[Paper Review] Natural selection maximizes Fisher information

Steven A. Frank|arXiv (Cornell University)|Jan 23, 2009

Advanced Thermodynamics and Statistical Mechanics13 references4 citations

TL;DR

This paper proposes that natural selection acts to maximize Fisher information, a statistical measure of estimation precision, as the mechanism driving evolutionary dynamics. By showing that Fisher's fundamental theorem of natural selection emerges directly from the maximization of Fisher information captured by hereditary particles, the study establishes a deep formal link between information theory and evolutionary biology, unifying key principles of selection and inference.

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.

Motivation & Objective

• To establish a formal connection between natural selection and information theory by identifying Fisher information as the intrinsic metric of evolutionary dynamics.
• To resolve the long-standing lack of a general mathematical framework for selection theory by grounding it in a well-defined information metric.
• To unify evolutionary dynamics with statistical inference by demonstrating that the Price equation and fundamental evolutionary principles emerge from maximizing Fisher information.
• To explore whether the maximization of Fisher information reflects a deeper principle linking measurement, information, and physical dynamics in biological systems.

Proposed method

• The paper applies Frieden's information-theoretic framework, which derives dynamical laws from the maximization of Fisher information.
• It models natural selection as a process where hereditary particles (e.g., genes) capture information about environmental fitness through changes in their frequencies.
• The method uses Fisher information as a metric to quantify how much information about environmental conditions is captured by the population’s genetic composition.
• It derives Fisher’s fundamental theorem of natural selection from the assumption that the information captured by hereditary particles is maximized under selection.
• The analysis extends to a generalized form of Fisher information that accounts for correlations between environmental information and population-level observations.
• It demonstrates equivalence between the generalized Fisher information framework and the Price equation for evolutionary change in any trait.

Experimental results

Research questions

• RQ1 Can Fisher information serve as the fundamental metric that describes how natural selection captures information from the environment?
• RQ2 Does the maximization of Fisher information in hereditary particles lead directly to Fisher’s fundamental theorem of natural selection?
• RQ3 How does the generalized Fisher information framework relate to the Price equation and other core equations in evolutionary dynamics?
• RQ4 What is the role of information loss and estimation error in the evolutionary process, as modeled through Fisher information?
• RQ5 Is the link between Fisher information and natural selection merely an analogy, or does it reflect a deeper principle connecting information, dynamics, and measurement?

Key findings

• Fisher’s fundamental theorem of natural selection is derived directly from the assumption that natural selection maximizes the Fisher information captured by hereditary particles in a population.
• The generalized form of Fisher information used in the model is mathematically equivalent to the Price equation, providing a unified framework for evolutionary change.
• The model shows that the rate of increase in mean fitness under selection corresponds exactly to the maximum Fisher information that can be captured by the population’s genetic frequencies.
• The framework reveals that natural selection acts as an inductive inference process, where hereditary particles serve as predictive hypotheses tested through differential reproduction.
• The analysis suggests that the structure of evolutionary dynamics arises naturally from information-theoretic principles, implying a deeper connection between information and physical dynamics.
• The study demonstrates that the bound information (environmental signal) and captured information (genetic response) can be formalized using Fisher information, with information loss quantified as negative Kullback-Leibler divergence.