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The mutation-drift balance in spatially structured populations.

David M Schneider1, Ayana B Martins1, Marcus A M de Aguiar1

  • 1Instituto de Física 'Gleb Wataghin', Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, SP, Brazil.

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Spatial structure impacts neutral mutation dynamics in finite populations. Low connectivity networks decrease the mutation threshold, promoting genetic diversity at lower mutation rates.

Keywords:
Allele distributionMoran modelMutation thresholdNetworks

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Area of Science:

  • Population Genetics
  • Theoretical Biology
  • Mathematical Biology

Background:

  • Neutral mutations and genetic drift balance in finite populations, determining allele distributions.
  • Well-mixed populations exhibit a mutation threshold (μc=1/2N) separating distinct equilibrium behaviors.
  • The influence of spatial structure on this threshold remains largely unexplored.

Purpose of the Study:

  • To investigate how spatial structure affects the mutation threshold in finite populations.
  • To analyze the stationary allele distribution on regular networks representing mating interactions.

Main Methods:

  • Utilized the Moran model to simulate population dynamics with neutral mutations.
  • Mapped the Moran model with mutations to the voter model with opinion makers.
  • Analyzed populations structured on regular networks where nodes represent potential mates.

Main Results:

  • Spatial structure significantly alters the mutation threshold only in populations with very few potential mates (low connectivity).
  • In such low-connectivity networks, the mutation threshold decreases substantially, enhancing genetic diversity at lower mutation rates.
  • The critical network degree (kc) for halving the mutation threshold grows slowly with population size, following a power law.

Conclusions:

  • Spatial structure, particularly low connectivity, can maintain genetic diversity by lowering the mutation threshold.
  • This finding highlights the importance of considering network topology in evolutionary dynamics.
  • The study provides a theoretical framework and simulation-based evidence for spatially structured population genetics.