Let Xj be the hidden state of the HMM that denotes which haplotype h k+1 copies at site j (so that ). This state variable is initialized at the disease locus as follows (6)The value of , as with LS, is Watterson's point estimate (Watterson, 1975) (7)Simulation of the hidden state of the HMM then proceeds using the following transition rule (8)where zj is the physical distance between markers j and j+1 (assumed known); and , where is the effective (diploid) population size, and cj is the average rate of crossover per unit physical distance, per meiosis, between sites j and j+1 (so that cjzj is the genetic distance between sites j and j+1). This transition matrix captures the idea that, if sites j and j+1 are a small genetic distance apart (i.e. cjzj is small) then they are highly likely to copy the same chromosome (i.e. Xj +1 = Xj).
