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      Analysis of epistatic interactions and fitness landscapes using a new geometric approach

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          Abstract

          Background

          Understanding interactions between mutations and how they affect fitness is a central problem in evolutionary biology that bears on such fundamental issues as the structure of fitness landscapes and the evolution of sex. To date, analyses of fitness landscapes have focused either on the overall directional curvature of the fitness landscape or on the distribution of pairwise interactions. In this paper, we propose and employ a new mathematical approach that allows a more complete description of multi-way interactions and provides new insights into the structure of fitness landscapes.

          Results

          We apply the mathematical theory of gene interactions developed by Beerenwinkel et al. to a fitness landscape for Escherichia coli obtained by Elena and Lenski. The genotypes were constructed by introducing nine mutations into a wild-type strain and constructing a restricted set of 27 double mutants. Despite the absence of mutants higher than second order, our analysis of this genotypic space points to previously unappreciated gene interactions, in addition to the standard pairwise epistasis. Our analysis confirms Elena and Lenski's inference that the fitness landscape is complex, so that an overall measure of curvature obscures a diversity of interaction types. We also demonstrate that some mutations contribute disproportionately to this complexity. In particular, some mutations are systematically better than others at mixing with other mutations. We also find a strong correlation between epistasis and the average fitness loss caused by deleterious mutations. In particular, the epistatic deviations from multiplicative expectations tend toward more positive values in the context of more deleterious mutations, emphasizing that pairwise epistasis is a local property of the fitness landscape. Finally, we determine the geometry of the fitness landscape, which reflects many of these biologically interesting features.

          Conclusion

          A full description of complex fitness landscapes requires more information than the average curvature or the distribution of independent pairwise interactions. We have proposed a mathematical approach that, in principle, allows a complete description and, in practice, can suggest new insights into the structure of real fitness landscapes. Our analysis emphasizes the value of non-independent genotypes for these inferences.

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          Most cited references44

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          Long-Term Experimental Evolution in Escherichia coli. I. Adaptation and Divergence During 2,000 Generations

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            Lectures on Polytopes

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              Evolution of digital organisms at high mutation rates leads to survival of the flattest.

              Darwinian evolution favours genotypes with high replication rates, a process called 'survival of the fittest'. However, knowing the replication rate of each individual genotype may not suffice to predict the eventual survivor, even in an asexual population. According to quasi-species theory, selection favours the cloud of genotypes, interconnected by mutation, whose average replication rate is highest. Here we confirm this prediction using digital organisms that self-replicate, mutate and evolve. Forty pairs of populations were derived from 40 different ancestors in identical selective environments, except that one of each pair experienced a 4-fold higher mutation rate. In 12 cases, the dominant genotype that evolved at the lower mutation rate achieved a replication rate >1.5-fold faster than its counterpart. We allowed each of these disparate pairs to compete across a range of mutation rates. In each case, as mutation rate was increased, the outcome of competition switched to favour the genotype with the lower replication rate. These genotypes, although they occupied lower fitness peaks, were located in flatter regions of the fitness surface and were therefore more robust with respect to mutations.
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                Author and article information

                Journal
                BMC Evol Biol
                BMC Evolutionary Biology
                BioMed Central (London )
                1471-2148
                2007
                13 April 2007
                : 7
                : 60
                Affiliations
                [1 ]Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA
                [2 ]Department of Mathematics, University of California, Berkeley, CA 94720, USA
                [3 ]Instituto de Biología Molecular y Celular de Plantas, Consejo Superior de Investigaciones Científicas-UPV, 46022 València, Spain
                [4 ]Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, MI 48824, USA
                Article
                1471-2148-7-60
                10.1186/1471-2148-7-60
                1865543
                17433106
                8cb8a063-e454-4fb7-9345-2c191d8e09ad
                Copyright © 2007 Beerenwinkel et al; licensee BioMed Central Ltd.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 17 October 2006
                : 13 April 2007
                Categories
                Research Article

                Evolutionary Biology
                Evolutionary Biology

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