Colored coalescent theory
Jianjun Paul Tian, Xiao-Song Lin · Conference Publications · 2005
We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices may change only when two vertices coalesce. Explicit computations of the expectation and the cumulative distribution function of the coalescent time are carried out. For example, when $x=1/2$, for a sample of $n$ colored individuals, the expected time for the colored coalescent process to reach a black MRCA or a white MRCA, respectively, is $3-2/n$. On the other hand, the expected time for the colored coalescent process to reach a MRCA, either black or white, is $2-2/n$, which is the same as that for the standard Kingman coalescent process.