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Geometric phase in the Crow-Kimura model of molecular evolution on dynamic environments
Vladimir Suvorov1, Ricard Solé2,3, David B Saakian4,5
1Auriga Incorporated, 400 TradeCenter, Suite 5900, Woburn, Massachusetts 01801, USA.
Physical Review. E
|December 23, 2025
Summary
Fluctuating environments challenge evolutionary dynamics. A geometric (Berry) phase in the Crow-Kimura model reveals new nonequilibrium adaptive evolution insights, especially with asymmetric mutations.
Area of Science:
- Evolutionary dynamics
- Theoretical biology
- Molecular evolution
Background:
- Classical evolutionary dynamics models often assume equilibrium conditions.
- Non-equilibrium conditions in fluctuating environments can alter adaptive evolution outcomes.
- The Crow-Kimura model is a foundational model for molecular evolution.
Purpose of the Study:
- To investigate the impact of nonequilibrium conditions on evolutionary dynamics.
- To explore the role of geometric (Berry) phase in the Crow-Kimura model.
- To analyze adaptive evolution under fluctuating fitness and mutation rates.
Main Methods:
- Derivation of analytical expressions for the Berry phase in the Crow-Kimura model.
- Analysis of changes in fitness and mutation parameters.
- Examination of periodically varying parameters in a two-dimensional case.
Main Results:
- A geometric (Berry) phase significantly contributes to nonequilibrium dynamics in the Crow-Kimura model.
- Analytical expressions for the Berry phase exhibit strong singularities at bulk transition points.
- The presence of asymmetric mutations is crucial for observing this Berry phase effect.
Conclusions:
- The study highlights the importance of considering nonequilibrium dynamics and geometric phases in evolutionary models.
- Findings have potential implications for understanding evolutionary processes and prebiotic scenarios.
- Reevaluation of classical evolutionary dynamics is necessary under fluctuating environmental conditions.
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