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.

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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 --> 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.
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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.
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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47 References

Data provided by Europe PubMed Central.


Hermisson, Theor. Pop. Biol. 62(), 2002

Hermisson, J. Stat. Phys. 102(), 2001
The selection mutation equation.
Hofbauer J., J Math Biol 23(1), 1985
PMID: 4078498

Jagers, Stoch. Proc. Appl. 32(), 1989

Jagers, J. Appl. Prob. 29(), 1992

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0

AUTHOR UNKNOWN, 0
Deleterious mutations and the evolution of sexual reproduction.
Kondrashov AS., Nature 336(6198), 1988
PMID: 3057385

AUTHOR UNKNOWN, 0

Leuthäusser, J. Stat. Phys. 48(), 1987

AUTHOR UNKNOWN, 0

Nowak, Mutation frequencies and the onset of Muller?s ratchet. J. Theor. Biol. 137(), 1989

AUTHOR UNKNOWN, 0

Redner, Edinburgh Math. Soc. 47(), 2004

Rouzine, PNAS 100(), 2003

AUTHOR UNKNOWN, 0

Thompson, Math. Biosci. 21(), 1974

Wagner, J. Stat. Phys. 92(), 1998

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