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Population structure and the rate of evolution.

Xinzhu Wei1, Lei Zhao1, Martin Lascoux2

  • 1Centre for Computational Systems Biology, Fudan University, Shanghai 200433, People׳s Republic of China.

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Summary

Population size, migration, and selection interact to influence the substitution rate. The study shows how scaled migration (M) and selection (S) parameters, dependent on population size (N), determine this rate, with complex relationships leading to varied outcomes.

Keywords:
Diffusion approximationMigrationPopulation subdivisionSpatially dependent selectionWright–Fisher model

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Area of Science:

  • Evolutionary biology
  • Population genetics

Background:

  • The interplay between population size, structure, and spatially varying selection on evolutionary substitution rates is not well understood.
  • Understanding these dynamics is crucial for predicting evolutionary trajectories in structured populations.

Purpose of the Study:

  • To investigate how population size (N), migration, and spatially dependent selection jointly impact the rate of evolutionary substitutions.
  • To analyze the roles of scaled migration rate (M) and scaled selection intensity (S) in this process.

Main Methods:

  • A two-patch model was developed with beneficial/deleterious mutant alleles in different patches.
  • Assumptions included zero spatial average of selection and independent random genetic drift within each patch of size N.

Main Results:

  • Population size (N) primarily influences substitution rates (R∞) through composite parameters M and S.
  • The relationship between M and S significantly affects how R∞ depends on N.
  • In simple cases where M and S are proportional to N, R∞ generally increases with N, unless S is large.

Conclusions:

  • The effect of population size on substitution rates is not monotonic and depends critically on the relationship between scaled migration and selection.
  • Complex dependencies between M and S can lead to substitution rates that increase or decrease with population size.
  • The findings highlight the importance of considering spatial structure and selection in evolutionary models.