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. SPRINGER. doi:10.1007/s00285-004-0281-7.

","apa_indent":"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

","apa":"Baake, E., Baake, M., Bovier, A., & Klein, M. (2005). An asymptotic maximum principle for essentially linear evolution models. Baake, Ellen, Baake, Michael, Bovier, Anton, and Klein, Markus. 2005. “An asymptotic maximum principle for essentially linear evolution models”. *JOURNAL OF MATHEMATICAL BIOLOGY* 50 (1): 83-114.

","harvard1":"Baake, E., et al., 2005. An asymptotic maximum principle for essentially linear evolution models. An asymptotic maximum principle for essentially linear evolution models.

JOURNAL OF MATHEMATICAL BIOLOGY 50(1): 83-114.","lncs":" 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)."},"pmid":1,"quality_controlled":"1","external_id":{"isi":["000226809800005"],"pmid":["15322822"]},"abstract":[{"text":"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.","lang":"eng"}],"publication":"JOURNAL OF MATHEMATICAL BIOLOGY","title":"An asymptotic maximum principle for essentially linear evolution models","intvolume":" 50","doi":"10.1007/s00285-004-0281-7"}]