We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.PACS numbers: 87.10.+e, 87.15.Aa, 87.23.Kg, We consider how quasispecies evolution changes in the presence of transfer of genetic information between individuals in a population. That is, we quantify by quasispecies theory the mutational load, if any, introduced by a model of recombination and gene transfer. Exchange of genetic information between individuals is believed to be pervasive in nature and crucial to evolutionary dynamics (for reviews, see [1,2,3]). Experiments and theory have emphasized that recombination and gene transfer in various forms increase the rate of laboratory directed protein evolution [4,5,6] (for reviews see [7,8]). Other experiments have amplified this point and have also suggested that, while significant in practice, the advantage of recombination may simply be to speed up the evolutionary process that would naturally occur by mutation alone in the limit of a long enough evolutionary time or a large enough population size [9,10,11].The Eigen [12] and Crow-Kimura [13], or parallel, models of viral quasispecies evolution are among the simplest that capture the basic processes of mutation, selection, and replication that occur in natural evolution. These mathematical models exhibit phase transitions, such that for mutation rates below critical values, an identifiable quasispecies forms. The Eigen and parallel quasispecies models are archetypes of biological evolution, and they have become a popular entry point to evolutionary biology for physicists [14,15,16,17,18,19,20,21]. Quantification of the mutational load of transfer of genetic information has been done by numerical solutions of the single-mutation-per-replication Eigen model for the special case of a linear replication rate function [22]. It was found that for intermediate population sizes and finite times, genetic transfer dramatically speeds up the rate of evolution. Phase diagrams were not determined, due to the focus on finite times and population sizes. We here derive by analytical calculation the mutational load and evolutionary advantage induced by transfer of genetic information for arbitrary replication rate functions in both the parallel and continuous-time Eigen models of quasispecies theory. That is, we find the infinitetime, infinite-genome-length, and infinite-population-size phase diagrams and mean fitness values of these models of quasispecies evolution in the general case. A...

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