Question

How Do You Calculate 2Pq?

Answer 1

Hint: In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or rule, says that in the absence of additional evolutionary effects, allele and genotype frequencies in a population would stay constant from generation to generation.

Complete solution
The Hardy Weinberg equation may be used to determine allele and genotype frequencies in a population and to analyse any evolution-related changes. The anticipated genotype frequencies under random mating are\[f\left( {AA} \right){\text{ }} = \;{p^2}\;\]for the AA homozygotes,\[f\left( {aa} \right){\text{ }} = \;{q^2}\]for the aa homozygotes, and\[\;f\left( {Aa} \right){\text{ }} = {\text{ }}2pq\] for the heterozygotes in the simplest case of a single locus with two alleles labelled A and a with frequencies \[f\left( A \right){\text{ }} = \;p\] and\[f\left( a \right){\text{ }} = \;q\] , respectively. Allele frequencies p and q are constant between generations in the absence of selection, mutation, genetic drift, or other factors, indicating that equilibrium has been attained. G. H. Hardy and Wilhelm Weinberg were the first to illustrate the idea numerically. Hardy's work aimed to disprove the notion that a dominant allele would naturally rise in frequency. Hardy–Weinberg genotype frequencies tests are now largely used to look for population stratification and other non-random mating patterns.
It is given by the equation
\[{p^2} + 2pq + {q^2} = 1\]
Where
${p^2}$ = dominant homozygous frequency (AA)
2pq = heterozygous frequency (Aa)
${q^2}$ = recessive homozygous frequency (aa)
To calculate the 2Pq – frequency of Aa (heterozygous).
We use
\[{p^2} + 2pq + {q^2} = 1\]
Hence upon rearranging we get
\[1 - {p^2} - {q^2} = 2pq\]
Hence \[ \Rightarrow 2pq = 1 - {p^2} - {q^2}\]

Note:
A de Finetti diagram can be used to graphically illustrate the genotype frequency distribution for a bi-allelic locus within a population. The distribution of the three genotype frequencies in relation to each other is represented using a triangle plot (also known as trilinear, triaxial, or ternary plot). The orientation of one of the axes has been reversed, which sets it apart from many other similar plots.