Editing Allele frequency (section)

== Calculation of allele frequencies from genotype frequencies==
The actual frequency calculations depend on the [[ploidy]] of the species for autosomal genes.

===Monoploids===
The frequency (''p'') of an allele '''A''' is the fraction of the number of copies (''i'') of the '''A''' allele and the population or sample size (''N''), so

:<math>p = i/N.</math>

===Diploids===
If <math>f(\mathbf{AA})</math>, <math>f(\mathbf{AB})</math>, and <math>f(\mathbf{BB})</math> are the frequencies of the three genotypes at a locus with two alleles, then the frequency ''p'' of the '''A'''-allele and the frequency ''q'' of the '''B'''-allele in the population are obtained by counting alleles.<ref>{{cite web|url=https://www.ndsu.edu/pubweb/~mcclean/plsc431/popgen/popgen2.htm|title=Population and Evolutionary Genetics|website=ndsu.edu}}</ref>

:<math>p=f(\mathbf{AA})+ \frac{1}{2}f(\mathbf{AB})= \mbox{frequency of A}</math>

:<math>q=f(\mathbf{BB})+ \frac{1}{2}f(\mathbf{AB})= \mbox{frequency of B}</math>

Because ''p'' and ''q'' are the frequencies of the only two alleles present at that locus, they must sum to 1. To check this:

:<math>p+q=f(\mathbf{AA})+f(\mathbf{BB})+f(\mathbf{AB})=1</math>

:<math>q=1-p</math> and <math>p=1-q</math>

If there are more than two different allelic forms, the frequency for each allele is simply the frequency of its homozygote plus half the sum of the frequencies for all the heterozygotes in which it appears.

(For 3 alleles see {{slink|Allele|Genotype frequencies}}) <!-- this main should sync with that 'summary'  -->

Allele frequency can always be calculated from [[genotype frequency]], whereas the reverse requires that the [[Hardy–Weinberg principle|Hardy–Weinberg conditions]] of random mating apply.

====Example====
Consider a locus that carries two alleles, '''A''' and '''B'''. In a diploid population there are three possible genotypes, two [[homozygous]] genotypes ('''AA''' and '''BB'''), and one [[heterozygous]] genotype ('''AB'''). If we sample 10 individuals from the population, and we observe the genotype frequencies
# freq ('''AA''') = 6
# freq ('''AB''') = 3
# freq ('''BB''') = 1
then there are <math> 6\times2 + 3 = 15 </math> observed copies of the '''A''' allele and <math> 1\times2 + 3 = 5 </math> of the '''B''' allele, out of 20 total chromosome copies. The frequency ''p'' of the '''A''' allele is ''p'' = 15/20 = 0.75, and the frequency ''q'' of the '''B''' allele is ''q'' = 5/20 = 0.25.