91Ó°ÊÓ

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.

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

Total number of VV population

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

Total number of homozygous recessive is.

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

Total number of vv population.

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

Total number of heterozygous dominant

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

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

Total number of heterozygous dominant (Vv)

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

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

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