BOX 1
FROM:
Evolution of allelic dimorphism in malarial surface antigens
S W Roy, M U Ferreira and D L Hartl
BACK TO ARTICLEBox 1. The one-fourth rule
The probability that two individuals in a sample of n individuals do not have a common ancestor more recently than the time of the eth common ancestor (coalescent event) in the sample is  , so the probability that two individuals' last common ancestor is the last common ancestor of the entire sample (LCA) (ie, the probability that they do not have a common ancestor by the second-to-last coalescent event, e=n-2) is  . The expected time to coalescence of two individuals for a haploid species is N generations, and the expected time to the last common ancestor of the sample (T
LCA) is  , so  , where x is the expected average time to the common ancestor of two individuals whose last common ancestor postdates the last common ancestor of the sample. This equation is solved when  , or one-fourth of the expected T
LCA. Thus, if we divide a sample into two maximally diverged allelic classes, the average degree of divergence between alleles from the same class should be roughly one-fourth the average divergence between alleles from opposite classes. |
