Chapter 19, Problem 1VCQ

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?

Summary Introduction

To analyze:

To solve the genetic structure using the Hardy Weinberg principle of equilibrium theory.

Introduction:

The Hardy−Weinberg principle is also known as the Hardy−Weinberg equilibrium, model, theorem, or law. According to principle in the absence of evolutionary influences, the frequencies of allele and genotype in a population will remain constant from one generation to the next generation, hence it also referred to as neutral equilibrium some time.

Explanation of Solution

Hardy-Weinberg Equation.

  $\text{p² + 2pq + q² = 1}$.

Where,

p²  depicts the frequency for homozygous genotype VV.

q² depicts the frequency for homozygous genotype vv.

2pq depicts the frequency for heterozygous genotype Vv.

For a population in genetic equilibrium:

  $\begin{array}{l}\text{p + q = 1}\hfill \\ \text{ p = 0}\text{.8}\hfill \\ \text{ q = 0}\text{.2}\hfill \end{array}$.

  $\text{Total number of population = 500}$.

Therefore, the total number of homozygous dominant.

  $\begin{array}{l}{\text{p}}^{\text{2}}\text{= 0}\text{.8 }\times \text{ 0}\text{.8}\hfill \\ \text{= 0}\text{.64}\hfill \end{array}$.

  $\begin{array}{l}\text{Total number of VV population}\hfill \\ \text{ = 0}\text{.65 × 500}\hfill \\ \text{ = 320}\hfill \end{array}$.

Total number of homozygous recessive is.

  $\begin{array}{l}{\text{q}}^{\text{2}}\text{ = 0}\text{.2 }\times \text{ 0}\text{.2}\hfill \\ \text{ = 0}\text{.040}\hfill \end{array}$.

  $\begin{array}{l}\text{Total number of vv population}\hfill \\ \text{=0}\text{.04 ×500}\hfill \\ \text{=20}\hfill \end{array}$.

  $\begin{array}{l}\text{Total number of heterozygous dominant}\hfill \\ \text{Substitute 0}\text{.8 for p and 0}\text{.2 for q}\hfill \\ \text{2pq = 2 }\times \text{ 0}\text{.8 }\times \text{ 0}\text{.2}\hfill \\ \text{ = 0}\text{.32}\hfill \\ \text{Total number of heterozygous dominant }\left(\text{Vv}\right)\hfill \\ \text{ = 0}\text{.32 }\times \text{ 500}\hfill \\ \text{ = 160}\hfill \end{array}$.

Hence, the expected total number of the violet flower is.

  $\begin{array}{l}\text{320}\left(\text{VV}\right)\text{ +160}\left(\text{Vv}\right)\hfill \\ \text{= 480}\hfill \end{array}$.

The expected total number of white flower ( $\text{vv}$) is.

  $\begin{array}{l}\text{500}-\text{number of violet flowers}\\ \text{= 500}-480\\ \text{= 20}\end{array}$.

Conclusion

Thus, the total number of the violet flower is 480 and a total number of white flower is 20.