dorsal/arxiv
View SchemaMutation, selection, and ancestry in branching models: a variational approach
| Authors | Ellen Baake, Hans-Otto Georgii |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0611018 |
| URL | https://arxiv.org/abs/q-bio/0611018 |
| DOI | 10.1007/s00285-006-0039-5 |
| Journal | J. Math. Biol. 54 (2007),257-303 |
Abstract
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.
{
"annotation_id": "2adb752a-6fb9-432c-ab1c-f64d1e772432",
"date_created": "2026-03-02T18:01:35.379000Z",
"date_modified": "2026-03-02T18:01:35.379000Z",
"file_hash": "da8cf588aac9f4c0840dc1fe2544bf8fbc5c46ebfd0f4ba73bb6505f8530dddf",
"private": false,
"record": {
"abstract": "We consider the evolution of populations under the joint action of mutation\nand differential reproduction, or selection. The population is modelled as a\nfinite-type Markov branching process in continuous time, and the associated\ngenealogical tree is viewed both in the forward and the backward direction of\ntime. The stationary type distribution of the reversed process, the so-called\nancestral distribution, turns out as a key for the study of mutation-selection\nbalance. This balance can be expressed in the form of a variational principle\nthat quantifies the respective roles of reproduction and mutation for any\npossible type distribution. It shows that the mean growth rate of the\npopulation results from a competition for a maximal long-term growth rate, as\ngiven by the difference between the current mean reproduction rate, and an\nasymptotic decay rate related to the mutation process; this tradeoff is won by\nthe ancestral distribution.\n Our main application is the quasispecies model of sequence evolution with\nmutation coupled to reproduction but independent across sites, and a fitness\nfunction that is invariant under permutation of sites. Here, the variational\nprinciple is worked out in detail and yields a simple, explicit result.",
"arxiv_id": "q-bio/0611018",
"authors": [
"Ellen Baake",
"Hans-Otto Georgii"
],
"categories": [
"q-bio.PE",
"math.PR"
],
"doi": "10.1007/s00285-006-0039-5",
"journal_ref": "J. Math. Biol. 54 (2007),257-303",
"title": "Mutation, selection, and ancestry in branching models: a variational approach",
"url": "https://arxiv.org/abs/q-bio/0611018"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "2d353271-9e7c-496c-bf22-6a3fb881f72b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}