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, frequencies are expressed as a proportion of the population, e.g.:

  • if every individual in the population has the homozygous dominant genotype (BB), its frequency will be 1

  • if half of the population show this genotype, then the frequency will be 0.5

Allele frequencies

• For a gene with two alleles (B and b):

  • 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 for this gene:

p + q = 1

• For example:

  • in a population of 100 individuals, there are 200 alleles

  • if there are 120 dominant (B) alleles, the frequency of the dominant allele = 120/200

  • therefore:

    • p = 120 ÷ 200 = 0.6

    • q = 1 - 0.6 = 0.4

Genotype frequencies

• Frequency of genotypes can also be represented; this is the proportion of all of the individuals with a particular genotype

• For a gene with two alleles (B and b):

  • the homozygous dominant (BB) genotype is represented by p²

  • the heterozygous genotype (Bb) is represented by 2pq

  • the homozygous recessive genotype (bb) is represented by q²

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

p² + q² + 2pq = 1