Sex-Linked Sleuth

Sex-Linked Sleuth

Two puzzles, and the same chromosome solves both. Why is a baby a boy or a girl? And why do conditions like haemophilia and red-green colour blindness run through the men of a family, appear to skip a generation, and then turn up again in a grandson? The second one is the harder question and the one worth marks at Higher tier, and it falls out of a single fact: a man has only one X chromosome, so there is nothing to mask what is written on it.

The sex chromosomes

Twenty-three pairs of chromosomes, and the last pair decides both puzzles:

Cross: XX × XY

Cross a mother (XX, down the side) with a father (XY, across the top). Fill in the four possible offspring.

• XX
• XY

Four daughters already

A couple have four daughters and would like a son. A friend tells them their chances must be better this time, since they are "due" a boy. What does the cross actually predict for their fifth child?

• A 50% chance, exactly as it was for each of the first four. Each fertilisation is a separate event, and whichever sperm happens to arrive carries no memory of the previous ones
• Better than 50%, because the odds must even out over a family
• Worse than 50%, since this couple evidently tend to produce daughters
• 25%, because there are four possible outcomes in the Punnett square and only some give a son

One X, or two

An X-linked recessive allele behaves completely differently depending on who carries it, and every feature of these conditions follows from that:

Cross: carrier mother × unaffected father

A carrier mother (X^NXⁿ, down the side) and an unaffected father (X^NY, across the top). Fill in the four possible offspring.

• XN XN
• XN Y
• XN Xn
• Xn Y

How many sons?

From that cross, what percentage of their SONS would be expected to be affected by the condition?

Sons, or children?

From the same cross, half of the sons are affected. A student writes that the couple therefore have a 50% chance of having an affected child. Why is that wrong, and what is the right figure?

• 25%. Only one of the four boxes is an affected child, because a child must be both a son and have received the recessive X. Half of children are sons, and half of those sons are affected, which is a quarter overall
• Nothing is wrong. Half the sons are affected, so half the children are
• 50% is right, but for a different reason: half the children inherit the recessive allele
• 0%, because the father is unaffected so the condition cannot be passed on

The affected father

An affected man is XⁿY, and what he passes on is fixed rather than chancy, because he has only one of each to give. No son of his can inherit it from him. A son gets his Y, and the allele is not on the Y. If a man and his son are both affected, the son got it from his mother. Every daughter of his is a carrier. A daughter gets his X, which carries the recessive allele, and she will be unaffected as long as her mother's X is normal. And that is why it seems to skip a generation. An affected grandfather passes it to all his daughters, who are carriers and show nothing at all, and each of their sons then has a 50% chance of being affected. The condition disappears for a generation and reappears in the grandsons, having travelled the whole way through women who never had it.

The grandsons

A man who is colour blind has three daughters with a woman who carries no recessive allele. None of the three daughters is colour blind. What is the risk to each of their future sons?

• Each daughter is certain to be a carrier, since she received her father's only X. So each of her sons has a 50% chance of being colour blind, depending which of her two Xs he receives
• No risk at all. None of the daughters is colour blind, so the condition has died out in this family
• 25%, since a quarter of children in an X-linked cross are affected
• Certain. The daughters carry the allele, so they must pass it to all their sons

Reading a family tree

A haemophilia pedigree, three generations, described in words. Affected individuals are shaded on a real diagram. Generation I. A man is affected. His wife is unaffected and has no family history. Their four children, two sons and two daughters, are all unaffected. Generation II. Both daughters are unaffected. One of them marries an unaffected man. Their three children include one son who is affected. What can be deduced, with certainty. The generation I father was XⁿY, so both his daughters must be carriers: each received his only X. His sons received his Y and are entirely clear, and neither they nor their descendants can inherit it from him. The generation II affected boy got his X from his mother, the carrier daughter. His father contributed a Y and is irrelevant to it. The pattern to recognise. Affected individuals are male, they are connected through unaffected women, and the condition passes from an affected man to his grandsons via his daughters, never to his own sons.

What does each genotype mean?

Which are true?

Select the THREE statements about X-linked recessive inheritance that are TRUE.

• There is no such thing as an unaffected male carrier of an X-linked recessive condition
• Every daughter of an affected man inherits the recessive allele from him
• A female can be affected, but it needs an affected father as well as a carrier mother
• An affected man passes the condition to half of his sons
• The condition genuinely disappears from a family for a generation and then re-emerges
• The mother's egg can carry either an X or a Y, which is what varies between children

Sleuth summary

Females are XX and males are XY, and since every egg carries an X it is the _____ whose gamete determines a baby's sex, in a 1:1 ratio. An X-linked recessive allele affects males far more often because a male has only one X and the Y carries _____ to mask it. A female with one recessive allele is an unaffected _____. An affected man passes the allele to every one of his daughters and to none of his _____, which is why the condition appears to skip a generation before reappearing in his grandsons.