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Evolutionary adaptation on rugged landscapes depends on population size. Intermediate populations favor easy mutations, while smaller and larger ones explore complex paths, crossing fitness valleys for greater evolutionary gains.

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Area of Science:

  • Evolutionary Biology
  • Theoretical Biology
  • Population Genetics

Background:

  • Rugged fitness landscapes present evolutionary challenges, often involving sign epistasis.
  • Adaptation can proceed via individually beneficial mutations or complex trajectories through fitness valleys/plateaus.
  • Understanding evolutionary path selection is key to predicting adaptation outcomes on complex landscapes.

Purpose of the Study:

  • To model the probability of evolution crossing fitness valleys/plateaus instead of taking immediately beneficial paths.
  • To analyze the influence of population size, mutation rates, and selection pressures on this probability.
  • To compare model predictions with Wright-Fisher simulations.

Main Methods:

  • Development of a simple mathematical model for evolutionary trajectory analysis.
  • Analytical calculation of valley-crossing probability based on key evolutionary parameters.
  • Comparison of analytical results with stochastic Wright-Fisher simulations.

Main Results:

  • Valley-crossing probability exhibits non-monotonic dependence on population size.
  • Intermediate populations tend to follow a 'greedy' strategy, selecting immediately beneficial mutations.
  • Larger and smaller populations are more prone to crossing fitness valleys to reach superior genotypes.

Conclusions:

  • Distinct evolutionary regimes (greedy vs. valley-crossing) are identified based on population size and other parameters.
  • Above a critical population size, the probability of reaching a distant peak simplifies to a function of a single parameter combination.
  • The study elucidates the complex interplay between population size and evolutionary strategy on rugged fitness landscapes.