The statistics of fixation times for systems with recruitment

TL;DR

This paper analyzes the distribution of fixation times in recruitment-driven systems, showing it follows an inverse Gaussian with exponential decay, and identifies how population size influences fixation dynamics.

Contribution

It introduces a model linking fixation times to population size and provides a method to estimate critical population thresholds from experimental data.

Findings

Fixation times follow an inverse Gaussian distribution with exponential decay.

The decay timescale depends on population size.

A critical population size for fixation can be estimated from data.

Abstract

We investigate the statistics of the time taken for a system driven by recruitment to reach fixation. Our model describes a series of experiments where a population is confronted with two identical options, resulting in the system fixating on one of the options. For a specific population size, we show that the time distribution behaves like an inverse Gaussian with an exponential decay. Varying the population size reveals that the timescale of the decay depends on the population size and allows the critical population number, below which fixation occurs, to be estimated from experimental data.