We present a mean-field theory for the evolution of RNA virus populations. The theory operates with a distribution of the population in a one-dimensional fitness space, and is valid for sufficiently smooth fitness landscapes. Our approach explains naturally the recent experimental observation (I.S.Novella et al, Proc. Natl. Acad. Sci. USA, 92, 5841-5844 (1995)) of two distinct stages in the growth of virus fitness.
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