The Pea Plant Puzzle
A student crosses two pea plants that both have purple flowers. The offspring are 78 purple and 26 white. She then crosses a purple plant from the offspring with a white plant and gets roughly equal numbers of purple and white offspring. She also notices that some offspring are short while the parents were tall. A classmate claims that because both parents were purple, all offspring should be purple, and that the appearance of white flowers shows the cross was done wrongly.
1. Use the numbers to explain the inheritance of flower colour and evaluate the classmate's claim.
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The ratio 78 purple to 26 white is very close to 3:1 (78/26 = 3). A 3:1 ratio in the offspring of two identical-looking parents is the classic result when both parents are heterozygous for a single gene with complete dominance. Let P be the purple allele and p the white allele. Both parents are Pp. Their gametes are P or p, and a Punnett square gives PP, Pp, Pp and pp in the ratio 1:2:1. PP and Pp are purple, pp is white, so the expected ratio is 3 purple to 1 white. The white offspring are not evidence of a mistake: they appear because each parent carried a hidden recessive allele. The classmate is wrong to assume that parents with the same appearance must pass on only that appearance. The result is consistent with Mendel's law of segregation.
2. The student then crosses a purple offspring with a white plant and gets about equal numbers of purple and white. Explain what this tells you about the purple parent.
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A white plant must be pp, because white is recessive and only shows when both alleles are recessive. It can pass on only p. If the purple parent were PP, all offspring would receive P and be purple. Since about half the offspring are white, the purple parent must be Pp: half its gametes carry P and half carry p. The cross Pp × pp gives Pp (purple) and pp (white) in a 1:1 ratio, which matches the result. This is a test cross: crossing an unknown dominant-looking individual with a homozygous recessive individual reveals whether the unknown is homozygous or heterozygous. The result shows the purple parent is heterozygous.
3. Explain how short offspring could appear from tall parents, and state what additional cross would confirm the explanation.
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Height is controlled by a separate gene. If tall (T) is dominant to short (t), then two tall parents that are both Tt can produce TT, Tt, Tt and tt offspring. The tt offspring are short. Short offspring appear only when both parents carry the recessive t allele, so both parents must be heterozygous. The two genes assort independently, so flower colour and height combinations appear in predictable ratios. To confirm, cross a short offspring (tt) with a tall parent of unknown genotype. If any short offspring appear, the tall parent must be Tt; if all offspring are tall, the tall parent is likely TT. This is again a test cross, and it demonstrates that recessive traits can be hidden in one generation and reappear in the next.