Numerical Example
As an example, let's consider a population of 100 four-o-'clock plants (Mirabilis jalapa) with the following genotypes:
49 red-flowered plants with the genotype AA
42 pink-flowered plants with genotype Aa
9 white-flowered plants with genotype aa
When calculating an allele frequency for a diploid species, remember that homozygous individuals have two copies of an allele, whereas heterozygotes have only one. In our example, each of the 42 pink-flowered heterozygotes has one copy of the a allele, and each of the 9 white-flowered homozygotes has two copies. Therefore, the allele freguency for a (the white color allele) equals
This result tells us that the allele frequency of a is 0.3. In other words, 30% of the alleles for this gene in the population are the a allele.
Compare genotype frequency: let's now calculate the genotype frequency of aa homozygotes (white-flowered plants).
Allele and genotype frequencies always sum to less than or equal to one (in other words, less than or equal to 100%).
The Hardy-Weinberg law describes the relationship between allele and genotype frequencies when a population is not evolving. Let's examine the Hardy-Weinberg equation using the population of four-o'clock plants that we considered above:
if the allele A frequency is denoted by the symbol p and the allele a frequency denoted by q, then p+q=1. For example, if p=0.7, then q must be 0.3. In other words, if the allele frequency of A equals 70%, the remaining 30% of the alleles must be a, because together they equal 100%.
For a gene that exists in two alleles, the Hardy-Weinberg equation states that (p2) + (2pq) + (q2) = 1
If we apply this equation to our flower color gene, then
- (genotype frequency of homozygotes)
- (genotype frequency of heterozygotes)
- (genotype frequency of homozygotes)
If p=0.7 and q=0.3, then
- = (0.7)2 = 0.49
- = 2×(0.7)×(0.3) = 0.42
- = (0.3)2 = 0.09
This result tells us that, if the allele frequency of A is 70% and the allele frequency of a is 30%, the expected genotype frequency of AA is 49%, Aa is 42%, and aa is 9%.
Genotype frequencies may be represented by a De Finetti diagram.
Read more about this topic: Genotype Frequency
Famous quotes containing the word numerical:
“The terrible tabulation of the French statists brings every piece of whim and humor to be reducible also to exact numerical ratios. If one man in twenty thousand, or in thirty thousand, eats shoes, or marries his grandmother, then, in every twenty thousand, or thirty thousand, is found one man who eats shoes, or marries his grandmother.”
—Ralph Waldo Emerson (1803–1882)
“The moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.”
—Franklin D. Roosevelt (1882–1945)