The Inherent Randomness of Evolving Populations

TL;DR

This paper computes and compares the entropy rates of key evolutionary processes like Wright-Fisher and Moran, revealing how mutation, selection, and population size influence their inherent randomness and variability.

Contribution

It provides the first analytical and computational analysis of entropy rates for these processes, establishing bounds and introducing a generational Moran process for comparison.

Findings

Entropy rates depend on mutation, selection, and population size.

Bounds for entropy rates are established for Moran and Wright-Fisher processes.

A new generational Moran process is introduced for comparative analysis.

Abstract

The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation dependent on both short-run and long-run behavior, and allow the relationships between mutation, selection, and population size to be examined. Bounds for the entropy rate are given for the Moran process (independent of population size) and for the Wright-Fisher process (bounded for fixed population size). A generational Moran process is also presented for comparison to the Wright-Fisher Process. Results include analytic results and computational extensions.