The Hardy-Weinberg equation describes allele frequencies in populations. It predicts the future genetic structure of a population the way that Punnett Squares predict the results of an individual cross. The equation calculates allele frequencies in non-evolving populations. It is based on the observation that in the absence of evolution, allele frequencies in large randomly breeding populations remain stable from generation to generation.

In real populations, evolution does occur and allele frequencies vary over time. This divergence between real, evolving populations and theoretical, non-evolving populations allows the Hardy-Weinberg equation to be used to explore the effect of evolution on populations. Two major factors that cause real populations to diverge from the equilibrium predicted by the Hardy-Weinberg equilibrium are genetic drift and natural selection.

The following illustration shows changes in actual allele frequencies over time compared to the stable structure predicted by the Hardy-Weinberg equation.

Number in first generation:

Structure of parent population:

Random

50/50 BB/bb

All Heterozygous

Random

50/50 BB/bb

All Heterozygous

Genetic drift is the random variation that results in specific individuals producing more or less offspring than predicted by chance alone. This is most pronounced in small populations and is a major reason real allele frequencies do not remain at Hardy-Weinberg equilibrium values. Genetic drift is random and as such does not result in populations becoming more adapted to their environment.:

Natural selection increases the frequency of a favored allele over another and can cause significant departures from Hardy-Weinberg equilibrium.

Assuming a trait controlled by two alleles where p is the frequency of one allele and q is the frequency of the other allele, the sum of the frequencies must equal 1:

p + q = 1

Given p and q, the Hardy-Weinberg equation is:

Where:

- p
^{2}equals the proportion of the population that is homozygous for allele 1 - q
^{2}equals the proportion of the population that is homozygous for allele 2 - 2pq is the proportion heterozygotes in the population.

The Hardy-Weinberg Equilibrium only holds if evolution is not occurring. For evolution to not occur, seven conditions need to be met:

- No mutations: changes in allele frequencies are not changing due to mutations.
- No natural selection - All genotypes have the same reproductive success.
- The population is infinitely large
- Mating is completely random
- No migration - There is no flow of genes in or out of the population due to migration.
- All individuals produce the same number of offspring.
- Generations are non-overlapping

While real populations donâ€™t maintain the stable allele frequencies predicted by the Hardy-Weinberg equilibrium, the equation can be used to determine the rates and types of evolutionary change and the types of changes occurring in a population.

Exploration of population dynamics using Hardy-Weinberg frequencies revels many patterns. For example, the Hardy-Weinberg equation shows how poorly represented alleles persist in populations and the role heterozygotes play in producing individuals with deleterious, homozygous recessive traits.

Test your understanding with the population genetics problem set

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