Hardy Weinberg Principle

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So what do these two equation represent and how are they different?

$p + q = 1$ is an allele equation and $p^2 + 2pq + q^2 = 1$ is a genotype equation.

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What are

p

and

q

?

$p$ is the frequency of dominant allele in a population, assume allele that does not carry a disease when talking about autosomal recessive disease.

$q$ is the frequency of recessive allele in a population, assume allele that carries a disease when talking about autosomal recessive disease.

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What are

p^2 , 2pq, and, q^2

?

$p^2$ is the frequency of homozygous dominant genotype (AA) or the individuals who are healthy

$2pq$ is the frequency of heterozygous genotype (Aa) or the carrier frequency

$q^2$ is the frequency of homozygous recessive genotype (aa) or the frequency of individuals with the disease.

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What does incidence of autosomal recessive disease translate into in terms of the equation?

$q^2$

Incidence of autosomal recessive disease means percentage or fraction of people with autosomal disease which means people with the genotype qq.

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What does

q^2

given in

p^2 + 2pq + q^2 =1

represent?

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How do you approach a question that mentions Hardy Weinberg population?

Start by identifying the disease mentioned disease's pattern of inheritance if not mentioned in the question. For example, CF is autosomal recessive (most common in this type of questions)
Then write two equations in your rough paper and translate the language given in the question into the components of the equation

For example, this is how you translate:

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A healthy 34 year old 👩🏻‍🦰who is planning a pregnancy says her sister has cystic fibrosis. The incidence of CF is 1/160000 in that population. The husband is healthy. What are the chances that husband is a carrier?

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What does each color code represent?

Healthy: They can be either (AA) or (Aa), so we don't know if they are genotypically healthy or a carrier.

Cystic Fibrosis: It is a Autosomal Recessive disease. Meaning (AA) is healthy or $p^2$ is the percentage or fraction of people who are healthy, (Aa) is a carrier or $2pq$ is the percentage or fraction of people who are carrier (of course phenotypically they will be healthy) and (aa) is diseased or $q^2$ is the percentage or number of people who are healthy.

Incidence of CF is 1/160000: That means 1 in every 160000 people have CF meaning their genotype is (aa). This also means $q^2 = 1/1600000$

Carrier: (Aa) or 2pq

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How do you translate this question?

Language	equation	Value
Healthy	either 2pq or P^2
CF	AR
Incidence of CF	q^2	1/160000
Carrier	2pq	?

So the translated question becomes if $q^2$ is 1/160000 what is $2pq$ ?

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What trick do you use to solve it?

Because $q^2$ is such a small number you can assume $p$ is 1

therefore $2pq$ is 2*1*1/400 equals 1/200

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What if the question asks probability of a couple having an affected child?

💡

A healthy 34 year old 👩🏻‍🦰who is planning a pregnancy says her sister has cystic fibrosis. The incidence of CF is 1/160000 in that population. The husband is healthy. What are the chances that the child is affected?

This is a probability question so let us start by calculating it:

$P.child(aa) = P.mom(Aa) * P.dad(Aa) * 1/4$ given that both mom and dad are phenotypically healthy and the child has to be (aa) to be affected.

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Why 1/4?

Allele	A	a
A	AA	Aa
a	Aa	aa

Calculate $P.dad(Aa)$ by calculating $2pq$ like in previous example

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So if the carrier frequency is

2pq

won't the

P.mom(Aa)

be the same?

Now we know $P.dad(Aa)$ is 1/200 and $P.mom(Aa)$ is 2/3, therefore $P.child (aa)$ is 1/200*2/3*1/4

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What changes in X-linked recessive disease?

Assume there are two population. A weird male population (use only $p + q = 1$ ) and a normal female population (use only $p^2 + 2pq + q^2 = 1$ ). Find p or q values for male population and use it for female population.

Allele frequency for males becomes the disease frequency for males. Meaning for males $q = q^2$ because they have only one X-chromosome.

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What are

p

and

q

for X-linked recessive disease?

$p$ is the frequency of dominant allele in a population, assume allele that does not carry a disease when talking about X-linked recessive disease $(XY)$ this also mean frequency of male with no disease so basically $p^2$ for males but not females.

$q$ is the frequency of recessive allele in a population, assume allele that carries a disease when talking about X-linked recessive disease $(X_dY)$ this also mean frequency of male with no disease so basically $q^2$ for males but not females.

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So what are carrier males represented by?

The allele frequency for male and female are same i.e. p and q are same for both.

Hardy Weinberg Principle

Translation of Question into Hardy's equation

Punnet square

Hardy Weinberg Principle

Translation of Question into Hardy's equation

Punnet square