Figure $19.2$In plants, violet flower color (V) is dominant over white (v). If $p=.8$and $q=0.2$in a population of $500$plants, how many individuals would you expect to be homozygous dominant (VV), heterozygous (Vv), and homozygous recessive (vv)? How many plants would you expect to have violet flowers, and how many would have white flowers?

The Hardy- Weinberg equilibrium, model, theory, or rule is also known as the Hardy- Weinberg principle. In the absence of evolutionary effects, the frequencies of alleles and genotypes in a population will, on average, remain constant from generation to generation.

Hardy- Weinberg equation :

$p^2+2pq+q^2=1$

where,

$p^2$is frequency for homozygous genotype VV.

$q^2$is frequency for homozygous genotype vv.

$2pq$ is frequency for heterozygous genotype Vv.

For a population in genetic equilibrium :

$$\begin{gathered} p+q=1 \\ p=0.8 \\ q=0.2 \end{gathered}$$

Total number of population = $500$.

Hence, the total number of homozygous dominant.

$$\begin{gathered} p^2=0.8\times 0.8 \\ =0.64 \end{gathered}$$

Total number of VV population

$$\begin{gathered} =0.65\times 500 \\ =320 \end{gathered}$$

Total number of homozygous recessive is.

$$\begin{gathered} q^2=0.2\times 0.2 \\ =0.040 \end{gathered}$$

Total number of vv population.

$$\begin{gathered} =0.04\times 500 \\ =20 \end{gathered}$$

Total number of heterozygous dominant

Substitute $0.8$for p and $0.2$for q

$$\begin{gathered} 2pq=2\times 0.8\times 0.2 \\ =0.32 \end{gathered}$$

Total number of heterozygous dominant (Vv)

$$\begin{gathered} =0.32\times 500 \\ =160 \end{gathered}$$

As a result, the total number of violet flowers projected is :

$$\begin{gathered} =320\left(VV\right)+160\left(Vv\right) \\ =480 \end{gathered}$$

The expected total number of white flower (vv) is

$500$- number of violet flowers

$$\begin{gathered} =500-480 \\ =20 \end{gathered}$$