The process of most recent common ancestors in an evolving coalescent
| dc.creator | Pfaffelhuber, P. | |
| dc.creator | Wakolbinger, A. | |
| dc.date | 2005-11-30 | |
| dc.date | 2006-04-17 | |
| dc.date.accessioned | 2026-07-07T06:51:56Z | |
| dc.date.available | 2026-07-07T06:51:56Z | |
| dc.description | 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 $A_t$, say. As time goes on, not only the population but also its genealogy evolves: some families will get lost from the population and eventually a new MRCA will be established. For a time-stationary situation and in the limit of infinite population size $N$ with time measured in $N$ generations, i.e. in the scaling of population genetics which leads to Fisher-Wright diffusions and Kingman's coalescent, we study the process $\mathcal A = (A_t)$ whose jumps form the point process of time pairs $(E,B)$ when new MRCAs are established and when they lived. By representing these pairs as the entrance and exit time of particles whose trajectories are embedded in the look-down graph of Donnelly and Kurtz (1999) we can show by exchangeability arguments that the times $E$ as well as the times $B$ from a Poisson process. Furthermore, the particle representation helps to compute various features of the MRCA process, such as the distribution of the coalescent at the instant when a new MRCA is established, and the distribution of the number of MRCAs to come that live in today's past. | |
| dc.identifier | https://arxiv.org/abs/math/0511743 | |
| dc.identifier | http://arxiv.org/abs/math/0511743 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105153 | |
| dc.subject | Probability | |
| dc.subject | Populations and Evolution | |
| dc.subject | 60K35 | |
| dc.title | The process of most recent common ancestors in an evolving coalescent | |
| dc.type | text |