Evolutionary branching in a finite population: deterministic branching vs. stochastic branching

Area of Science:

• Evolutionary Biology
• Theoretical Ecology
• Population Genetics

Background:

• Adaptive dynamics theory predicts evolutionary branching from unimodal to bimodal trait distributions in constant environments.
• Previous studies primarily analyzed evolutionary branching in infinitely large populations, neglecting the impact of finite population size.

Purpose of the Study:

• To investigate the effects of stochasticity, arising from finite population size, on the process of evolutionary branching.
• To determine the conditions under which evolutionary branching occurs in finite populations and characterize different branching patterns.

Main Methods:

• Analysis of trait variance dynamics to establish the condition for evolutionary branching.
• Mathematical derivation of conditions for deterministic and stochastic branching, including mean branching-out times.
• Validation through direct computer simulations of an individual-based model.

Main Results:

• Genetic drift in finite populations reduces trait variance and introduces stochastic fluctuations, inhibiting branching in very small populations.
• Evolutionary branching can occur in larger finite populations through two distinct modes: rapid deterministic branching or delayed stochastic branching.
• Conditions for both branching modes and their timing are dependent on population size, mutation effects, and selection intensity.

Conclusions:

• Finite population size significantly alters evolutionary branching dynamics compared to infinite population models.
• Stochasticity plays a crucial role, leading to different branching patterns and timing in finite populations.
• The study provides a quantitative framework for understanding evolutionary branching under realistic population size constraints.