THE HARDY-WEINBERG EQUATION

INTRODUCTION

Godfrey Hardy and Wilhelm Weinberg are credited with independently generating the mathematical

HARDY

relationship behind the Hardy-Weinberg principle in 1908. The principle describes how genetic alleles will be inherited from generation to generation and was the foundation to the study of population genetics. Diploid organisms, all animals and many plants, have two copies of an allele, one from each parent. The Hardy-Weinberg principle calculates the proportion of the population with a given combination of alleles, or genotype.

WEINBERG

DEFINITION

The Hardy-Weinberg equilibrium is a principle stating that the genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors

FACTORS THAT CONTRIBUTE TO HARDY-WEINBERG’S EQUATION

The population is very large

Individuals in the population mate randomly

There is no migration into or out of the population

Natural selection does not act on any specific genotypes

Males and females have the same allele frequencies

Individuals are diploid and reproduce sexually

No mutations occur

Generations are non-overlapping

THE FORMULA

In the simplest case of a single locus with two alleles denoted A and a with frequencies f(A) = p and f(a) = q, respectively, the expected genotype frequencies are f(AA) = p² for the AA homozygote, f(aa) = q² for the aa homozygote, and f(Aa) = 2pq for the heterozygote. The genotype proportions p², 2pq, and q² are called the Hardy–Weinberg proportions. Note that the sum of all genotype frequencies of this case is the binomial expansion of the square of the sum of p and q, and such a sum, as it represents the total of all possibilities, must be equal to 1. Therefore, (p + q)² = p² + 2pq + q² = 1. A solution of this equation is q = 1 – p.

In short, two equations were derived from hardy and Weinberg’s experiment:

1.       The sum of p and q must be 1, p + q = 1

2.       The expansion of the squared sum of p and q is also 1, p² + q² = 1