Chromosomal disorders and the chi-square idea

Too many or too few chromosomes

A chromosomal disorder is caused by the absence, the excess or the abnormal arrangement of chromosomes. The usual cause of a wrong number is non-disjunction: the chromosomes or the chromatids fail to separate during a division, and both go to the same cell.

• If it happens in meiosis I, all four gametes are abnormal: two with $n + 1$ and two with $n - 1$.
• If it happens in meiosis II, two gametes are normal and two are abnormal.

A gamete with $n + 1$ chromosomes gives a zygote with $2n + 1$ chromosomes, a trisomy. A gamete with $n - 1$ gives $2n - 1$, a monosomy. The loss or gain of single chromosomes is aneuploidy.

Down syndrome

Down syndrome is a trisomy of chromosome 21. A person has three copies of chromosome 21 and so 47 chromosomes.

• The person is short in height, with a small round head and a furrowed tongue. The mouth is partly open.
• The palm is broad and has a deep crease.
• Physical, psychomotor and mental development are slow.

The chance of Down syndrome rises with the age of the mother. A test of the fetus, called amniocentesis, can show the extra chromosome.

Klinefelter syndrome

Klinefelter syndrome is caused by an extra X chromosome, so the karyotype is 47, XXY. The person is a male with an overall masculine body, but also with some feminine traits, such as enlarged breasts. The person is sterile.

Turner syndrome

Turner syndrome is caused by the absence of one X chromosome, so the karyotype is 45, X (written XO). The person is a female. The ovaries are small and not developed, so she is sterile, and the secondary sexual characters are poorly developed.

Polyploidy

Some plants have three, four or more complete sets of chromosomes. This is polyploidy. It is often seen in plants, and it is a source of larger flowers and fruits in crops. It can happen when cytokinesis fails after the chromosomes have separated.

The chi-square idea

The chi-square test is not in the NTA syllabus, but A-Level and IB ask it, and every breeder needs it. A real cross never gives exactly 3 : 1. Is a count of 70 tall and 30 dwarf plants a fair result of a 3 : 1 cross, or does it show that the cross is not 3 : 1? The test works in three steps.

1. Work out the expected numbers from the ratio. For 100 plants, 75 tall and 25 dwarf.
2. Work out the chi-square value: $\chi^2 = \sum \dfrac{(O - E)^2}{E}$, where $O$ is the observed number and $E$ is the expected number, added over all the classes.
3. Compare it with the critical value. For two classes, the number of degrees of freedom is 1, and the value at the 5 per cent level is 3.84. If $\chi^2$ is smaller than 3.84, the difference is small enough to be chance, and the ratio fits.

For 70 tall and 30 dwarf: $\dfrac{(70 - 75)^2}{75} + \dfrac{(30 - 25)^2}{25} = 0.33 + 1.00 = 1.33$. This is below 3.84, so the ratio 3 : 1 fits.

You should see that a count of 70 or 80 tall plants fits, and that a count of 65 or 85 does not.

Try it in Python

The first program counts the gametes and zygotes of a cell with non-disjunction, and the second does a chi-square test.

Practise with new numbers

Common mistakes

• Saying that Turner syndrome is XXY. Turner is XO, with 45 chromosomes. Klinefelter is XXY, with 47.
• Mixing up trisomy and polyploidy. Trisomy is one extra chromosome. Polyploidy is a whole extra set.
• Putting per cents into the chi-square formula. Use the real numbers that you counted.
• Saying that a chi-square above the critical value proves the ratio is wrong for sure. It only means that chance alone is an unlikely reason.

Remember these

• Non-disjunction gives gametes with $n + 1$ and $n - 1$ chromosomes.
• Down syndrome: trisomy 21, 47 chromosomes. Klinefelter: 47, XXY. Turner: 45, X.
• Chi-square is the sum of $(O - E)^2 / E$. For 1 degree of freedom, the 5 per cent critical value is 3.84.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A girl has Down syndrome. How many chromosomes does she have in each body cell, and which chromosome is present three times?

2. Which gametes can give a Turner girl?

3. A male is 47, XXY. What is the syndrome, and is he fertile?

4. In a cross, the observed numbers are 40 and 60 against the expected 50 and 50. What is the chi-square value, and does the ratio fit?

5. Why does meiosis II non-disjunction give two normal gametes but meiosis I non-disjunction gives none?

References

• NCERT (2023). Biology, Textbook for Class XII, chapter 4, section on chromosomal disorders.
• Clark M. A., Douglas M. and Choi J. (2018). Biology 2e, OpenStax, chapter 13.2, Chromosomal Basis of Inherited Disorders.