[{"quality_controlled":"1","author":[{"id":"161046","first_name":"Ellen","full_name":"Baake, Ellen","last_name":"Baake"},{"full_name":"Baake, Michael","last_name":"Baake","first_name":"Michael","id":"115942"},{"full_name":"Bovier, Anton","last_name":"Bovier","first_name":"Anton"},{"first_name":"Markus","last_name":"Klein","full_name":"Klein, Markus"}],"_id":"1604953","issue":"1","title":"An asymptotic maximum principle for essentially linear evolution models","date_created":"2010-04-28T12:40:33Z","doi":"10.1007/s00285-004-0281-7","page":"83-114","year":"2005","citation":{"chicago":"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.

","apa":"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","angewandte-chemie":"E. Baake, M. Baake, A. Bovier, and M. Klein, “An asymptotic maximum principle for essentially linear evolution models”, *JOURNAL OF MATHEMATICAL BIOLOGY*, **2005**, *50*, 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).","dgps":"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.

","frontiers":"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.","mla":"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.","default":"Baake E, Baake M, Bovier A, Klein M (2005)

*JOURNAL OF MATHEMATICAL BIOLOGY* 50(1): 83-114.","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

","wels":"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.","bio1":"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.","ieee":" E. Baake, et al., “An asymptotic maximum principle for essentially linear evolution models”, *JOURNAL OF MATHEMATICAL BIOLOGY*, vol. 50, 2005, pp. 83-114.","ama":"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.","harvard1":"Baake, E., et al., 2005. An asymptotic maximum principle for essentially linear evolution models. *JOURNAL OF MATHEMATICAL BIOLOGY*, 50(1), p 83-114."},"volume":50,"department":[{"_id":"201230"},{"_id":"10060"},{"_id":"10020"}],"publication_identifier":{"issn":["0303-6812"],"eissn":["1432-1416"]},"status":"public","date_updated":"2019-03-27T13:15:29Z","keyword":["ancestral distribution","models","mutation-selection","lumping","asymptotics of leading eigenvalue","reversibility"],"intvolume":" 50","type":"journal_article","user_id":"29676584","isi":1,"external_id":{"pmid":["15322822"],"isi":["000226809800005"]},"abstract":[{"lang":"eng","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."}],"article_type":"original","publisher":"SPRINGER","language":[{"iso":"eng"}],"pmid":1,"publication":"JOURNAL OF MATHEMATICAL BIOLOGY","publication_status":"published"}]