Tomato Cross: Do the Numbers Fit Independent Assortment?
A grower crosses a true-breeding tall, red-fruited tomato with a true-breeding short, yellow-fruited tomato. All F1 plants are tall with red fruit. The grower self-pollinates the F1 and counts 160 F2 plants: 89 tall red, 31 tall yellow, 30 short red, and 10 short yellow. The grower expected a 9:3:3:1 ratio and is worried that the short yellow class is too small, suggesting the two genes are linked. A neighbouring breeder says the result is fine because “the numbers are close enough”, but the grower wants a statistical check. The grower also wants to know whether any of the tall red F2 plants can be used to produce a true-breeding tall red line, and what cross would show this.
1. Calculate the expected counts for a 9:3:3:1 ratio and perform a chi-square test. What conclusion is justified?
Read the worked answer
Total F2 = 160. Expected counts for 9:3:3:1:
- Tall red: 9/16 × 160 = 90
- Tall yellow: 3/16 × 160 = 30
- Short red: 3/16 × 160 = 30
- Short yellow: 1/16 × 160 = 10
χ² = Σ(O − E)²/E = (89 − 90)²/90 + (31 − 30)²/30 + (30 − 30)²/30 + (10 − 10)²/10 = 0.011 + 0.033 + 0 + 0 = 0.044
With 3 degrees of freedom, the 5% critical value is 7.81. Since 0.044 is far below 7.81, the data are consistent with independent assortment. The short yellow class is not significantly small. With only 160 plants, the test has limited power to detect loose linkage; it does not prove the genes are unlinked.
2. Explain why all F1 are tall red and what this indicates about dominance and the parental genotypes. Use symbols.
Read the worked answer
All F1 being tall red shows that tall is dominant to short and red is dominant to yellow. Let T = tall, t = short; R = red, r = yellow.
The true-breeding parents are TTRR × ttrr. Their gametes are TR and tr, so all F1 are TtRr and show the dominant tall red phenotype. When F1 self-pollinates, the expected F2 ratio is 9 T_R_ : 3 T_rr : 3 ttR_ : 1 ttrr if the genes assort independently. The observed 89:31:30:10 is very close to that expectation, so there is no strong evidence against independent assortment.
3. A tall red F2 plant could be TTRR, TTRr, TtRR, or TtRr. Describe a test cross and the expected offspring that would identify a true-breeding TTRR plant.
Read the worked answer
Cross the tall red F2 plant with a short yellow tester, genotype ttrr.
- If the plant is TTRR, all gametes are TR; all offspring are TtRr, so all are tall red.
- If the plant is TtRR, half its gametes are tR; half the offspring are ttRr, so short red plants appear.
- If the plant is TTRr, half its gametes are Tr; half the offspring are Ttrr, so tall yellow plants appear.
- If the plant is TtRr, the offspring show all four phenotypes in a 1:1:1:1 ratio.
A line is identified as true-breeding TTRR only if a reasonably large test-cross progeny are all tall red. Score enough offspring (for example 16–20) because small samples can hide heterozygosity by chance.