Chapter 21, Problem 13P

In 1927, the ophthalmologist George Waaler tested 9049 schoolboys in Oslo, Norway, for red-green color blindness and found 8324 of them to be normal and 725 to be color blind. He also tested 9072 schoolgirls and found 9032 that had normal color vision while 40 were color blind.

a.	Assuming that the same sex-linked recessive allele c causes all forms of red-green color blindness, calculate the allele frequencies of c and C (the allele for normal vision) from the data for the schoolboys. (Hint: Refer to your answer to Problem 12a.)
b.	Does Waaler’s sample demonstrate Hardy-Weinberg equilibrium for alleles of this gene? Explain your answer by describing observations that are either consistent or inconsistent with this hypothesis. On closer analysis of these schoolchildren, Waaler found that there was actually more than one c allele causing color blindness in his sample: one kind for the prot type (cp ) and one for the deuter type (cd ). (Protanopia and deuteranopia are slightly different forms of red-green color blindness.) Importantly, some of the apparently normal females in Waaler’s studies were probably of genotype cp /cd . Through further analysis of the 40 color-blind females, he found that 3 were prot (cp /cp ), and 37 were deuter (cd /cd ).
c.	Based on this new information, what are the frequencies of the cp, cd, and C alleles in the population examined by Waaler? Calculate these values as if the frequencies obey the Hardy-Weinberg equilibrium. (Note: Again, refer to your answer to Problem 12a.)
d.	Calculate the frequencies of all genotypes expected among men and women if the population is at equilibrium.
e.	Do these results make it more likely or less likely that the population in Oslo is indeed at equilibrium for red-green color blindness? Explain your reasoning.

Summary Introduction

a.

To determine:

The allele frequencies of c and C.

Introduction:

George Waaler conducted a survey on color blindness. This survey was conducted in the year 1927. Around 9049 school boys and 9072 school girls were tested during this survey. The aim of this survey was to detect the average number of boys and girls that suffered from color blindness.

Explanation of Solution

Color blindness is a recessive trait. It is an X-linked disorder. This reflects that males are hemizygous for this trait. As a result, boys are the common sufferers of color-blindness.

The given information is as follows;

$\begin{array}{rll}\text{Number of boys tested for color blindness}& =& \text{9049}\\ \text{No}\text{. of boys that do no suffered from colorblindness}& =& \text{8324}\\ \text{No}\text{. of boys that suffered from color blindness}& =& \text{725}\end{array}$

C is the allele for normal vision while c is the allele for color-blindness.

The formula to be used is as follows:

$\text{Allele frequency of genotype}=\frac{\text{No}\text{. of population with a particular genotype}}{\text{Total number of alleles}}$

Substituting the given information in the above formula:

$\begin{array}{rll}\text{Allele frequency of }C& =& \frac{\text{No}\text{. of population with genotype }C}{\text{Total population}}\\ & =& \frac{8324}{9049}\\ & =& 0.92\end{array}$

$\begin{array}{rll}\text{Allele frequency of }c& =& \frac{\text{No}\text{. of population with genotype }c}{\text{Total population}}\\ & =& \frac{725}{9049}\\ & =& 0.08\end{array}$

The allele frequencies of c and C are 0.92 and 0.08.

Summary Introduction

b.

To determine:

Whether Waaler’s sample demonstrated Hardy-Weinberg equilibrium for alleles.

Introduction:

Geoffrey H. Hardy was a scientist who proposed the concept of Hardy-Weinberg equilibrium. This concept is used to associate the allele frequency with the genotype frequency. The populations that have allele frequency and the genotypic frequency at equilibrium follow the concept of Hardy-Weinberg equilibrium.

Explanation of Solution

In case the population is at Hardy-Weinberg equilibrium, then the allele frequency of girls should be equal to the allele frequency of boys.

The given information is as follows:

$\begin{array}{rll}\text{Number of girls tested for color blindness}& =& \text{9072}\\ \text{No}\text{. of girls that do no suffered from colorblindness}& =& 9032\\ \text{No}\text{. of girls that suffered from color blindness}& =& 40\end{array}$

Thus,

$\begin{array}{rll}\text{Genotype frequencies of color blindness (}cc\text{) in girls}& =& \frac{\text{40}}{\text{9072}}\\ & =& \text{0}\text{.0044}\end{array}$

In case, the allele frequency of girls is at Hardy-Weinberg equilibrium, then

$\begin{array}{rll}\text{Allele frequency of }c& =& \sqrt{\text{Genotype frequency of }cc}\\ & =& \sqrt{\text{0}\text{.0044}}\\ & =& \text{0}\text{.066}\end{array}$

However, the allele frequency of c in boys is 0.08. This reflects that Waaler’s sample does not demonstrate Hardy-Weinberg equilibrium for alleles.

Summary Introduction

c.

To determine:

The frequencies of the c^P, c^d, and C alleles when the values of frequencies obey Hardy-Weinberg equilibrium:

Introduction:

Waaler discovered that there are two types of c alleles that are responsible for color blindness. These are prot type c allele (c^p) and deuter type c allele (c^d). The prot allele codes for protanopia color blindness while deuter allele codes for deuteranopia color blindness.

Explanation of Solution

The given information is as follows:

$\begin{array}{rll}\text{Total number of school girls that were tested}& =& \text{9072}\\ \text{No}\text{. of girls that had protanopia color blindness}& =& \text{3}\\ \text{No}\text{. of girls that had deuteranopia color blindness}& =& \text{37}\end{array}$

The people suffering from protanopia have c^pc^p while people deuteranopia has c^dc^d .

The formula to be used is as follows:

$\begin{array}{rll}\text{Frequency of a particular genotype}& =& \frac{\text{No}\text{. of people with a particular genotype}}{\text{Total number of people}}\\ \text{Frequency of allele}& =& \sqrt{\text{Frequency of genotype}}\end{array}$

$\begin{array}{rll}\text{Frequency of }{c}^p{c}^p\text{ genotype in girls}& =& \frac{\text{3}}{\text{9072}}\frac{1}{2}\\ & =& \text{3}\text{.3}\times {\text{10}}^{-\text{4}}\end{array}$

$\begin{array}{rll}\text{Frequency of }{c}^p\text{ allele}& =& \sqrt{\text{3}\text{.3}}{\text{×10}}^{-\text{4}}\\ & =& \text{0}\text{.018}\end{array}$

$\begin{array}{rll}\text{Frequency of }{c}^d{c}^d\text{ genotype in girls}& =& \frac{\text{37}}{\text{9072}}\\ & =& 0.0041\end{array}$

$\begin{array}{rll}\text{Frequency of }{c}^d\text{ allele}& =& \sqrt{0.0041}\\ & =& \text{0}\text{.064}\end{array}$

$\begin{array}{lll}\text{Allele frequency of }c& =& \text{Allele frequency of }{c}^p+\text{Allele frequency of }{c}^d\\ & =& \text{0}\text{.018}+\text{0}\text{.064}\\ & =& \text{0}\text{.082}\end{array}$

According to Hardy-Weinberg equilibrium:

$p+q=1$

Where:

p is the allele frequency of C

q is the allele frequency of c

The allele frequency of c (q) has been calculated as 0.082.

The frequency of C can be calculated by using the above formula:

$\begin{array}{rll}p& =& 1-q\\ & =& 1-0.82\\ & =& 0.918\end{array}$

Thus, frequencies of the c^P, c^d, and C alleles are 0.018, 0.064 and 0.918 respectively.

Summary Introduction

d.

To determine:

The frequencies of all genotypes if the population is at equilibrium.

Introduction

The set of the alleles in DNA that carries the information for the expression of a trait in an individual is known as its genotype. For example, genotype ‘TT’ expresses the tallness in plants.

Explanation of Solution

In case the population is at equilibrium, then the allele frequency and genotype frequencies of boys must be equal to the allele and genotype frequencies of girls.

Thus, frequencies of the c^P, c^d, and C alleles in boys are as follows:

$\begin{array}{rll}\text{Genotype frequency of }C\text{ in boys (Normal vision)}& =& \text{0}\text{.918}\\ \text{Genotype frequency of }{c}^d\text{ in boys (Color blindness vision)}& =& \text{0}\text{.064}\\ \text{Genotype frequency of }{c}^p\text{ in boys (Color blindness vision)}& =& \text{0}\text{.018}\end{array}$

The genotype frequencies in girls are as follows:

$\begin{array}{rllll}\text{Genotype frequency of }CC\text{ in girls (Normal vision)}& =& 0.92\times 0.92& =& \text{0}\text{.843}\\ \text{Genotype frequency of }C{c}^d\text{ in girls (Normal vision)}& =& 0.92\times 0.064& =& \text{0}\text{.058}\\ \text{Genotype frequency of }C{c}^p\text{ in girls (Normal vision)}& =& 0.092\times 0.018& =& \text{0}\text{.001}\end{array}$

$\begin{array}{rllll}\text{Genotype frequency of }{c}^p{c}^p\text{ in girls (Color blindness vision)}& =& 0.018\times 0.018& =& 3.3\times {10}^{-4}\\ \text{Genotype frequency of }{c}^d{c}^d\text{ in girls (Color blindness vision)}& =& 0.064\times 0.064& =& \text{0}\text{.004}\\ \text{Genotype frequency of }{c}^d{c}^p\text{ in girls (Normal vision)}& =& 0.064\times 0.018& =& \text{0}\text{.002}\end{array}$

Summary Introduction

e.

To determine:

Whether the population in Oslo is more likely or less likely at equilibrium for color blindness.

Introduction:

The survey that was conducted by George Waaler was done on the school boys and school girls of Oslo. This survey helped in understanding the importance of Hardy-Weinberg equilibrium in studying red-green color blindness.

Explanation of Solution

The allele frequency of C is same in both boys and girls. The allele frequency of c in boys is also same as the allele frequency of c in girls. The frequencies of genotypes with normal and color blind vision are same in both boys and girls. This reflects that the population in Oslo is more likely at equilibrium for color blindness.