How are two genes inherited together, and what is the basis of the 9:3:3:1 dihybrid ratio?
Explain dihybrid inheritance and the law of independent assortment, including the use of the chi-squared test
A focused answer to the H2 Biology Inheritance and Evolution outcome on dihybrid inheritance. The law of independent assortment, constructing a dihybrid cross to give the 9:3:3:1 ratio, and testing observed ratios against expected ones using the chi-squared test.
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What this dot point is asking
SEAB wants you to explain dihybrid inheritance (two genes at once), to state and apply the law of independent assortment that gives the 9:3:3:1 ratio, and to use the chi-squared test to decide whether observed results fit an expected ratio. This extends monohybrid crosses and leads into linkage.
The answer
Two genes at once
A dihybrid cross follows two genes. If they are on different chromosomes (or far apart on the same one), they are inherited independently.
The law of independent assortment
The law of independent assortment states that the alleles of one gene segregate into gametes independently of the alleles of another gene. So a TtRr individual makes four equally likely gametes: TR, Tr, tR and tr.
The 9:3:3:1 ratio
Crossing two double heterozygotes (TtRr x TtRr) and combining all sixteen gamete combinations gives a 9:3:3:1 phenotypic ratio: 9 showing both dominant traits, 3 showing the first dominant and second recessive, 3 the reverse, and 1 showing both recessive. This ratio is the signature of two independently assorting genes, each heterozygous.
The chi-squared test
Real data rarely match the expected ratio exactly. The chi-squared test decides whether the difference is due to chance:
where O is observed and E is expected. Compare the calculated value with the critical value (at degrees of freedom equal to categories minus one, usually at probability 0.05). If calculated is less than critical, the difference is not significant (the data fit the ratio); if greater, the difference is significant (the ratio does not hold, perhaps because of linkage).
Examples in context
Example 1. Mendel's pea experiments. Mendel crossed peas differing in two traits and obtained close to a 9:3:3:1 ratio, which led him to the law of independent assortment. The ratio is historically the evidence that two characteristics can be inherited independently.
Example 2. When the ratio fails. If a dihybrid cross gives a chi-squared value far above the critical value, the genes are probably linked on the same chromosome and do not assort independently. The breakdown of the expected ratio is itself informative, pointing to linkage.
Try this
Q1. State the phenotypic ratio expected from a cross between two organisms heterozygous for two unlinked genes. [1 mark]
- Cue. 9:3:3:1.
Q2. State the four types of gamete produced by an organism with genotype AaBb, assuming the genes assort independently. [1 mark]
- Cue. AB, Ab, aB and ab.
Q3. A chi-squared test gives a calculated value greater than the critical value at the 0.05 level. State the conclusion. [1 mark]
- Cue. The difference between observed and expected is significant and unlikely to be due to chance, so the data do not fit the expected ratio.
Exam-style practice questions
Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Original5 marksIn a plant, allele T (tall) is dominant to t (short) and allele R (round seed) is dominant to r (wrinkled seed). Two plants heterozygous for both genes are crossed. Construct a genetic diagram to predict the phenotypic ratio of the offspring.Show worked answer →
Examiners want the gametes, a 4 by 4 combination, and the 9:3:3:1 ratio.
Both parents have the genotype TtRr. Each produces four types of gamete in equal proportions: TR, Tr, tR and tr, because the two genes assort independently.
Combining the four gametes of one parent with the four of the other (a 4 by 4 Punnett square) gives sixteen combinations. Counting the phenotypes: 9 tall and round, 3 tall and wrinkled, 3 short and round, 1 short and wrinkled.
The expected phenotypic ratio is therefore 9:3:3:1.
Markers reward the correct four gamete types from each parent, the combination of all sixteen, and the 9:3:3:1 phenotypic ratio with the phenotypes correctly assigned.
Original5 marksA dihybrid cross is expected to give a 9:3:3:1 ratio. The observed numbers differ slightly from the expected. Describe how the chi-squared test would be used to decide whether the difference is significant, and state what conclusion a large chi-squared value would support.Show worked answer →
The answer should outline the method and the interpretation.
The chi-squared test compares observed and expected frequencies. For each category you calculate the difference between observed and expected, square it, and divide by the expected value, then sum these values across all categories to give chi-squared.
This value is compared with a critical value from a table at the appropriate degrees of freedom (the number of categories minus one) and a chosen probability level, usually 0.05.
If the calculated chi-squared is less than the critical value, the difference between observed and expected is not significant and is attributed to chance, supporting the expected ratio. If the calculated value is greater than the critical value, the difference is significant and unlikely to be due to chance alone, suggesting the genes do not assort as a simple 9:3:3:1 (for example because of linkage).
Markers reward the formula in words, the comparison with a critical value at the correct degrees of freedom and probability, and the correct interpretation of a large value as a significant departure from the expected ratio.
Related dot points
- Explain monohybrid inheritance using genetic diagrams, including dominant, recessive, codominant and sex-linked alleles
A focused answer to the H2 Biology Inheritance and Evolution outcome on monohybrid inheritance. Alleles, genotype and phenotype, dominant and recessive inheritance, codominance, sex linkage, and how to construct genetic diagrams and predict ratios.
- Explain autosomal linkage, recombination by crossing over, and epistasis as causes of departure from expected ratios
A focused answer to the H2 Biology Inheritance and Evolution outcome on linkage and gene interaction. Autosomal linkage and recombination by crossing over, why linked genes give non-Mendelian ratios, and epistasis where one gene masks another.
- Explain the sources of genetic variation: mutation, meiosis (crossing over and independent assortment) and random fertilisation
A focused answer to the H2 Biology Inheritance and Evolution outcome on variation. Mutation as the source of new alleles, the role of meiosis (crossing over and independent assortment) and random fertilisation in shuffling alleles, and the contrast with environmental variation.
- Use the Hardy-Weinberg principle to calculate allele and genotype frequencies and state the conditions for equilibrium
A focused answer to the H2 Biology Inheritance and Evolution outcome on population genetics. The Hardy-Weinberg equations, calculating allele and genotype frequencies including carriers, the conditions required for equilibrium, and how departures indicate evolution.