Hardy-Weinberg Equilibrium (College Board AP® Biology): Study Guide

Conditions for Hardy-Weinberg equilibrium

• The Hardy-Weinberg principle states that, if certain conditions are met,then the allele frequencies of a gene within a population will not change from one generation to the next

• The Hardy-Weinberg equation allows for the calculation of allele and genotype frequencies within populations

• It also allows for predictions to be made about how these frequencies will change in future generations

• Conditions that must be met for the Hardy-Weinberg principle to hold true include:

  • a large population size

  • no migration into or out of the population

  • no mutations give rise to new alleles

  • mating is random

  • natural selection is not acting on the population

• The assumptions listed are very rarely, if ever, all present in nature

• Despite this, the Hardy-Weinberg equilibrium concept can provide a useful null hypothesis when evaluating the effects of genetic changes

The Hardy-Weinberg equation

• If the phenotype of a trait in a population is determined by a single gene with only two alleles (we will use B / b as examples throughout this section), then the population will consist of individuals with three possible genotypes:

  • Homozygous dominant (BB)

  • Heterozygous (Bb)

  • Homozygous recessive (bb)

•  When using the Hardy-Weinberg equation, the frequency of a genotype is represented as a proportion of the population

  • For example, the BB genotype could be 0.40

  • Whole population = 1

  • The letter p represents the frequency of the dominant allele (B)

  • The letter q represents the frequency of the recessive allele (b)

  • As there are only two alleles at a single gene locus for this phenotypic trait in the population:

p + q = 1

• The chance of an individual being homozygous dominant is p²

  • In this instance, the offspring would inherit dominant alleles from both parents ( p x p = p² )

•  The chance of an individual being heterozygous is 2pq

  • Offspring could inherit a dominant allele from the father and a recessive allele from the mother ( p x q ) or offspring could inherit a dominant allele from the mother and a recessive allele from the father ( p x q ) = 2pq

• The chance of an individual being homozygous recessive is q² 

  •  In this instance, the offspring would inherit recessive alleles from both parents ( q x q = q² )

• As these are all the possible genotypes of individuals in the population, the following equation can be constructed:

p² + q² + 2pq = 1