Probability of (un)equal marker alleles given the IBD pattern

ProbabilityaValuebappendix equation
P(yk = 0 | π = 1n)cEmbedded ImageA1
P(yk = 0 | π = [0 | 0]′)dEmbedded ImageA3
P(y1 = 0 | π = [ | 0]′)eEmbedded ImageA2
P(yk = 1 | π)1 − P(yk = 0 | π)
  • a Where possible, the position of the marker k is denoted by “|” within the vector of IBD and non-IBD segments π.

  • b N, effective population size; u, mutation rate. Note that 4Nu may be approximated by marker heterozygosity, Hk, if u is unknown.

  • c k is on an IBD segment of size c (note that k may be right at the edge of this segment).

  • d k is in between two non-IBD segments, each of size c.

  • e The marker is at the start of the chromosome and next to a non-IBD region of size c. Due to symmetry, the same Equation applies at the end of the chromosome.