N ov 2 00 5 The process of most recent common ancestors in an evolving coalescent
نویسندگان
چکیده
In a population of constant size, whose family sizes evolve as Wright-Fisher diffusions, all individuals alive at time t have a most recent common ancestor (MRCA) who lived at time A(t), say. The process (A(t)) has piecewise constant paths. At each jump time En, a new MRCA takes over, who lived at time Bn := A(En). We construct the random sequence (Bn, En) in terms of a look-down process and investigate its dynamics as well as that of (A(t)). In particular, we find the joint distribution of the waiting time from t to the next MRCA change and of the time when this next MRCA will have lived.
منابع مشابه
The process of most recent common ancestors in an evolving coalescent
Consider a haploid population which has evolved through an exchangeable reproduction dynamics , and in which all individuals alive at time t have a most recent common ancestor (MRCA) who lived at time At, say. As time goes on, not only the population but also its ge-nealogy evolves: some families will get lost from the population and eventually a new MRCA will be established. For a time-station...
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