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Asexual evolution waves fluctuations and universality by Daniel Fisher in 2013

Outline

Abstract

  • __In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix__

Introduction

  • Outline
  • Model and fitness distribution

Heuristics

  • Staircase model
  • Instability and fluctuation of the nose
  • Predominant mutations with short-tailed mu of s

Branching process at fixed speed

  • Fixation probability
  • Fixation probability at fixed speed
  • Sharp shoulder approximation
  • Fixation probability and determination of N
  • Comparison with results of Good et al

Dynamics and distribution of N(t) at fixed speed

  • Distribution of N(t)
  • Typical rho(x) and weighted fixation probability

Feedback and coupled dynamics of nose and mean

  • Dynamics of feedback
  • Jumps in mean fitness and clustering of fixation probabilities
  • Average fitness distribution

Conditioning on behavior at infinite time

  • Exactly solvable suppressed-fluctuation model
  • Distribution of population size
  • Moments and correlations of rho(chi, t)
  • Relationship to Hallatschek model

Field theoretic approaches

  • Soft constraints on the population size

Summary and extensions

  • Universality for huge populations with short-tailed mutation distributions
  • Beyond the universal limit
  • Extensions

Appendix A: Average fitness distribution at fixed speed

  • Formal steady-state fitness distribution

Appendix B: Well-behaved solution in linear region

  • Moderate speeds, v«
  • High speeds, v»

Appendix C: Sharp shoulder approximation

Appendix D: Dynamics of phi

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