Two Tomato Crosses: Independent Assortment or Linkage?
A tomato breeder has two true-breeding lines: one is tall with red fruit, the other is short with yellow fruit. A cross of these lines produces F1 plants that are all tall with red fruit. The breeder allows F1 plants to self-pollinate and counts 540 F2 plants: 305 tall red, 98 tall yellow, 105 short red, and 32 short yellow. In a second experiment, the breeder crosses a different true-breeding tall red line with a different true-breeding short yellow line. All F1 are tall red. The F2 from these F1 plants includes 420 tall red and 140 short yellow, but no tall yellow or short red plants. The breeder wonders whether both experiments show independent assortment and whether the second result is just an unusual chance outcome. Assume the same two genes are involved in both experiments and that no lethal alleles are present.
1. Use the first experiment's F2 data to evaluate whether the two genes assort independently. Include expected numbers in your reasoning.
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For independent assortment, a dihybrid F2 cross should give a 9:3:3:1 ratio. With 540 plants, expected numbers are 9/16 × 540 = 303.75 tall red, 3/16 × 540 = 101.25 tall yellow, 101.25 short red, and 33.75 short yellow. Observed: 305, 98, 105, 32. These are very close to the expectation; the small differences are consistent with chance sampling. The observed ratio is about 9.5:3:3.3:1, not a distorted ratio such as 3:1. Therefore the first experiment supports independent assortment, meaning the two genes are likely on different chromosomes or far enough apart on the same chromosome to behave independently. The conclusion should be stated with the understanding that a statistical test would confirm whether the deviation is significant.
2. Explain the second experiment's F2 result. Does it support independent assortment? What is the most likely genetic explanation, and why is chance an unlikely explanation?
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The second F2 shows 420 tall red and 140 short yellow, a 3:1 ratio, with no tall yellow or short red. Independent assortment would predict about 315 tall red, 105 tall yellow, 105 short red, and 35 short yellow from 560 plants. Observing zero of both recombinant classes is not a small chance deviation; it suggests the two genes are inherited together. The most likely explanation is linkage: the tall and red alleles are on the same chromosome, and the short and yellow alleles are on the homologous chromosome, with little or no crossing over between them. Because the F1 produces mainly two gamete types (tall-red and short-yellow), the F2 resembles a monohybrid 3:1 ratio. Complete linkage is rare but possible if the genes are very close. A chromosomal rearrangement could also suppress recombination, but linkage is the simplest explanation.
3. The breeder selects one tall yellow F2 plant from the first experiment. Describe a test cross that could determine whether it is true-breeding, and give the expected results for both possible genotypes.
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A tall yellow F2 plant has the genotype T_yy. To test whether it is TTyy or Ttyy, cross it with a short yellow plant, ttyy, which produces only ty gametes. If the tall yellow parent is TTyy, all gametes are Ty, and all offspring will be Ttyy: tall yellow. If the parent is Ttyy, half its gametes are Ty and half are ty; the offspring will be about 1 tall yellow (Ttyy) : 1 short yellow (ttyy). The presence of any short yellow offspring proves the parent was heterozygous. Because the test cross uses a homozygous recessive parent, the offspring phenotypes directly reveal the unknown parent's gametes. The breeder should grow enough offspring to avoid a misleading small-sample result.