IMAT Biology · Genetics and Inheritance

Pedigree Analysis and Allele Frequencies

A pedigree is a family tree of a trait: its pattern reveals how the trait is inherited, and the same reasoning scaled up to a population gives allele frequencies.

All Genetics and Inheritance notes

Why this matters

Pedigree diagrams appeared in 2013, 2014, 2019, 2021 and 2022: name the pattern a family rules out, give each person's genotype, or the chance that someone carries the allele. The 2023 ministry paper asked for an allele frequency from a short list of genotypes.

Concept 1 of 3: Reading a pedigree: symbols and the five inheritance patterns

A pedigree question is a logic puzzle. A few family events can only happen under certain patterns: two unaffected parents with an affected child, two affected parents with an unaffected child, or a father passing a trait to his son. Find one such event, and it rules whole patterns in or out.

Definition

Symbols: square = male, circle = female, filled = affected, half-filled or dotted = carrier; a horizontal line joins parents, a vertical line leads to their children; generations are numbered I, II, III.

Unaffected parents, affected child: the allele is recessive (both parents carry it).
Affected parents, unaffected child: the allele is dominant (both parents are heterozygous).
Unaffected father, affected daughter: it cannot be X-linked recessive (her father would be affected).
Affected father, affected son: it cannot be X-linked (a son gets his father's Y).
A new mutation can explain one affected person in an otherwise unaffected family.

Pattern	Typical clues	Proof or key rule
Autosomal recessive	Skips generations; both sexes equally	Two unaffected parents have an affected child
Autosomal dominant	Appears in every generation; both sexes equally	Two affected parents have an unaffected child
X-linked recessive	Mostly males; passed through unaffected carrier mothers	An affected woman's father and all her sons are affected
X-linked dominant	More females than males affected	An affected man has all daughters and no sons affected
Y-linked	Males only	Passed from father to every son

Practice this conceptself-check · 3 quick reps

An affected boy with unaffected parents fits several patterns

An affected son of two unaffected parents fits autosomal recessive (both parents carriers), X-linked recessive (carrier mother) and a new mutation. It does not fit any dominant pattern, because a dominant allele inherited from a parent would show in that parent.

Concept 2 of 3: Probabilities from a pedigree, including the two-thirds rule

First fix every genotype the family proves. Then, for people whose genotype is uncertain, use what you know about them. An unaffected child of two carriers cannot be

aa

, so only three of the four Punnett boxes remain, and two of those three are carriers. Then multiply the chances along the family line.

Definition

Write the certain genotypes first: affected people with a recessive condition are $aa$ ; their unaffected parents are $Aa$ .
Two-thirds rule: an unaffected child of two carriers is a carrier with probability $\tfrac23$ (not $\tfrac12$ ).
For X-linked recessive: the unaffected sister of an affected boy (with an unaffected father) is a carrier with probability $\tfrac12$ .
Multiply each uncertain step: $P(\text{parent 1 carrier}) \times P(\text{parent 2 carrier}) \times P(\text{child affected, if both are})$ .

Chance of an affected child from uncertain carriers

P(\text{affected child}) = P_1 \times P_2 \times \tfrac14

$P_1, P_2$ probability that each parent is a carrier
$\tfrac14$ chance two carriers have an affected child

Worked example

Cystic fibrosis is autosomal recessive. Luca is unaffected, but his sister has cystic fibrosis and his parents are unaffected. (a) What is the probability that Luca is a carrier? (b) Luca's partner is a known carrier. What is the probability that their first child has cystic fibrosis? (c) What if instead his partner is an unrelated person from a population where 1 in 25 people is a carrier?

Practice this conceptself-check · 4 quick reps

An unaffected sibling of an affected person is a carrier with 2/3, not 1/2

Of the four equally likely children of two carriers, one is

aa

. If we know the child is unaffected, that box is gone; of the three left (

AA

Aa

aA

), two are carriers. Using

\tfrac12

\tfrac14

here gives one of the wrong options.

Concept 3 of 3: Allele frequencies and the Hardy-Weinberg principle

Count alleles, not people. Every person carries two alleles of a gene, so a population of N people carries 2N alleles. The frequency of an allele is its share of those. If mating is random and nothing changes the alleles, the genotype shares in the next generation follow simply from the allele shares, like drawing two alleles at random.

Definition

Allele frequency = copies of the allele / total alleles. Each homozygote has 2 copies, each heterozygote 1.
With two alleles of frequencies $p$ and $q$ : $p + q = 1$ .
Hardy-Weinberg principle: the genotype frequencies are $p^2$ ( $AA$ ), $2pq$ ( $Aa$ ), $q^2$ ( $aa$ ), and they stay constant across generations.
It holds only if: the population is large, mating is random, and there is no mutation, no selection and no migration. A population that departs from it is evolving.
For a recessive condition, the affected share is $q^2$ , so $q = \sqrt{\text{affected share}}$ .

Hardy-Weinberg equations

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

$p$ frequency of the dominant allele $A$
$q$ frequency of the recessive allele $a$
$2pq$ frequency of heterozygotes (carriers)

Worked example

The MN blood group is controlled by two codominant alleles, M and N. A sample of 200 people contains 98 MM, 84 MN and 18 NN. Find the allele frequencies, then check whether the sample fits Hardy-Weinberg proportions.

Practice this conceptself-check · 4 quick reps

Count alleles, not individuals

The frequency of

A

is not the share of people with an

A

. Each

AA

person contributes two copies, each

Aa

one, and the total is twice the number of people. Dividing by the number of people, or counting

AA

once, gives a wrong option.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Probabilities from a pedigree, including the two-thirds rule
Chance of an affected child from uncertain carriers
$P(\text{affected child}) = P_1 \times P_2 \times \tfrac14$
Allele frequencies and the Hardy-Weinberg principle
Hardy-Weinberg equations
$p + q = 1 \qquad p^2 + 2pq + q^2 = 1$

Reference tables (1)

Reading a pedigree: symbols and the five inheritance patterns5 rows

Pattern	Typical clues	Proof or key rule
Autosomal recessive	Skips generations; both sexes equally	Two unaffected parents have an affected child
Autosomal dominant	Appears in every generation; both sexes equally	Two affected parents have an unaffected child
X-linked recessive	Mostly males; passed through unaffected carrier mothers	An affected woman's father and all her sons are affected
X-linked dominant	More females than males affected	An affected man has all daughters and no sons affected
Y-linked	Males only	Passed from father to every son

Watch out for (3)

An affected boy with unaffected parents fits several patterns
→ Reading a pedigree: symbols and the five inheritance patterns
An unaffected sibling of an affected person is a carrier with 2/3, not 1/2
→ Probabilities from a pedigree, including the two-thirds rule
Count alleles, not individuals
→ Allele frequencies and the Hardy-Weinberg principle

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