APPENDIX A

Transition probabilities when the selected mutation separates the neutral loci

Configuration at end of selection phaseProbability given starting configurationConfiguration at start of neutral phase
Embedded ImageEmbedded ImageEmbedded Image
Embedded ImageEmbedded Image00O
Embedded ImageEmbedded ImageEmbedded Image0O
Embedded ImageEmbedded ImageEmbedded Image0O
Embedded ImageEmbedded ImageEmbedded Image0B
Embedded ImageEmbedded ImageEmbedded ImageEmbedded ImageO
Embedded ImageEmbedded ImageEmbedded ImageEmbedded ImageO
Embedded ImageEmbedded ImageEmbedded ImageEmbedded ImageB
Embedded ImageEmbedded ImageEmbedded ImageEmbedded ImageC
Embedded ImageEmbedded ImageEmbedded ImageEmbedded ImageC
Embedded ImageEmbedded ImageEmbedded ImageEmbedded ImageC
Embedded Image0Embedded Image0O
Embedded Image0Embedded ImageEmbedded ImageO
Embedded Image0Embedded ImageEmbedded ImageO
Embedded Image00Embedded ImageO
  • An example of the transition probabilities for the changes in configuration that occur during the selection is given in Figure 2. Here we give the transition probabilities for the different starting configurations. For notation, let Embedded Image represent the configuration where at locus x (to the left of the selected site) the two chromosomes i and j have been sampled and both carry the selected allele and at locus y the same two chromosomes have been sampled and again, both carry the selected allele. Using this notation, Embedded Image is, for example, the configuration where at locus x chromosome i carries the selected allele and chromosome j carries the wild type, while at locus y chromosome i has again been sampled (and therefore by necessity carries the selected allele), while a third chromosome, k, carries the wild-type allele. The transition probabilities during the selection phase for each of the three starting configurations are given below. Note that Embedded Image and that the labels i, j, k, and l are arbitrary identifiers for chromosomes drawn at random (with replacement) from the sample. For example, the configurations Embedded Image and Embedded Image would be equivalent.