The statistical mechanics of a polygenic character under stabilizing selection, mutation and drift

Area of Science:

• Evolutionary Biology
• Statistical Mechanics
• Quantitative Genetics

Background:

• Studying the evolution of polygenic traits involves complex allele frequency distributions.
• Previous models often require arbitrary truncation of infinite series, limiting accuracy.

Purpose of the Study:

• To develop a simplified, accurate framework for modeling polygenic trait evolution.
• To analyze trait dynamics under stabilizing selection, mutation, and genetic drift.

Main Methods:

• Utilized an analogy between population genetics and statistical mechanics.
• Tracked four macroscopic variables (trait mean, its square, genetic variance, heterozygosity measure) derived from an entropy-maximizing generating function.
• Developed a well-defined approximation procedure, avoiding arbitrary truncation.

Main Results:

• The four macroscopic variables accurately describe the dynamics of trait mean and genetic variance.
• Approximations are accurate even for systems with few loci (e.g., five).
• Included genetic drift minimally alters expected genetic variance under directional selection, and hysteresis was observed.

Conclusions:

• The statistical mechanics approach offers a powerful and accurate simplification for polygenic trait evolution.
• The framework captures complex dynamics, including memory effects (hysteresis), even with genetic drift.
• This method provides a robust alternative to traditional moment-based approaches.