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      A Markov chain model of evolution in asexually reproducing populations: insight and analytical tractability in the evolutionary process

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          Abstract

          The evolutionary process has been modelled in many ways using both stochastic and deterministic models. We develop an algebraic model of evolution in a population of asexually reproducing organisms in which we represent a stochastic walk in phenotype space, constrained to the edges of an underlying graph representing the genotype, with a time-homogeneous Markov Chain. We show its equivalence to a more standard, explicit stochastic model and show the algebraic model's superiority in computational efficiency. Because of this increase in efficiency, we offer the ability to simulate the evolution of much larger populations in more realistic genotype spaces. Further, we show how the algebraic properties of the Markov Chain model can give insight into the evolutionary process and allow for analysis using familiar linear algebraic methods.

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          Error Detecting and Error Correcting Codes

          R. Hamming (1950)
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            Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes.

            Having multiple peaks within fitness landscapes critically affects the course of evolution, but whether their presence imposes specific requirements at the level of genetic interactions remains unestablished. Here we show that to exhibit multiple fitness peaks, a biological system must contain reciprocal sign epistatic interactions, which are defined as genetic changes that are separately unfavorable but jointly advantageous. Using Morse theory, we argue that it is impossible to formulate a sufficient condition for multiple peaks in terms of local genetic interactions. These findings indicate that systems incapable of reciprocal sign epistasis will always possess a single fitness peak. However, reciprocal sign epistasis should be pervasive in nature as it is a logical consequence of specificity in molecular interactions. The results thus predict that specific molecular interactions may yield multiple fitness peaks, which can be tested experimentally. Copyright © 2010 Elsevier Ltd. All rights reserved.
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              PERSPECTIVE: SIGN EPISTASIS AND GENETIC COSTRAINT ON EVOLUTIONARY TRAJECTORIES

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                Author and article information

                Journal
                1301.4193

                Evolutionary Biology,Probability
                Evolutionary Biology, Probability

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