2. Mendel's Laws of Inheritance

Probability and Genetics

Open Question
A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering 'rib-it rib-it' and has purple eyes. The other line croaks more softly by muttering 'knee-deep knee-deep' and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing F₁ frogs that were all utterers and had blue eyes. A large F₂ generation then yielded the following ratios:27/64 blue-eyed, 'rib-it' utterer12/64 green-eyed, 'rib-it' utterer9/64 blue-eyed, 'knee-deep' mutterer9/64 purple-eyed, 'rib-it' utterer4/64 green-eyed, 'knee-deep' mutterer3/64 purple-eyed, 'knee-deep' muttererAfter years of experiments, the geneticist isolated pure-breeding strains of all six F₂ phenotypes. Indicate the F₁ and F₂ phenotypic ratios of the following cross using these pure-breeding strains: blue-eyed, 'knee-deep' 'rib-it' utterer.
Open Question
A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering 'rib-it rib-it' and has purple eyes. The other line croaks more softly by muttering 'knee-deep knee-deep' and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing F₁ frogs that were all utterers and had blue eyes. A large F₂ generation then yielded the following ratios:27/64 blue-eyed, 'rib-it' utterer12/64 green-eyed, 'rib-it' utterer9/64 blue-eyed, 'knee-deep' mutterer9/64 purple-eyed, 'rib-it' utterer4/64 green-eyed, 'knee-deep' mutterer3/64 purple-eyed, 'knee-deep' muttererIndicate the genotypes of the six F₂ phenotypes.
Open Question
A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering 'rib-it rib-it' and has purple eyes. The other line croaks more softly by muttering 'knee-deep knee-deep' and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing F₁ frogs that were all utterers and had blue eyes. A large F₂ generation then yielded the following ratios:27/64 blue-eyed, 'rib-it' utterer12/64 green-eyed, 'rib-it' utterer9/64 blue-eyed, 'knee-deep' mutterer9/64 purple-eyed, 'rib-it' utterer4/64 green-eyed, 'knee-deep' mutterer3/64 purple-eyed, 'knee-deep' muttererAssign gene symbols for all phenotypes and indicate the genotypes of the P₁ and F₁ frogs.
Open Question
A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering 'rib-it rib-it' and has purple eyes. The other line croaks more softly by muttering 'knee-deep knee-deep' and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing F₁ frogs that were all utterers and had blue eyes. A large F₂ generation then yielded the following ratios: 27/64 blue-eyed, 'rib-it' utterer 12/64 green-eyed, 'rib-it' utterer 9/64 blue-eyed, 'knee-deep' mutterer 9/64 purple-eyed, 'rib-it' utterer 4/64 green-eyed, 'knee-deep' mutterer 3/64 purple-eyed, 'knee-deep' muttererOf these, how many are controlling eye color? How can you tell? How many are controlling croaking?
Open Question
A geneticist from an alien planet that prohibits genetic research brought with him to Earth two pure-breeding lines of frogs. One line croaks by uttering 'rib-it rib-it' and has purple eyes. The other line croaks more softly by muttering 'knee-deep knee-deep' and has green eyes. With a newfound freedom of inquiry, the geneticist mated the two types of frogs, producing F₁ frogs that were all utterers and had blue eyes. A large F₂ generation then yielded the following ratios:27/64 blue-eyed, 'rib-it' utterer12/64 green-eyed, 'rib-it' utterer9/64 blue-eyed, 'knee-deep' mutterer9/64 purple-eyed, 'rib-it' utterer4/64 green-eyed, 'knee-deep' mutterer3/64 purple-eyed, 'knee-deep' muttererHow many total gene pairs are involved in the inheritance of both traits? Support your answer.
Open Question
Alkaptonuria is an infrequent autosomal recessive condition. It is first noticed in newborns when the urine in their diapers turns black upon exposure to air. The condition is caused by the defective transport of the amino acid phenylalanine through the intestinal walls during digestion. About 4 people per 1000 are carriers of alkaptonuria.
Sara and James had never heard of alkaptonuria and were shocked to discover that their first child had the condition. Sara's sister Mary and her husband, Frank, are planning to have a family and are concerned about the possibility of alkaptonuria in one of their children.
The four adults (Sara, James, Mary, and Frank) seek information from a neighbor who is a retired physician. After discussing their family histories, the neighbor says, 'I never took genetics, but I know from my many years in practice that Sara and James are both carriers of this recessive condition. Since their first child had the condition, there is a very low chance that the next child will also have it, because the odds of having two children with a recessive condition are very low. Mary and Frank have no chance of having a child with alkaptonuria because Frank has no family history of the condition.' The two couples each have babies and both babies have alkaptonuria.

The couples are worried that one of their grandchildren will inherit alkaptonuria. How would you assess the risk that one of the offspring of a child with alkaptonuria will inherit the condition?
Open Question
Alkaptonuria is an infrequent autosomal recessive condition. It is first noticed in newborns when the urine in their diapers turns black upon exposure to air. The condition is caused by the defective transport of the amino acid phenylalanine through the intestinal walls during digestion. About 4 people per 1000 are carriers of alkaptonuria.
Sara and James had never heard of alkaptonuria and were shocked to discover that their first child had the condition. Sara's sister Mary and her husband, Frank, are planning to have a family and are concerned about the possibility of alkaptonuria in one of their children.
The four adults (Sara, James, Mary, and Frank) seek information from a neighbor who is a retired physician. After discussing their family histories, the neighbor says, 'I never took genetics, but I know from my many years in practice that Sara and James are both carriers of this recessive condition. Since their first child had the condition, there is a very low chance that the next child will also have it, because the odds of having two children with a recessive condition are very low. Mary and Frank have no chance of having a child with alkaptonuria because Frank has no family history of the condition.' The two couples each have babies and both babies have alkaptonuria.

What is the chance that the third child of Sara and James will be free of the condition?
Open Question
Alkaptonuria is an infrequent autosomal recessive condition. It is first noticed in newborns when the urine in their diapers turns black upon exposure to air. The condition is caused by the defective transport of the amino acid phenylalanine through the intestinal walls during digestion. About 4 people per 1000 are carriers of alkaptonuria.
Sara and James had never heard of alkaptonuria and were shocked to discover that their first child had the condition. Sara's sister Mary and her husband, Frank, are planning to have a family and are concerned about the possibility of alkaptonuria in one of their children.
The four adults (Sara, James, Mary, and Frank) seek information from a neighbor who is a retired physician. After discussing their family histories, the neighbor says, 'I never took genetics, but I know from my many years in practice that Sara and James are both carriers of this recessive condition. Since their first child had the condition, there is a very low chance that the next child will also have it, because the odds of having two children with a recessive condition are very low. Mary and Frank have no chance of having a child with alkaptonuria because Frank has no family history of the condition.' The two couples each have babies and both babies have alkaptonuria.

What is the probability that the second child of Mary and Frank will have alkaptonuria?
Open Question
Humans vary in many ways from one another. Among many minor phenotypic differences are the following five independently assorting traits that (sort of) have a dominant and a recessive phenotype: (1) forearm hair (alleles F and f)—the presence of hair on the forearm is dominant to the absence of hair on the forearm; (2) earlobe form (alleles E and e)—unattached earlobes are dominant to attached earlobes; (3) widow's peak (alleles W and w)—a distinct 'V' shape to the hairline at the top of the forehead is dominant to a straight hairline; (4) hitchhiker's thumb (alleles H and h)—the ability to bend the thumb back beyond vertical is dominant and the inability to do so is recessive; and (5) freckling (alleles D and d)—the appearance of freckles is dominant to the absence of freckles. In reality, the genetics of these traits are more complicated than single gene variation, but assume for the purposes of this problem that the patterns in families match those of other single-gene variants.
If a couple with the genotypes Ff Ee Ww Hh Dd and Ff Ee Ww Hh Dd have children, what is the chance the children will inherit the following characteristics?

the same phenotype as the parents
Open Question
Students taking a genetics exam were expected to answer the following question by converting data to a 'meaningful ratio' and then solving the problem. The instructor assumed that the final ratio would reflect two gene pairs, and most correct answers did. Here is the exam question: 'Flowers may be white, orange, or brown. When plants with white flowers are crossed with plants with brown flowers, all the F₁ flowers are white. For F₂ flowers, the following data were obtained: 48 white 12 orange 4 brown Convert the F₂ data to a meaningful ratio that allows you to explain the inheritance of color. Determine the number of genes involved and the genotypes that yield each phenotype.'We now have a dilemma. The data are consistent with two alternative mechanisms of inheritance. Propose an experiment that executes crosses involving the original parents that would distinguish between the two solutions proposed by the students. Explain how this experiment would resolve the dilemma.
Open Question
Students taking a genetics exam were expected to answer the following question by converting data to a 'meaningful ratio' and then solving the problem. The instructor assumed that the final ratio would reflect two gene pairs, and most correct answers did. Here is the exam question: 'Flowers may be white, orange, or brown. When plants with white flowers are crossed with plants with brown flowers, all the F₁ flowers are white. For F₂ flowers, the following data were obtained: 48 white 12 orange 4 brown Convert the F₂ data to a meaningful ratio that allows you to explain the inheritance of color. Determine the number of genes involved and the genotypes that yield each phenotype.'A number of students failed to reduce the ratio for two gene pairs as described above and solved the problem using three gene pairs. When examined carefully, their solution was deemed a valid response by the instructor. Solve the problem using three gene pairs
Open Question
Students taking a genetics exam were expected to answer the following question by converting data to a 'meaningful ratio' and then solving the problem. The instructor assumed that the final ratio would reflect two gene pairs, and most correct answers did. Here is the exam question:'Flowers may be white, orange, or brown. When plants with white flowers are crossed with plants with brown flowers, all the F₁ flowers are white. For F₂ flowers, the following data were obtained:48 white12 orange4 brownConvert the F₂ data to a meaningful ratio that allows you to explain the inheritance of color. Determine the number of genes involved and the genotypes that yield each phenotype.'Solve the problem for two gene pairs. What is the final F₂ ratio?
Open Question
Humans vary in many ways from one another. Among many minor phenotypic differences are the following five independently assorting traits that (sort of) have a dominant and a recessive phenotype: (1) forearm hair (alleles F and f)—the presence of hair on the forearm is dominant to the absence of hair on the forearm; (2) earlobe form (alleles E and e)—unattached earlobes are dominant to attached earlobes; (3) widow's peak (alleles W and w)—a distinct 'V' shape to the hairline at the top of the forehead is dominant to a straight hairline; (4) hitchhiker's thumb (alleles H and h)—the ability to bend the thumb back beyond vertical is dominant and the inability to do so is recessive; and (5) freckling (alleles D and d)—the appearance of freckles is dominant to the absence of freckles. In reality, the genetics of these traits are more complicated than single gene variation, but assume for the purposes of this problem that the patterns in families match those of other single-gene variants.
If a couple with the genotypes Ff Ee Ww Hh Dd and Ff Ee Ww Hh Dd have children, what is the chance the children will inherit the following characteristics?

four dominant traits and one recessive trait
Open Question
Humans vary in many ways from one another. Among many minor phenotypic differences are the following five independently assorting traits that (sort of) have a dominant and a recessive phenotype: (1) forearm hair (alleles F and f)—the presence of hair on the forearm is dominant to the absence of hair on the forearm; (2) earlobe form (alleles E and e)—unattached earlobes are dominant to attached earlobes; (3) widow's peak (alleles W and w)—a distinct 'V' shape to the hairline at the top of the forehead is dominant to a straight hairline; (4) hitchhiker's thumb (alleles H and h)—the ability to bend the thumb back beyond vertical is dominant and the inability to do so is recessive; and (5) freckling (alleles D and d)—the appearance of freckles is dominant to the absence of freckles. In reality, the genetics of these traits are more complicated than single gene variation, but assume for the purposes of this problem that the patterns in families match those of other single-gene variants.
If a couple with the genotypes Ff Ee Ww Hh Dd and Ff Ee Ww Hh Dd have children, what is the chance the children will inherit the following characteristics?

all recessive traits
Open Question
Humans vary in many ways from one another. Among many minor phenotypic differences are the following five independently assorting traits that (sort of) have a dominant and a recessive phenotype: (1) forearm hair (alleles F and f)—the presence of hair on the forearm is dominant to the absence of hair on the forearm; (2) earlobe form (alleles E and e)—unattached earlobes are dominant to attached earlobes; (3) widow's peak (alleles W and w)—a distinct 'V' shape to the hairline at the top of the forehead is dominant to a straight hairline; (4) hitchhiker's thumb (alleles H and h)—the ability to bend the thumb back beyond vertical is dominant and the inability to do so is recessive; and (5) freckling (alleles D and d)—the appearance of freckles is dominant to the absence of freckles. In reality, the genetics of these traits are more complicated than single gene variation, but assume for the purposes of this problem that the patterns in families match those of other single-gene variants.
If a couple with the genotypes Ff Ee Ww Hh Dd and Ff Ee Ww Hh Dd have children, what is the chance the children will inherit the following characteristics?

the genotype Ff EE Ww hh dd