Dihybrid tomato counts on a farm
A farmer in Nalgonda crosses a pure-breeding tomato variety that is tall with red fruit with a pure-breeding dwarf variety with yellow fruit. All the F1 plants are tall with red fruit. He self-pollinates the F1 and raises 480 F2 plants in a field. At harvest he counts 268 tall red, 92 tall yellow, 88 dwarf red and 32 dwarf yellow. A neighbour says the results are useless because about 20 seedlings died after a heavy rain and because the numbers are not exactly in the textbook ratio. The farmer wants to know whether his data support independent assortment of the two genes, whether the dead seedlings change his conclusion, and what proportion of the tall red F2 plants will breed true for both traits if he selects them for seed production next season.
1. Work out the expected F2 numbers for a dihybrid cross and decide whether the farmer's data support independent assortment.
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One gene controls height (T/t), the other fruit colour (R/r). F1 is TtRr, so F2 should show 9 tall red : 3 tall yellow : 3 dwarf red : 1 dwarf yellow. For 480 plants: 9/16×480 = 270; 3/16×480 = 90; 3/16×480 = 90; 1/16×480 = 30. Observed 268, 92, 88, 32 - every count is within 2 of its expectation. The data are consistent with independent assortment of two genes on different chromosomes (or far apart on the same chromosome), not with linkage.
2. Do the 20 dead seedlings change the conclusion? Explain the reasoning and state the assumption involved.
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If the 20 dead seedlings are treated as part of a 500-plant population, expected survivors after random loss would be 480 × 9/16 = 270 tall red, 480 × 3/16 = 90 tall yellow, 90 dwarf red and 30 dwarf yellow - almost exactly the observed counts. So random death does not change the conclusion. It would matter only if deaths were phenotype-biased, for example if dwarf plants were more easily submerged. The farmer should check whether the dead seedlings were a random sample. The conclusion is therefore supported, with the usual sampling uncertainty.
3. What proportion of the tall red F2 plants will breed true for both traits? Show how you obtain it.
Read the worked answer
Among the 9/16 tall red F2, the genotypes are TTRR (1), TTRr (2), TtRR (2) and TtRr (4). Only TTRR breeds true for both traits, so 1 of every 9 tall red plants is pure for both. That is 1/9 ≈ 11.1%, or about 30 of the 268 tall red plants. The rest carry at least one recessive allele and will segregate when selfed.