Population genetics* is the study of the genetic of interbreeding populations and how they change over time.

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 don’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

- Illustrations
- Problem Sets

The relationship between allele frequencies and genotype frequencies in populations at Hardy-Weinberg Equilibrium is usually described using a trait for which there are two alleles present at the locus of interest.

This calculator demonstrates the application of the Hardy-Weinberg equations to loci with more that two alleles. Visit the genetic drift and selection illustration for more on the Hardy-Weinberg Equilibrium.

Graph:

Number of alleles:
2

p^{2} + q^{2} + 2(p)(q) = 1

Update the values by changing the the allele frequency in the blue box below the graph. The calculator has a check that prevents the allele frequences from summing to any value other than 1. To avoid having your values changed, make sure your values sum to one and enter them from top to bottoms (p then q then r ...)

**Number of genotypes for a given number of alleles**
Given n alleles at a locus, the number genotypes possible is the sum of the integers between 1 and n:

- With 2 alleles, the number of genotypes is 1 + 2 = 3
- 3 alleles there are 1 + 2 + 3 = 6 genotypes
- 4 alleles there are 1 + 2 + 3 + 4 = 10 genotypes.

The general formula for finding the sum of a set of integers from 1 to n is:

Genotypes = n * n+1 / 2

The calculator does not go beyond 5 alleles and 15 possible genotypes. However, The equation above can be used to calculate the number of genotypes for a locus with any number alleles.

If a population has 10 alleles for a specific gene, the combined, total number of homozygous and heterozygous genotypes present in the population will be:

(10 * 11) / 2 = 55

This breaks down to 10 homozygous genotypes and 45 heterozygous genotypes. The sum of the allele frequencies would still need to equal 1 :

p + q + r + s + t + u + v + w + x + y = 1

As would the sum of the genotype frequencies:

p^{2} + 2pq + 2pr + 2ps + 2pt + 2pu + 2pv + 2pw + 2px + 2py + q^{2} + 2qr + 2qs + 2qt +2qu + 2qv + 2qw + 2qx + 2qy + r^{2} + 2rs + 2rt + 2ru + 2rv + 2rw + 2rx + 2ry + s^{2} + 2st+ 2su + 2sv + 2sw + 2sx + 2sy + t^{2} + 2tu + 2tv + 2tw + 2tx + 2ty + u^{2} + 2uv + 2uw +2ux + 2uy + v^{2} + 2vw + 2vx + 2vy + w^{2} + 2wx + 2wy + x^{2} + 2xy + y^{2} = 1

- Illustrations
- Problem Sets