The transition and emission probabilities of our model [6] depend explicitly on k. The intuition is that, as k gets larger, jumps between different copied haplotypes should become less likely and those haplotypes should be copied with higher fidelity; this is because a chromosome will coalesce faster into a larger genealogy, leaving less time for recombination and mutation events to occur [18]. The underlying theory assumes that the haplotypes in question were sampled randomly from a population, which is clearly not the case when we select k haplotypes in the manner described above. To account for the fact that these haplotypes will find common ancestors (going backwards in genealogical time) more quickly than would k haplotypes chosen at random, we replace k with the total number of available haplotypes when specifying the HMM parameters for a phasing update.
