and by how much, we simulated data with parameters in a grid of time points around the estimated points and estimated the parameters from these simulated data. Figure S12 shows the results with the estimated time points and the admixture proportions together with simulated data, where the simulated values are shown as black points and the corresponding estimated parameters are shown as red error bars (these error bars are wider since we used smaller datasets for the simulated data for computational reasons).

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