Chapter 27, Problem 2EQ

You will need to refer to question 2 in More Genetic TIPS to answer this question. The gene for coat color in rabbits can exist in four alleles termed C(full coat color),  $c^{ch}$ (chinchilla),  $c^h$ (Himalayan), and c (albino). In a population of rabbits in Hardy-Weinberg equilibrium, the allele frequencies are

$C =0.34$

$c^{ch}=0.17$

$c^h=0.44$

$c =0.05$

Assume that C is dominant to the other three alleles, $c^{ch}$ is dominant to  $c^h$ and c, and  $c^h$ is dominant to c.

A. What is the frequency of albino rabbits?

B. Among 1000 rabbits, how many would you expect to have a Himalayan coat color?

C. Among 1000 rabbits, how many would be heterozygotes with a chinchilla coat color?

Summary Introduction

To review:

In a population of rabbits in Hardy-Weinberg equilibrium, determinethe:

Frequency of albino rabbits

Number of rabbits to have a Himalayan coat color

Number of rabbits to be heterozygous with a chinchilla coat color

Introduction:

The Hardy-Weinberg equilibrium is a principle, which states that in a given population, the frequency of occurrence of alleles of a gene or a locus can be determined. The frequency is supposed to remain fixed and even remain the same throughout the generation. In other words, the principle says that allele frequency in a population is stable and is constant from generation to generation.

Explanation of Solution

The Hardy- Weinberg equation in its standard form (two-allele) indicates that each individual inherits two copies of each gene, one from each parent. For a two-allele condition, it can also be expressed as ${\text{(p}+\text{q)}}^{\text{2}}=\text{1}$.

This equation can be expanded to include three or more than three alleles. For the given situation in the question, there a gene exists as four alleles: C(full coat color), c^ch (chinchilla), c^h (Himalayan), and c (albino). The allele frequency of C is designated by the letter p, c^ch by the letter q, c^h by the letter r, and c by the letter s.The allele frequencies are listed below:

$\begin{array}{l}\text{C}=\text{0}\text{.34}\\ {\text{c}}^{\text{ch}}=\text{0}\text{.17}\\ {\text{c}}^{\text{h}}=\text{0}\text{.44}\\ \text{c}=\text{0}\text{.05}\end{array}$

Under these conditions, the Hardy- Weinberg equation can be written as follows:

$\begin{array}{c}{\text{(p}}^{+}=\text{1}\\ {\text{p}}^{\text{2}}+{\text{q}}^{\text{2}}+{\text{r}}^{\text{2}}+{\text{s}}^{\text{2}}+\text{2pq}+\text{2qr}+\text{2pr}+\text{2ps}+\text{2rs}+\text{2qs}=\text{1}\end{array}$.

where,

p² is the genotype of the frequency of CC

q² is the genotype frequency of c^chc^ch

r² is the genotype frequency of c^hc^h

s² is the genotype frequency of cc

2pq is the genotype frequency of Cc^ch

2qr is the genotype frequency of c^chc^h

2pr is the genotype frequency of Cc^h

2ps is the genotype frequency of Cc

2rs is the genotype frequency of c^hc

2qs is the genotype frequency of c^chc

Now,

$\begin{array}{c}{\text{p}}^{\text{2}}\left(\text{the genotype frequency of CC, which produces full coat color}\right)={\left(\text{0}\text{.34}\right)}^{\text{2}}\\ {\text{p}}^{\text{2}}=\text{0}\text{.1156}\end{array}$

$\begin{array}{c}{\text{q}}^{\text{2}}\left({\text{the genotype frequency of c}}^{\text{ch}}{\text{c}}^{\text{ch}}\text{, which produces chinchilla coat color}\right)={\left(0.17\right)}^2\\ {\text{q}}^{\text{2}}=0.0289\end{array}$$\begin{array}{c}{r}^2\left(\text{the genotype frequency of}{\text{c}}^{\text{h}}{\text{c}}^{\text{h}}\text{, which produces Himalayan coat color}\right)={\left(0.44\right)}^2\\ r^2=0.1936\end{array}$$\begin{array}{c}{\text{s}}^{\text{2}}\text{ is the genotype frequency of cc, which produces albino coat color)}={\left(0.05\right)}^2\\ {\text{s}}^{\text{2}}=0.0025\end{array}$$\begin{array}{c}\text{2pq}\text{ (the genotype frequency of}{\text{Cc}}^{\text{ch}}\text{, which produces full coat color)}=2\left(0.34\right)\left(0.17\right)\\ \text{2pq}=0.1156\end{array}$$\begin{array}{c}{\text{2qr (the genotype frequency of c}}^{\text{ch}}{\text{c}}^{\text{h}}\text{, which produces chinchilla coat color)}=2\left(0.17\right)\left(0.44\right)\\ \text{2qr}=0.1496\end{array}$$\begin{array}{c}{\text{2pr (the genotype frequency of Cc}}^{\text{h}}\text{, which produces full coat color)}=2\left(0.34\right)\left(0.44\right)\\ \text{2pr}=0.2992\end{array}$$\begin{array}{c}\text{2ps (the genotype frequency of}\text{Cc, which produces full coat color)}=2\left(0.34\right)\left(0.05\right)\\ \text{2ps }=0.034\end{array}$

$\begin{array}{c}\text{2rs (the genotype frequency of}{\text{c}}^{\text{h}}\text{c, which produces Himalayan coat color)}=2\left(0.44\right)\left(0.05\right)\\ \text{2rs}=0.044\end{array}$ $\begin{array}{c}\text{2qs}\text{(the genotype frequency of}{\text{c}}^{\text{ch}}\text{c, which produces chinchilla coat color)}=2\left(0.17\right)\left(0.05\right)\\ \text{2qs}=0.017\end{array}$

The frequency of albino rabbits is s², which is equal to 0.0025 or 0.25%.\

$\begin{array}{c}\text{ Frequency of rabbits with Himalayan coat color}=\text{0}\text{.1936}+\text{0}\text{.044 }\\ \text{Frequency of rabbits with Himalayan coat color}=\text{0}\text{.2376 or 23}\text{.76\%}\text{.}\end{array}$

$\begin{array}{c}\text{Among 1000 rabbits, the number of rabbits with Himalayan coat color}=\text{23}\text{.76\% of 1000}\\ \text{Thus, the number of rabbits with Himalayan coat color}=\text{237}\text{.6 or 237 }\left(\text{approx}\text{.}\right)\end{array}$

C.

$\begin{array}{l}\text{Frequency of rabbits that are heterozygotes with chinchilla coat color}=\text{0}\text{.1496}+\text{0}\text{.017 }\\ \text{frequency of rabbits that are heterozygotes with chinchilla coat color}=\text{0}\text{.1666 or 16}\text{.66\% }\end{array}$

The number of rabbits that are heterozygotes with chinchilla coat color among 1000 rabbits can be calculated as follows:

$\begin{array}{c}\text{The number of rabbits that are heterozygotes with chinchilla coat color}=\text{16}\text{.66\% of 1000}\\ \text{The number of rabbits that are heterozygotes with chinchilla coat color}=\text{166}\text{.6 or 166}\left(\text{approx}\text{.}\right)\end{array}$

Conclusion

Therefore, it can be concluded that the frequency of the albino rabbits is 0.0025 or 0.25%.The number of rabbits with a Himalayan coat color would be 237 (approx.).The number of rabbits that are heterozygotes with chinchilla coat color would be 166 (approx.).