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Small world effects in evolution.

F Bagnoli1, M Bezzi

  • 1Dipartimento di Matematica Applicata, Università di Firenze, Via S. Marta, 3 I-50139 Firenze, Italy. bagnoli@dma.unifi.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2001
PubMed
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Asexual organisms exhibit local point mutations and long-range genetic jumps. Even a few long-range jumps create a "small-world effect," simplifying population genetics models and leading to a Boltzmann equilibrium distribution.

Area of Science:

  • Population genetics
  • Evolutionary biology
  • Theoretical biology

Background:

  • Asexual organisms have diverse mutation types: local point mutations and long-range genetic rearrangements.
  • Understanding how these mutations affect population spread and equilibrium is crucial in evolutionary studies.

Purpose of the Study:

  • To investigate the spreading and equilibrium properties of asexual populations on different fitness landscapes.
  • To determine the impact of long-range jumps on population dynamics and compare it to models with equiprobable mutations.

Main Methods:

  • Simulating population spread on flat and smooth fitness landscapes.
  • Analyzing the effect of a small fraction of quenched long-range jumps.
  • Characterizing the equilibrium distribution of the population.

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Main Results:

  • A small-world effect was observed: a minor proportion of long-range jumps made population dynamics indistinguishable from models assuming all mutations are equiprobable.
  • The equilibrium distribution follows a Boltzmann distribution, analogous to statistical mechanics.
  • Fitness acts as energy, and mutations as temperature in this biological system.

Conclusions:

  • Long-range genetic jumps significantly simplify population genetics models by inducing a small-world effect.
  • The analogy to Boltzmann distribution provides a powerful framework for understanding evolutionary equilibrium in asexual populations.