Continuous and Discontinuous Phase Transitions in the evolution of a polygenic trait under stabilizing selective pressure

TL;DR

This study investigates phase transition phenomena in the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift, revealing critical points and hysteresis behaviors through numerical simulations.

Contribution

It introduces a phase diagram for polygenic trait evolution, identifying critical and discontinuous transitions influenced by mutation rate and selection strength.

Findings

Identifies a line of critical points for weak selection.

Discovers discontinuous phase transitions with hysteresis under strong selection.

Suggests analogy with the mean field Ising model near the threshold.

Abstract

The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model system, we analyze the evolution of a population of $N$ diploid hermaphrodites in random mating regime. The population evolves under the effect of drift, selective pressure in form of viability on an additive polygenic trait, and mutation. The analysis allows to determine a phase diagram in the plane of mutation rate and strength of selection. The involved pattern of phase transitions is characterized by a line of critical points for weak selective pressure (smaller than a threshold), whereas discontinuous phase transitions, characterized by metastable hysteresis, are observed for strong selective pressure. A finite size scaling analysis suggests the analogy between our system and the mean field Ising model for selective pressure approaching the threshold from weaker values. In this framework, the mutation rate, which allows the system to explore the accessible microscopic states, is the parameter controlling the transition from large heterozygosity (disordered phase) to small heterozygosity (ordered one).