An asymptotic maximum principle for essentially linear evolution models
- 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
Author details: | Ellen Baake, Michael Baake, Anton Bovier, Markus KleinGND |
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ISSN: | 0303-6812 |
Publication type: | Article |
Language: | English |
Year of first publication: | 2005 |
Publication year: | 2005 |
Release date: | 2017/03/24 |
Source: | Journal of Mathematical Biology. - ISSN 0303-6812. - 50 (2005), 1, S. 83 - 114 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |