Can evolution paths be explained by chance alone?

TL;DR

This paper introduces a probabilistic model explaining the evolution of population maximum fitness, revealing a logarithmic number of upward jumps and path patterns consistent with experimental observations.

Contribution

It presents a universal probabilistic framework for evolution paths, demonstrating that upward fitness jumps follow a logarithmic pattern regardless of mutation probability or fitness distribution.

Findings

Number of upward jumps is approximately ln(n) after n births

Evolution paths typically show a steep rise followed by plateaux

Parallel evolution paths are observed across independent runs

Abstract

We propose a purely probabilistic model to explain the evolution path of a population maximum fitness. We show that after $n$ births in the population there are about $\ln n$ upwards jumps. This is true for any mutation probability and any fitness distribution and therefore suggests a general law for the number of upwards jumps. Simulations of our model show that a typical evolution path has first a steep rise followed by long plateaux. Moreover, independent runs show parallel paths. This is consistent with what was observed by Lenski and Travisano (1994) in their bacteria experiments.