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Nonequilibrium time dynamics of genetic evolution.

Hamid-Reza Rastegar-Sedehi1, Chandrashekar Radhakrishnan2, Samer Intissar Nehme3

  • 1State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China and Department of Physics, Jahrom University, 74137-66171, Jahrom, Iran.

Physical Review. E
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PubMed
Summary
This summary is machine-generated.

This study introduces a generalized master equation to model biological evolution, capturing selection, mutation, and reproduction dynamics. It reveals entropy production aligns with nonequilibrium statistical mechanics for evolving populations.

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Area of Science:

  • Statistical mechanics
  • Evolutionary biology
  • Theoretical biology

Background:

  • Biological systems are complex, open, and far from equilibrium, posing challenges for statistical mechanics.
  • While evolutionary statistics are studied, time-dependent nonequilibrium dynamics remain less explored.

Purpose of the Study:

  • To derive a generalized master equation for diploid organisms.
  • To incorporate selection, mutation, recombination, and reproduction into a unified framework.
  • To analyze the nonequilibrium dynamics and timescales of biological evolution.

Main Methods:

  • Derivation of a generalized master equation in genotype space.
  • Continuous-time model accommodating arbitrary gene loci and alleles.
  • Analytical solutions for prototypical cases.
  • Calculation of entropy production and application of the Glansdorff-Prigogine criterion.

Main Results:

  • The master equation successfully models the interplay of evolutionary processes.
  • Calculated entropy production aligns with nonequilibrium statistical mechanics predictions.
  • Entropy production is high when populations evolve toward more viable genotypes.
  • The nonequilibrium steady state was confirmed as stable.

Conclusions:

  • The developed master equation provides a robust framework for studying evolutionary nonequilibrium dynamics.
  • The findings support the applicability of statistical mechanics principles to complex biological systems.
  • This work offers insights into the timescales and stability of evolutionary processes.