Natural selection maximizes Fisher information

TL;DR

This paper demonstrates that Fisher information naturally describes the process of natural selection, linking it to evolutionary dynamics and unifying concepts of information in biology and statistics.

Contribution

It establishes Fisher information as the intrinsic metric of natural selection and connects it to Fisher's fundamental theorem and Shannon information.

Findings

Fisher information arises as the key metric in natural selection.

Maximizing Fisher information leads to Fisher's fundamental theorem.

A relationship between Fisher and Shannon information is proposed.

Abstract

In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher information arises as the intrinsic metric of natural selection and evolutionary dynamics. Maximizing the amount of Fisher information about the environment captured by the population leads to Fisher's fundamental theorem of natural selection, the most profound statement about how natural selection influences evolutionary dynamics. I also show a relation between Fisher information and Shannon information (entropy) that may help to unify the correspondence between information and dynamics. Finally, I discuss possible connections between the fundamental role of Fisher information in statistics, biology, and other fields of science.