Eur. Phys. J. B 63, 245-254 (2008)
https://doi.org/10.1140/epjb/e2008-00229-3

Does sex induce a phase transition?

¹ Instituto de Física, Universidade Federal Fluminense; Av. Litorânea s/n, Boa Viagem, Niterói, 24210-340 RJ, Brazil
² Laboratoire PMMH, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris, France
³ Institute for Theoretical Physics, Cologne University, 50923 Köln, Germany
⁴ Department of Genomics, Wrocław University, ul. Przybyszewskiego 63/77, 51-148 Wrocław, Poland
⁵ Institute of Theoretical Physics, Wrocław University, pl. Maxa Borna 9, 50-204 Wrocław, Poland

Corresponding author: ^a pmco@if.uff.br

Received: 1 October 2007
Revised: 22 February 2008
Published online: 20 June 2008

Abstract

We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule applied to diploid bit-strings with both fundamental ingredients to drive Darwin's evolution: (1) random mutations and crossings which act in the sense of increasing the entropy (or diversity); and (2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough, and thus the wild genotype dominates the steady-state population. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point m_c. Above this point, the “bad” alleles (represented by 1-bits) spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < m_c, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough “chromosome” lengths L, through lengthy computer simulations. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that m_c is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.