Quantifying the potential and flux landscapes of multi-locus evolution

Area of Science:

• Evolutionary Biology
• Theoretical Biology
• Complex Systems

Background:

• Multi-locus evolution is crucial for understanding evolutionary dynamics.
• Recombination and epistasis create complex evolutionary trajectories.
• Existing theories like Wright, Fisher, and quasi-linkage equilibrium (QLE) are limited to simplified scenarios.

Purpose of the Study:

• To develop a novel non-equilibrium potential and flux landscape theory for multi-locus evolution.
• To move beyond the limitations of Wright, Fisher, and QLE theories.
• To globally analyze the stability and function of multi-locus evolutionary systems.

Main Methods:

• Developed a non-equilibrium potential and flux landscape theory.
• Utilized a Lyapunov function for global stability analysis in the zero noise limit.
• Investigated multi-locus systems under recombination, epistasis, and mutation, including a two-locus system example.

Main Results:

• Identified potential landscape and curl flux as key driving forces in multi-locus evolution.
• Demonstrated that recombination, frequency-dependent selection, and mutation can generate non-zero curl flux.
• Observed non-equilibrium phase transitions and analyzed epistasis effects on stability (mono-stability and bi-stability).
• Explained the Red Queen hypothesis origin via curl flux and quantified energy dissipation using entropy production rate.

Conclusions:

• The developed landscape and flux framework provides a powerful tool for analyzing complex multi-locus evolutionary systems.
• This theory offers a more general approach applicable to systems with recombination and epistasis.
• The framework successfully explains fundamental evolutionary concepts like the Red Queen hypothesis.