The Ancestral Recombination Graph
Using coalescent theory, we sampled the posterior distribution of the ancestral recombination graph with the 1,008 haplotypes, including 121 sickle haplotypes, from the 504 continental Africans from the 1000 Genomes Project. Over a grid of 15 pairs of mutation and recombination rates, a mutation rate of 0.97×10−8 mutations per generation per site and a recombination rate of 1.5×10−8 recombinations per generation per site yielded the best fit to the data. Given these two rates, the trace of the posterior number of recombination events visually indicated convergence to a stationary distribution (Figure S1). More formally, Geweke’s diagnostic indicated that the sampled values came from a stationary distribution (p=0.063). Heidelberger and Welch’s diagnostic also indicated that the sampled values came from a stationary distribution (p=0.163) and further indicated that there was no need to discard initial iterations. We estimated the age of the sickle mutation as 259 (95% credible interval [123,395]) generations, or approximately 7,300 years (95% credible interval from 3,400 to 11,100 years).