Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape

Yuri Bakhtin, Mikhail I. Katsnelson, Yuri I. Wolf, Eugene V. Koonin

Research output: Contribution to journalArticlepeer-review

Abstract

A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape. The periods of stasis are punctuated by fast transitions, in lnNe/s time (Ne, effective population size; s, selection coefficient of a mutation), when a new beneficial mutation is fixed in the evolving population, which accordingly moves to a different saddle, or on much rarer occasions from a saddle to a local peak. Phenomenologically, this mode of evolution of a large population resembles punctuated equilibrium (PE) whereby phenotypic changes occur in rapid bursts that are separated by much longer intervals of stasis during which mutations accumulate but the phenotype does not change substantially. Theoretically, PE has been linked to self-organized criticality (SOC), a model in which the size of “avalanches” in an evolving system is power-law-distributed, resulting in increasing rarity of major events. Here we show, however, that a PE-like evolutionary regime is the default for a very simple model of an evolving population that does not rely on SOC or any other special conditions.

Original languageEnglish (US)
Article numbere2015665118
JournalProceedings of the National Academy of Sciences of the United States of America
Volume118
Issue number4
DOIs
StatePublished - Jan 26 2021

Keywords

  • Fitness landscapes
  • Low mutation limit
  • Punctuated equilibrium
  • Saddle points
  • Self-organized criticality

ASJC Scopus subject areas

  • General

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