Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island...

Area of Science:

• Molecular Ecology
• Population Genetics
• Information Theory

Background:

• Shannon entropy (H) and related measures are valuable in population genetics and molecular ecology.
• Unlike heterozygosity or allele number, entropy weighs alleles by population fraction, capturing unique aspects of frequency distributions.
• These measures connect to information theory and possess additive and hierarchical properties.

Purpose of the Study:

• Derive new expressions for Shannon entropy at equilibrium under infinite allele and stepwise mutation models.
• Link entropy-based and heterozygosity-based measures and explore their validity.
• Apply these measures to subdivided populations and develop a neutrality test.

Main Methods:

• Derivation of novel mathematical expressions for expected Shannon entropy.
• Simulations to assess the approximate validity of derived relationships.
• Application of entropy measures to the finite island model for population structure analysis.

Main Results:

• Simple expressions for equilibrium Shannon entropy were derived for two mutation models.
• Entropy and heterozygosity measures were linked, showing approximate validity even out of equilibrium.
• New measures for Shannon differentiation in subdivided populations were obtained and applied to starling data.

Conclusions:

• Developed a robust framework using Shannon entropy for analyzing genetic diversity and population structure.
• The derived measures offer a powerful tool for neutrality testing, resilient to equilibrium assumption violations.
• The study provides a bridge between different mutation models and advances the application of information theory in population genetics.