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Evolution in a flat fitness landscape

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Abstract

A simple model of a population of asexually reproducing individuals, evolving in a flat fitness landscape, is defined. It is shown that the model is equivalent to a dynamical system with stochastic dynamics, the Annealed Random Map Model. Thus, it is possible to solve exactly for the genealogy statistics and for the genetic variability of the population. Fluctuations of quantities, like the average relatedness and the variability, which also take place in the limit of an infinitely large population, are computed.

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Author notes

  1. Bernard Derrida

    Present address: Service de Physique Théorique de Saclay, Institut de Recherche Fondamentale, F-91191, Gif-Sur-Yvette Cedex, France

  2. Luca Peliti

    Present address: Dipartimento di Scienze Fisiche and Unità INFM, Università di Napoli, Mostra d'Oltremare, Pad. 19, I-80125, Napoli, Italy

Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Studies, 08540, Princeton, NJ, USA

    Bernard Derrida

  2. Groupe de Physico-Chimie Théorique, URA 1382, E.S.P.C.I., 10, rue Vauquelin, F-75231, Paris Cedex 05, France

    Luca Peliti

Authors
  1. Bernard Derrida
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  2. Luca Peliti
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Derrida, B., Peliti, L. Evolution in a flat fitness landscape. Bltn Mathcal Biology 53, 355–382 (1991). https://doi.org/10.1007/BF02460723

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  • DOI: https://doi.org/10.1007/BF02460723

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