dorsal/arxiv
View SchemaAncestral processes with selection: Branching and Moran models
| Authors | E. Baake, R. Bialowons |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0702002 |
| URL | https://arxiv.org/abs/q-bio/0702002 |
| Journal | Banach Center Publications 80 (2008), 33-52 |
Abstract
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyze the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced back into the past. The second approach is the Moran model with selection. Here, the population has constant size N. Individuals reproduce (at rates depending on their types), the offspring inherits the parent's type, and replaces a randomly chosen individual (to keep population size constant). Independently of the reproduction process, individuals can change type. As in the branching model, we consider the ancestral lines of single individuals chosen from the equilibrium population. We use analytical results of Fearnhead (2002) to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution in forward time.
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"abstract": "We consider two versions of stochastic population models with mutation and\nselection. The first approach relies on a multitype branching process; here,\nindividuals reproduce and change type (i.e., mutate) independently of each\nother, without restriction on population size. We analyze the equilibrium\nbehaviour of this model, both in the forward and in the backward direction of\ntime; the backward point of view emerges if the ancestry of individuals chosen\nrandomly from the present population is traced back into the past.\n The second approach is the Moran model with selection. Here, the population\nhas constant size N. Individuals reproduce (at rates depending on their types),\nthe offspring inherits the parent\u0027s type, and replaces a randomly chosen\nindividual (to keep population size constant). Independently of the\nreproduction process, individuals can change type. As in the branching model,\nwe consider the ancestral lines of single individuals chosen from the\nequilibrium population. We use analytical results of Fearnhead (2002) to\ndetermine the explicit properties, and parameter dependence, of the ancestral\ndistribution of types, and its relationship with the stationary distribution in\nforward time.",
"arxiv_id": "q-bio/0702002",
"authors": [
"E. Baake",
"R. Bialowons"
],
"categories": [
"q-bio.PE",
"math.PR"
],
"journal_ref": "Banach Center Publications 80 (2008), 33-52",
"title": "Ancestral processes with selection: Branching and Moran models",
"url": "https://arxiv.org/abs/q-bio/0702002"
},
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