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 a cross between two double heterozygotes for two traits with complete dominance (AaBb × AaBb), state what phenotypic ratios are to be expected in the offspring and which two conditions must be met in order to obtain exactly those ratios.

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.

A pea plant with yellow, smooth seeds, of genotype AaBb, is crossed with a plant with green, wrinkled seeds (aabb). Knowing that both genes assort independently, state the gametes formed by each plant and the genotypic and phenotypic ratios of the offspring.

In pea plants, a tall stem (T) is dominant over a dwarf stem (t) and the axial position of the flowers (A) is dominant over the terminal position (a). A double heterozygous plant is crossed with a dwarf plant with terminal flowers. a) State the genotypes of both parents and the gametes each one produces. b) Determine the phenotypic ratios expected in the offspring. c) State which of Mendel's laws allows this result to be predicted and what it consists of.

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.

Two pea plants with yellow, smooth seeds are crossed and the offspring obtained has three quarters yellow seeds and one quarter green seeds, all of them smooth. Deduce, with reasoning, the genotypes of the two parents for each of the two traits.

In dogs, black hair (B) is dominant over brown (b) and short hair (L) is dominant over long hair (l). Two black, short-haired dogs, both of genotype BbLl, are crossed with each other. a) State how many types of gametes each parent produces and what they are. b) Calculate the expected proportion of black, long-haired puppies. c) Calculate the expected proportion of double heterozygous puppies.

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.

A plant with the dominant phenotype for two independent traits is subjected to a test cross and the offspring consists of four phenotypic classes in equal proportions. a) Deduce the genotype of the plant in question and justify it. b) State what offspring would have been obtained in the test cross if the plant had been homozygous dominant for both traits.

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.

A double heterozygous plant (AaBb) for two independent genes with complete dominance is self-fertilised. a) Calculate what proportion of the offspring will show the recessive phenotype for both traits. b) Calculate what proportion will show the dominant phenotype for only one trait. c) Explain what Mendel's third law (the law of independent assortment) consists of and how it relates to the previous question.

The Punnett square in the diagram represents the classic dihybrid cross ($AaBb \times AaBb$) for two independently assorting genes:

1. a) Suppose these two genes control pigment synthesis in flower petals via a metabolic pathway: the colorless precursor is converted by functional enzyme A into yellow pigment, which in turn is converted by functional enzyme B into red pigment. Recessive alleles $a$ and $b$ encode non-functional enzymes (recessive epistasis). Deduce the expected phenotypic ratios in the offspring (red, yellow, and white).
2. b) If the homozygous recessive condition for gene A ($aa$) caused embryonic lethality prior to germination, calculate what proportion of the surviving adult plants will show the dominant phenotype for both traits.
3. c) When crossing two individuals heterozygous for both genes in another species, only two phenotypic classes are obtained in the offspring in a 3:1 ratio (individuals with both dominant traits and individuals with both recessive traits). Justify the physical relationship between genes A and B on the chromosomes of this species and state the linkage phase (coupling or repulsion) of the parents.

A rabbit farm aims to establish a pure commercial breed of brown, short-haired rabbits. Black color (N) is dominant over brown (n) and short hair (R) over long hair (r), these being independent autosomal genes.

You have a black, short-haired breeding buck and three does:

• Doe 1: brown, long-haired.

• Doe 2: brown, short-haired.

• Doe 3: black, long-haired.

When crossing this buck with Doe 1, offspring of all four possible phenotypes are born in approximately equal proportions (1:1:1:1).

1. a) Deduce the genotype of the parental buck. With this information, predict the phenotypes and their proportions when crossing it with Doe 3, knowing that this doe's father was brown.
2. b) Design a strategy in a maximum of two generations (F1 and F2) to obtain brown, short-haired individuals that are pure lines for both traits, using solely the offspring of the cross between the buck and Doe 2 (whose genotype for hair length is unknown a priori).
3. c) A breeder claims that if a brown, short-haired kit resulting from the cross with Doe 2 is crossed with any black, long-haired individual and yields any long-haired kit, it is proven that the mother (Doe 2) was heterozygous. Justify whether this statement is correct or incorrect.

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.

A research team replicates Mendel's dihybrid cross with pea plants heterozygous for color (yellow A dominates over green a) and appearance (round B dominates over wrinkled b). In a sample of 1600 seeds of the offspring, they obtain the following counts: 885 yellow round, 310 green round, 295 yellow wrinkled, and 110 green wrinkled.

A member of the team states: "Since the counts are not exactly 900, 300, 300, and 100, Mendel's third law does not hold and the genes must be linked."

1. a) Refute the researcher's claim by explaining why empirical frequencies can fluctuate with respect to theoretical ones without invalidating independent assortment.
2. b) Design a test cross that allows conclusively discriminating between two alternative hypotheses: that both genes are independent or that they are completely linked (in coupling phase and without recombination). Indicate the parental genotypes and phenotypes and the expected percentages in the offspring for each hypothesis.
3. c) If a yellow and round seed from the original offspring is chosen at random and grown to be self-fertilized, calculate the probability that all of its progeny will be phenotypically uniform.

In a plant species with two independent traits showing complete dominance (flower color: red R over white r; stem length: long L over short l), two parental plants (P1 and P2) are crossed, yielding offspring with the following phenotypic ratio: 3/8 red flower and long stem, 3/8 red flower and short stem, 1/8 white flower and long stem, and 1/8 white flower and short stem.

1. a) Deduce the genotypes of P1 and P2 by analyzing the segregation of each trait separately. Justify whether there is only one possible parental genotypic combination.
2. b) From the offspring obtained, two individuals are chosen at random: a plant with red flowers and long stem and another with white flowers and short stem, and they are crossed with each other. Determine all possible phenotypic ratios that can arise in this new cross and calculate the probability of each one occurring, considering the genotypic variability of the selected red-flowered, long-stemmed parent.
3. c) Would it be possible to obtain any plant homozygous dominant for both traits (RRLL) from a single cross between any two individuals from the original offspring of P1 and P2? Justify your answer by indicating the necessary parental genotypes and the probability of obtaining it.

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.

In a plant of agronomic interest, resistance to a fungal infection (R vs. susceptibility r) and fruit shape (L for elongated fruit vs. l for round fruit) are independent traits with complete dominance. Upon self-fertilizing a double heterozygous plant (RrLl), 640 viable seeds are obtained.

1. a) A technician claims that in this offspring there will theoretically be 160 plants that can serve directly as stable pure lines for both traits. Justify whether this figure is correct, identifying all genotypes that constitute pure lines and how many individuals are expected of each.
2. b) If all adult plants with a resistant and elongated fruit phenotype are isolated and each is allowed to self-fertilize separately, predict what fraction of them will produce offspring with a 9:3:3:1 phenotypic segregation. Justify your deduction based on the genotypes present in that group.
3. c) Assume that the recessive allele r, in homozygosity (rr), causes 50 % embryonic lethality (half of the rr embryos die before the seed matures). Predict the new phenotypic ratio in the adult plants that manage to germinate and calculate how many round-fruited plants are to be expected in a sample of 640 adult plants.

Two different species of dipterans are investigated (Species 1 and Species 2), both with a chromosome complement of 2n = 4. In both species, two biallelic monogenic traits are analyzed (A/a and B/b).

When dihybrid females (AaBb) undergo a test cross with double recessive males (aabb), the following phenotypic results are recorded in the progeny:

• Species 1: 25 % AB, 25 % Ab, 25 % aB, and 25 % ab.

• Species 2: 44 % AB, 44 % ab, 6 % Ab, and 6 % aB.

Furthermore, in an anomalous strain of Species 1, it is cytologically confirmed that, during female meiosis, the pair of homologous chromosomes carrying gene A fails to separate during anaphase I, with both chromosomes migrating toward the same cell pole.

1. a) Justify the chromosomal behavior during metaphase I and anaphase I that gives rise to the proportions of Species 1, and indicate which Mendelian law is illustrated by this behavior.
2. b) Interpret the results of Species 2 by deducing the arrangement of alleles on the chromosomes of the parental females (coupling or repulsion phase), explain the meiotic mechanism that originates the minority classes, and calculate the genetic distance between both loci in centimorgans (cM).
3. c) Deduce the genetic content and chromosomal complement of the ova formed in the anomalous strain of Species 1 after the completion of meiosis, and reason which Mendelian principle is violated in this process.