Master equation approach to structured coalescent for two demes
Abstract
Given an evolutionary model, the n-coalescent problem consists of going backward in time to characterize the random variable "time to the most recent common ancestor" and the topology of the tree. For well mixed populations, the solution for one-step models are known and I recently showed that by using a master equation approach, the solution for general exchangeable models can also be easily obtained. Natural populations however are structured into demes with the additional effect of migration between them that introduces more complicated correlations. Here I show how the master equation approach can be adapted to treat these problems in a straightforward manner. In particular, I give the complete solution for two demes, with arbitrary initial population in each deme. I will also discuss the possibility for the extension of this work to more complicated systems.
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BibTeX
@misc{houchmandzadeh2026master,
title = {{Master equation approach to structured coalescent for two demes}},
author = {Bahram Houchmandzadeh},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05789400v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Master equation approach to structured coalescent for two demes
AU - Bahram Houchmandzadeh
PY - 2026
DA - 2026/10/09
PB - HAL
UR - https://hal.science/hal-05789400v1
AB - Given an evolutionary model, the n-coalescent problem consists of going backward in time to characterize the random variable "time to the most recent common ancestor" and the topology of the tree. For well mixed populations, the solution for one-step models are known and I recently showed that by using a master equation approach, the solution for general exchangeable models can also be easily obtained. Natural populations however are structured into demes with the additional effect of migration between them that introduces more complicated correlations. Here I show how the master equation approach can be adapted to treat these problems in a straightforward manner. In particular, I give the complete solution for two demes, with arbitrary initial population in each deme. I will also discuss the possibility for the extension of this work to more complicated systems.
ER -