Chapter 26, Problem 4EQ

Summary Introduction

To analyze:

On the basis of the given data of two codominant alleles of five human population:

A. The allele frequencies of 5 populations.

B. Identify populations included in Hardy-Weinberg equilibrium.

C. The populations that experienced significant intermixing because of migration.

Introduction:

Hardy-Weinberg principle proposes that allele frequencies remain constant in a few generations when the evolutionary influences are not present. This stability is called genetic equilibrium and is equal to 1. The gene pool, that is, the summation of the genes and its respective alleles in a population, also remains constant.

Explanation of Solution

The data obtained from 5 human populations are as follows:

Population	Place	MM	MN	NN
Inuit	East Greenland	83.5	15.6	0.9
Navajo Indians	New Mexico	84.5	14.4	1.1
Finns	Karajala	45.7	43.1	11.2
Russians	Moscow	39.9	44.0	16.1
Aborigines	Queensland	2.4	30.4	67.2

The Hardy-Weinberg equation helps to calculate and determine genotype frequencies in large populations that meet the requirements of equilibrium. The equation of Hardy-Weinberg is:

$\begin{array}{c}{\text{(p+q)}}^{\text{2}}\text{=1}\\ {\text{p}}^{\text{2}}{\text{+2pq+q}}^{\text{2}}\text{=1}\end{array}$

For a gene with two possible alleles, the allelic frequency is represented by p and q. In this case, p is the M allele and q is the N allele. For the MM and NN genotypes, every individual has two identical alleles, so the allelic frequency for those members can just be carried over from the genotype frequencies. For the MN genotype, half the alleles will be M and half will be N, so it needs to be split in half for each allele and then added to the frequencies from MM and NN individuals. It can be represented as:

$$ $\begin{array}{c}\text{The frequency of ‘M’ = }f(MM)+\frac{1}{2}f(MN)\\ \text{The frequency of ‘N’ = }f(NN)+\frac{1}{2}f(MN)\end{array}$

A. Here, in the question, there are five populations. The allele frequencies in five populations are as follows:

Population: Inuit

Place:East Greenland

$\begin{array}{c}\text{The frequency of 'M'}=f(MM)+\frac{1}{2}f(MN)\\ \text{The frequency of 'M'}=0.835+\frac{1}{2}(0.156)\\ \text{The frequency of 'M'}=0.835+0.078\\ \text{The frequency of 'M'}=0.913\end{array}$

$\begin{array}{c}\text{The frequency of 'N'}=f(NN)+\frac{1}{2}f(MN)\\ \text{The frequency of 'N'}=0.009+\frac{1}{2}(0.156)\\ \text{The frequency of 'N'}=0.009+0.078\\ \text{The frequency of 'N'}=0.087\end{array}$

Population: Navajo Indians

Place: New Mexico

$\begin{array}{c}\text{The frequency of 'M'}=f(MM)+\frac{1}{2}f(MN)\\ \text{The frequency of 'M'}=0.845+\frac{1}{2}(0.144)\\ \text{The frequency of 'M'}=0.845+0.072\\ \text{The frequency of 'M'}=0.917\end{array}$

$\begin{array}{c}\text{The frequency of 'N'}=f(NN)+\frac{1}{2}f(MN)\\ \text{The frequency of 'N'}=0.011+\frac{1}{2}(0.144)\\ \text{The frequency of 'N'}=0.011+0.072\\ \text{The frequency of 'N'}=0.083\end{array}$

Population: Finns

Place: Karajala

$\begin{array}{c}\text{The frequency of 'M'}=f(MM)+\frac{1}{2}f(MN)\\ \text{The frequency of 'M'}=0.457+\frac{1}{2}(0.431)\\ \text{The frequency of 'M'}=0.457+0.2155\\ \text{The frequency of 'M'}=0.6725\end{array}$

$\begin{array}{c}\text{The frequency of 'N'}=f(NN)+\frac{1}{2}f(MN)\\ \text{The frequency of 'N'}=0.112+\frac{1}{2}(0.431)\\ \text{The frequency of 'N'}=0.112+0.2155\\ \text{The frequency of 'N'}=0.3275\end{array}$

Population: Russians

Place: Moscow

$\begin{array}{c}\text{The frequency of 'M'}=f(MM)+\frac{1}{2}f(MN)\\ \text{The frequency of 'M'}=0.399+\frac{1}{2}(0.44)\\ \text{The frequency of 'M'}=0.399+0.22\\ \text{The frequency of 'M'}=0.619\end{array}$

$\begin{array}{c}\text{The frequency of 'N'}=f(NN)+\frac{1}{2}f(MN)\\ \text{The frequency of 'N'}=0.161+\frac{1}{2}(0.44)\\ \text{The frequency of 'N'}=0.161+0.22\\ \text{The frequency of 'N'}=0.383\end{array}$

Population: Aborigines

Place: Queensland

$\begin{array}{c}\text{The frequency of 'M'}=f(MM)+\frac{1}{2}f(MN)\\ \text{The frequency of 'M'}=0.024+\frac{1}{2}(0.304)\\ \text{The frequency of 'M'}=0.024+0.152\\ \text{The frequency of 'M'}=0.176\end{array}$

$\begin{array}{c}\text{The frequency of 'N'}=f(NN)+\frac{1}{2}f(MN)\\ \text{The frequency of 'N'}=0.672+\frac{1}{2}(0.304)\\ \text{The frequency of 'N'}=0.672+0.152\\ \text{The frequency of 'N'}=0.824\end{array}$

B. For the given circumstances in the question, a gene exists as two alleles: M and N. To determine if the given populations are in equilibrium, the Hardy-Weinberg equation can be used to calculate the number of individuals with each genotype.

Inuit:

$\begin{array}{c}MM={(}^{0.913}\\ MM=0.833\end{array}$

$\begin{array}{c}MN=2(0.913)(0.087)\\ MN=0.159\end{array}$

$\begin{array}{l}NN={(}^{0.087}\\ NN=0.76\end{array}$

Navajo Indians:

$\begin{array}{c}MM={(}^{0.917}\\ MM=0.84\end{array}$

$\begin{array}{c}MN=2(0.917)(0.083)\\ MN=0.159\end{array}$

$\begin{array}{l}NN={(}^{0.083}\\ NN=0.006\end{array}$

Finns:

$\begin{array}{l}MM={(}^{0.6725}\\ MM=0.452\end{array}$

$\begin{array}{c}MN=2(0.6725)(0.3275)\\ MN=0.44\end{array}$

$\begin{array}{l}NN={(}^{0.3275}\\ NN=0.107\end{array}$

Russians:

$\begin{array}{l}MM={(}^{0.619}\\ MM=0.383\end{array}$

$\begin{array}{c}MN=2(0.619)(0.383)\\ MN=0.474\end{array}$

$\begin{array}{l}NN={(}^{0.383}\\ NN=0.147\end{array}$

Aborigines:

$\begin{array}{c}MM={(}^{0.176}\\ MM=0.031\end{array}$

$\begin{array}{c}MN=2(0.176)(0.824)\\ MN=0.29\end{array}$

$\begin{array}{l}NN={(}^{0.824}\\ NN=0.679\end{array}$

In general, these values agree pretty well with the equilibrium. Thus, it can be said that all five populations are in Hardy-Weinberg equilibrium.

C. Hardy-Weinberg equilibrium is affected by several factors, which include genetic isolation, mutation, natural selection, and non-random mating. Migration or gene flow is also one of the factors that affect the Hardy-Weinberg equilibrium. It usually causes changes in the allele frequency and hence results in subtle deviations from the Hardy-Weinberg equilibrium. Based on similar allele frequencies, the Inuit and Navajo Indians appear to have interbred as well as the Finns and Russians.

Conclusion

Therefore, it can be concluded that,

A. The allelic frequencies of the five populations are:

Inuit: p = 0.913, q = 0.087

Navajo Indians: p = 0.917, q = 0.083

Finns: p = 0.6725, q = 0.3275

Russians: p = 0.619, q = 0.383

Aborigines: p = 0.176, q = 0.824

B. All the five populations are in Hardy-Weinberg equilibrium.

C. Inuit and Navajo Indian populations may have interbred, as well the Finns and Russians, due to the similarities in their allelic frequencies.