Exercises: Mendelian crosses

In pea plants, the allele for smooth seeds (R) is dominant over that for wrinkled seeds (r). Two heterozygous plants are crossed. State the genotypes of the parents, the gametes each one produces and the expected genotypic and phenotypic ratios in the offspring.

In tomato plants, red fruit (R) is dominant over yellow (r). A homozygous red-fruited plant is crossed with a yellow-fruited plant. State the genotype and the phenotype of the whole F1 and reason whether any yellow-fruited plant can appear in it.

What is a test cross and what is it used for? Design the cross that would make it possible to find out whether a black-coated mouse (a dominant trait) is homozygous or heterozygous, stating what results you would expect in each case.

In dogs, short hair (L) is dominant over long hair (l). State all the possible genotypes of a short-haired dog and the genotype of a long-haired dog, and explain why there is no doubt about the genotype when the phenotype is recessive.

In rabbits, a black coat (N) is dominant over a brown one (n). A heterozygous male is crossed with a brown-coated female. State the ratios expected in the offspring and calculate how many rabbits of each phenotype are to be expected in a litter of 40 young.

Two pure-breeding lines of an ornamental plant, one with red flowers and one with white flowers, are crossed, and the whole F1 has red flowers. State the genotypes of the parental generation and of the F1, and the phenotypic ratios expected in the F2 obtained by self-fertilisation of the F1.

When two purple-flowered plants are crossed with each other, the offspring consists of 37 purple-flowered plants and 13 white-flowered ones. a) Deduce the genotypes of the parental plants and justify your answer from the observed ratios. b) Explain which cross you would carry out to find out whether a purple plant from the offspring is homozygous or heterozygous, stating what results would be expected in each case.

When two agouti-coated mice, heterozygous for the colour trait, are crossed with each other, a litter of 96 young is obtained. a) State how many young of each phenotype would theoretically be expected. b) In the actual litter, 68 agouti mice and 28 non-agouti mice are born: reason whether these results are compatible with the expected Mendelian ratio and what explains the small deviations from the theoretical values.

Polydactyly (having extra fingers) is due in humans to an autosomal dominant allele (P), while the normal number of fingers depends on the recessive allele (p). A heterozygous polydactylous man has children with a woman with the normal number of fingers. a) State the genotypes of both. b) Calculate the probability that their first child will be polydactylous. c) Calculate the probability that their first two children will have the normal number of fingers.

In cattle, the polled trait (hornless, P) is dominant over the presence of horns (p). A farmer acquires a polled bull with the commercial guarantee that it is homozygous dominant (PP).

1. a) Design a test cross to empirically verify the bull's homozygosity. Specify the genotype and phenotype of the cows with which it should be crossed and justify why this choice minimizes the number of crosses needed.
2. b) The farmer crosses the bull with a group of horned cows and obtains 7 calves in a row, all of them polled. Calculate the probability of having obtained this offspring if the bull were actually heterozygous (Pp) and reason whether the farmer can certify 100% that the bull is genetically pure.
3. c) Assuming that the bull is indeed homozygous (PP), in another cross this same bull mates with a polled cow whose mother was horned, giving birth to a polled calf. The farmer claims that this calf has a 0.5 probability of being homozygous. Demonstrate, by calculating the conditional probability, whether this statement is correct or false.

In a genetic counseling session, a family's history is analyzed regarding oculocutaneous albinism, an autosomal recessive condition (allele a versus normal pigmentation A).

• Seán and Aoife have normal pigmentation, but Seán's father and Aoife's mother were albino.

• Seán and Aoife have two healthy children: Cian and Niamh.

• Cian plans to have offspring with his first cousin Saoirse (daughter of a healthy sister of Aoife and a healthy man with no family history of albinism).

1. a) Draw the family pedigree using standard genetic symbols and indicate the definite or probabilistic genotype of each of the individuals mentioned.
2. b) A family member claims: "Since there was never albinism in Saoirse's paternal branch and Cian does not have it, it is impossible for their child to be born albino." Refute this argument and calculate the exact probability that Cian and Saoirse's first child will be albino.
3. c) If Cian and Saoirse were to have a first albino child, calculate and justify what the probability would be that a second child would also exhibit albinism. Explain the reason for the difference with respect to the probability calculated in the previous section.