An asymptotic maximum principle for essentially linear evolution models

Baake E, Baake M, Bovier A, Klein M (2005)
JOURNAL OF MATHEMATICAL BIOLOGY 50(1): 83-114.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
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 --> infinity (where N, or N-d with d greater than or equal to 1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N-d 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.
Stichworte
ancestral distribution; models; mutation-selection; lumping; asymptotics of leading eigenvalue; reversibility
Erscheinungsjahr
2005
Zeitschriftentitel
JOURNAL OF MATHEMATICAL BIOLOGY
Band
50
Ausgabe
1
Seite(n)
83-114
ISSN
0303-6812
eISSN
1432-1416
Page URI
https://pub.uni-bielefeld.de/record/1604953

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Baake E, Baake M, Bovier A, Klein M. An asymptotic maximum principle for essentially linear evolution models. JOURNAL OF MATHEMATICAL BIOLOGY. 2005;50(1):83-114.
Baake, E., Baake, M., Bovier, A., & Klein, M. (2005). An asymptotic maximum principle for essentially linear evolution models. JOURNAL OF MATHEMATICAL BIOLOGY, 50(1), 83-114. doi:10.1007/s00285-004-0281-7
Baake, E., Baake, M., Bovier, A., and Klein, M. (2005). An asymptotic maximum principle for essentially linear evolution models. JOURNAL OF MATHEMATICAL BIOLOGY 50, 83-114.
Baake, E., et al., 2005. An asymptotic maximum principle for essentially linear evolution models. JOURNAL OF MATHEMATICAL BIOLOGY, 50(1), p 83-114.
E. Baake, et al., “An asymptotic maximum principle for essentially linear evolution models”, JOURNAL OF MATHEMATICAL BIOLOGY, vol. 50, 2005, pp. 83-114.
Baake, E., Baake, M., Bovier, A., Klein, M.: An asymptotic maximum principle for essentially linear evolution models. JOURNAL OF MATHEMATICAL BIOLOGY. 50, 83-114 (2005).
Baake, Ellen, Baake, Michael, Bovier, Anton, and Klein, Markus. “An asymptotic maximum principle for essentially linear evolution models”. JOURNAL OF MATHEMATICAL BIOLOGY 50.1 (2005): 83-114.

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PMID: 15322822
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