A Central Limit Theorem for Punctuated Equilibrium

TL;DR

This paper develops a Central Limit Theorem for punctuated equilibrium in evolutionary biology, showing that rapid adaptation requires diminishing variability in phenotypic jumps for normality to emerge.

Contribution

It introduces a mathematical framework capturing punctuated changes in phenotypes, extending traditional gradual models with a new CLT for such jumps.

Findings

Fast adaptation leads to normal distribution of phenotypic traits

Variability in jumps must decrease over time for convergence

Provides a rigorous probabilistic foundation for punctuated equilibrium

Abstract

Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated-the phenotype can jump. Such a jump could especially occur at speciation, i.e. dramatic change occurs that drives the species apart. Here we derive a Central Limit Theorem for punctuated equilibrium. We show that, if adaptation is fast, for weak convergence to normality to hold, the variability in the occurrence of change has to disappear with time.