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An asymptotic maximum principle for essentially linear evolution models

E. Baake·M. Baake·A. Bovier·M. Klein
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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 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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E. Baake, M. Baake, A. Bovier, M. Klein. 2004-06-08. An asymptotic maximum principle for essentially linear evolution models. https://doi.org/10.1007/s00285-004-0281-7

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