# American Institute of Mathematical Sciences

2005, 2005(Special): 833-845. doi: 10.3934/proc.2005.2005.833

## Colored coalescent theory

 1 Mathematical Biociences Institute, The Ohio State University, Columbus, OH 43210, United States 2 Department of Mathematics, University of California, Riverside, Riverside, CA 92521, United States

Received  September 2004 Revised  April 2005 Published  September 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.
Citation: Jianjun Tian, Xiao-Song Lin. Colored coalescent theory. Conference Publications, 2005, 2005 (Special) : 833-845. doi: 10.3934/proc.2005.2005.833
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