Re-imagining the Hardy-Weinberg Law

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.