Editing Quantitative genetics (section)

=== Random fertilization===

Male and female gametes within the actual fertilizing pool are considered usually to have the same frequencies for their corresponding alleles. (Exceptions have been considered.) This means that when '''''p''''' male gametes carrying the '''''A''''' allele randomly fertilize '''''p''''' female gametes carrying that same allele, the resulting zygote has genotype '''''AA''''', and, under random fertilization, the combination occurs with a frequency of '''''p''''' x '''''p''''' (= '''''p<sup>2</sup>'''''). Similarly, the zygote '''''aa''''' occurs with a frequency of '''''q<sup>2</sup>'''''. Heterozygotes ('''''Aa''''') can arise in two ways: when '''''p''''' male ('''''A''''' allele) randomly fertilize '''''q''''' female ('''''a''''' allele) gametes, and ''vice versa''. The resulting frequency for the heterozygous zygotes is thus '''''2pq'''''.<ref name="Crow & Kimura"/>{{rp|32}} Notice that such a population is never more than half heterozygous, this maximum occurring when '''p'''='''q'''= 0.5.

In summary then, under random fertilization, the zygote (genotype) frequencies are the quadratic expansion of the gametic (allelic) frequencies: <math display="inline"> (p+q)^2 = p^2 + 2pq + q^2 = 1 </math>. (The "=1" states that the frequencies are in fraction form, not percentages; and that there are no omissions within the framework proposed.)

Notice that "random fertilization" and "panmixia" are ''not'' synonyms.