dorsal/arxiv
View SchemaAn asymptotic maximum principle for essentially linear evolution models
| Authors | E. Baake, M. Baake, A. Bovier, M. Klein |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0311020 |
| URL | https://arxiv.org/abs/q-bio/0311020 |
| DOI | 10.1007/s00285-004-0281-7 |
| Journal | J. Math. Biol. 50 (2005), 83--114 |
Abstract
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N to infinity (where N is the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible N by N matrices and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types.
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"abstract": "Recent work on mutation-selection models has revealed that, under specific\nassumptions on the fitness function and the mutation rates, asymptotic\nestimates for the leading eigenvalue of the mutation-reproduction matrix may be\nobtained through a low-dimensional maximum principle in the limit N to infinity\n(where N is the number of types). In order to extend this variational principle\nto a larger class of models, we consider here a family of reversible N by N\nmatrices and identify conditions under which the high-dimensional Rayleigh-Ritz\nvariational problem may be reduced to a low-dimensional one that yields the\nleading eigenvalue up to an error term of order 1/N. For a large class of\nmutation-selection models, this implies estimates for the mean fitness, as well\nas a concentration result for the ancestral distribution of types.",
"arxiv_id": "q-bio/0311020",
"authors": [
"E. Baake",
"M. Baake",
"A. Bovier",
"M. Klein"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1007/s00285-004-0281-7",
"journal_ref": "J. Math. Biol. 50 (2005), 83--114",
"title": "An asymptotic maximum principle for essentially linear evolution models",
"url": "https://arxiv.org/abs/q-bio/0311020"
},
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