Re-imagining the Hardy-Weinberg Law

TL;DR

This paper presents simplified proofs of the Hardy-Weinberg Law, revealing conditions under which allelic independence persists even with fertility selection, expanding understanding of genetic equilibrium.

Contribution

It introduces new, simplified proofs of the Hardy-Weinberg Law and demonstrates that allelic independence can hold under certain fertility selection scenarios.

Findings

Simplified proof based on Mendel's First Law

Allelic independence can persist under fertility selection

Theoretical conditions for the existence of such selection coefficients

Abstract

Under random mating, a progeny's alleles are independently sampled from the parental gene pools. Here is a new proof which avoids the usual algebraic complexity, based on a restated Mendel's First Law. Another simplified proof along the old approach led to the discovery that allelic independence can hold under random mating and fertility selection. The theoretical existence and number of such selection coefficients are established.