January 2024

Here is a problem to illustrate how the Hardy-Weinberg Principle is applied.

In a population of 130,000 special mice, green fur is dominant over orange. If there are 300 orange mice in the population of 130,000, find the following:
Frequency of green allele
Frequency of orange allele
Frequency of each genotype

p + q = 1
p² + 2 pq + q² = 1

We must start with orange as it is the recessive one. It is because, from the dominant (green) colour, it is impossible to say that it is homozygous dominant or heterozygous. Whereas only homozygous recessive has orange fur.

q² = 300/130,000 = 0.0023
q = sqrt(q²) = 0.048
p = 1 – q = 0.95

Genotype Frequencies:
homozygous dominant = p² = 0.90
Heterozygous = 2pq = 0.0456 = 0.091
Homozygous recessive = q² = 0.0023

Reference

The Hardy-Weinberg Principle: Watch your Ps and Qs: ThePenguinProf

We have seen the terms allele, dominant, recessive, genotype, phenotype, etc. Consider a population with five individuals with the following gene pairs. Assume they dictate the hair colour. So, the red gene is for red hair colour and black for black. But red is recessive, and black is dominant. That means.

red-red = red hair
red-black = black hair
black-black = black hair

So we have two people with red hair (homozygous recessive) and three with black hair (two heterozygous and one homozygous dominant).

Hardy Weinberg rule

The rule states that allele and genotype frequencies in a population will remain constant in the absence of other evolutionary processes such as migration, mutation, selection, etc.

To estimate the allele frequency, we create the gene pool, the aggregate of all alleles of the population. Our gene pool has ten alleles, with six reds and four blacks.

Let p represent the allele frequency of the dominant trait and q that of the recessive.
p = 4/10 = 0.4
q = 6/10 = 0.6
p + q = constant = 1

To estimate genotype frequency, consider the following. If we take one random gene from the pool, what is the probability that it is red? It will be q. What is the chance of picking two genes to form a homozygous recessive? It will be q x q = q². Similarly, to pull out a black followed by another black is p² and a black and a red is 2pq (black followed by red OR red followed by black; add them because of OR rule).

The genotype frequency is the sum of those three types, i.e., p² + 2 pq + q². Needless to say, that will be 1. To summarise, the following are the two governing equations.

p + q = 1
p² + 2 pq + q² = 1

We have two copies of every gene; each copy is called an allele. If both copies of alleles are the same, it’s homozygous. On the other hand, if they are different, it’s heterozygous. The terms dominant and recessive mean two different inheritance patterns of traits.

Imagine hair colour as a trait. The dominant is black, and the recessive is red. Note this doesn’t mean black hair dominates or anything like that. It only means:

black allele + black allele = black trait
black allele + red allele = black trait
red allele + red allele = red trait

Simply put, you need both the recessive alleles to get a recessive trait, whereas one dominant allele is sufficient to get the dominant trait.

Also, the allele pairs (black, black), (black, red) and (red, red) are all genotypes. On the other hand, the traits – black hair and red hair are two phenotypes. If a genotype is what your genes are, then a phenotype is what you look like!

Before Hardy and Weinberg, people used to get puzzled by the fact that the population did not end up having only the dominant traits. Their principle (developed independently) states that frequencies of alleles and genotypes in a population will remain constant over time in the absence of other evolutionary influences.