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Effects of motion in structured populations.

Madison S Krieger1, Alex McAvoy1, Martin A Nowak2

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Individual movement in structured populations can suppress natural selection, especially with combined birth-death and death-birth updating rules. Purely birth-death updating remains unaffected by this motion.

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Area of Science:

  • Evolutionary biology
  • Population genetics
  • Mathematical modeling

Background:

  • Population structure significantly influences natural selection dynamics.
  • Individual movement alters the distribution of genetic types, impacting evolutionary trajectories.
  • Understanding motion's role is crucial for realistic models of evolution.

Purpose of the Study:

  • To analyze the effect of individual motion on natural selection in structured populations.
  • To investigate how different updating rules (birth-death, death-birth) interact with motion.
  • To explore motion's impact on various graph structures, including dynamic ones.

Main Methods:

  • Modeling individual motion as swapping or shuffling between reproductive updates on graphs.
  • Analyzing fixation probabilities and selection effects on one-dimensional cycles, square lattices, and weighted graphs.
  • Extending the analysis to dynamic graphs with spatial flow.

Main Results:

  • Motion suppresses natural selection under death-birth (DB) updating or combined birth-death (BD) and DB updating.
  • Purely BD updating shows no change in fixation probability with motion.
  • On weighted graphs, motion can amplify or suppress selection, dependent on reproductive rates; continuous motion also suppresses selection.

Conclusions:

  • Individual motion is a complex factor that can significantly alter the strength of natural selection.
  • The effect of motion is dependent on the specific updating rules and population structure.
  • Motion generally suppresses natural selection, highlighting its importance in evolutionary graph theory.