Shannon Mutual Information Applied to Genetic Systems

TL;DR

This paper applies Shannon mutual information to genetic systems, analyzing how allele diversity and information evolve over generations, revealing insights into genetic stability, diversity, and the role of mutations.

Contribution

It introduces a novel application of Shannon information theory to model genetic evolution over generations, including real data analysis and simulation.

Findings

Mutual information increases over generations without mutations, reaching a maximum.

Genetic diversity remains constant in the absence of mutations after many generations.

Mutual information effectively measures allele fixation and genetic stability.

Abstract

Shannon information has, in the past, been applied to quantify the genetic diversity of many natural populations. Here, we apply the Shannon concept to consecutive generations of alleles as they evolve over time. We suppose a genetic system analogous to the discrete noisy channel of Shannon, where the signal emitted by the input (mother population) is a number of alleles that will form the next generation (offspring). The alleles received at a given generation are conditional upon the previous generation. Knowledge of this conditional probability law allows us to track the evolution of the allele entropies and mutual information values from one generation to the next. We apply these laws to numerical computer simulations and to real data (Stryphnodendron adstringens). We find that, due to the genetic sampling process, in the absence of new mutations the mutual information increases between generations toward a maximum value. Lastly, after sufficient generations the system has a level of mutual information equal to the entropy (diversity) that it had at the beginning of the process (mother population). This implies no increase in genetic diversity in the absence of new mutations. Now, obviously, mutations are essential to the evolution of species. In addition, we observe that when a population shows at least a low level of genetic diversity, the highest values of mutual information between the generations occurs when the system is neither too orderly nor too disorderly. We also find that mutual information is a valid measure of allele fixation.