The Hardy Weinberg Equation

In 1908, G.H. Hardy and W. Weinberg independently suggested a scheme whereby evolution could be viewed as changes in frequency of alleles in a population of organisms. In this scheme, if A and a are alleles for a particular gene, and each diploid individual has two alleles, then p can be designated as the frequencey of the A allele and q as the frequency of the a allele. For example, in a population of 100 individuals in which 40% of the alleles are A, p would be .40. The rest of the alleles (60%) would be a and q would be equal to 0.60. p+q = 1. These are referred to as allele frequencies. The frequency of the possible diploid comibinations of these alleles: AA, Aa, or aa, is expressed as:

p² + 2pq + q² = 1.0

Hardy and Weinberg also argued that if certain conditions were met, the population's alleles and genotype frequencies will remain constant from generation to generation. These conditions are:

• the breeding population is large
• mating is random
• no mutation
• no migration
• no selection

Can you think of any population in which all five conditions would be met? Probably not. The point of the Hardy-Weinberg equilibrium is to provide a measurement by which changes in allele frequency can be measured. If the population's allele frequencies are changing, then that population is undergoing evolution. Since no population is likely to meet all five conditions, evolution is likely occurring and the hardy-weinberg equation quanitifies those changes.

How to Solve The Equation

The main point of the HW equation is to determine the number of organisms in a population that are AA, Aa, and aa for a gene, given that you have a sample population. Follow these steps to be successful at using the HW equation.

1. Determine the proportion of individuals that are homozygous recessive (aa) by dividing the number that exhibit the recessive trait by the number that is sampled. This number is q²

2. Take the square root of this number to determine q

3. To find p, subtract q from 1. Remember p + q = 1.

4. Now that you know both p and q (the allele frequencies) you can determine the number of individuals that are homozygous dominant: p^{2 (Remember this number is a proportion, so the problem may call for you to state actual number of individuals in your population. Multiply this number by your total population)}

5. You can also determine the proportion of individuals that are heterozygous by this part of the equation: 2pq = the number of heterozygous individuals.

6. Check you work by making sure that your numbers all add to 1.0.

The Hardy Weinberg principle explains why we don't always see dominant traits being most common. In humans, for instant, polydactyly (having an extra finger) is a dominant trait. However, the vast majority of humans have 5 fingers which is the recessive (aa) trait. The reasons for this may be unclear..for instance, in the past a human with extra fingers may have trouble finding a mate or even surviving if it made it difficult to perform tasks. This means that the dominant trait was selected against, though it still exists in the population. Selection may eventually change this fact, if for some reason the extra digit makes survival or reproduction easier (though not likely in this day and age).

Sometimes we see isolated populations with a skew of these principles, due to genetic drift. For instance, in isolated populations, a larger amount of people may display an uncommon trait because their gene pool is so small. If a few founding members had an allele, then all their descendents and the smaller breeding population may amplify the incidence of the trait. Polydactyly is more common in Amish populations than it is in other populations, for instance.