8.2: Mendelian Genetics and Probability
- Page ID
- 159104
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Procedure:
- Watch the short film “The Making of the Fittest: Natural Selection in Humans” (a resource provided by HHMI BIOINTERACTIVE). While watching, pay close attention to the genetics of sickle cell trait and the connection to malaria infection.
- Answer the following questions regarding genetics, probability, and pedigrees.
- If two people with sickle cell trait have children, what is the chance that a child will have normal RBCs in both high- and low-oxygen environments? What is the chance that a child will have sickle cell disease? Write the possible genotypes in the Punnett square.
- What is the chance that a child will have sickle cell trait?
- What are the chances that these parents will have three children who are homozygous for normal RBCs? Show your work.
- What are the chances that these parents will have three children with sickle cell trait? Show your work.
- What are the chances that all three of their children will have sickle cell disease? Show your work.
- What are the chances that these parents will have two children with sickle cell trait and one with sickle cell disease? Show your work.
- An individual who has the sickle cell trait has children with a person who does not carry the HbS (sickle cell) allele.
- What are the genotypes of the parents? ___________________
- In the Punnett square, show all the possible genotypes of their children.
- What are the chances that any one of this couple’s children will have sickle cell disease?
- If this couple lives in the lowlands of East Africa, what are the chances that one of their children would be resistant to malaria if exposed to the malaria parasite?
- A woman with sickle cell disease has children with a man who has sickle cell trait. Answer the following questions:
- What are the genotypes of the parents? __________________
- What is the genetic makeup of the gametes the mother can produce? _____________
- What is the genetic makeup of the gametes the father can produce? ______________
- In the Punnett square, show all the possible genotypes of their children. Then, summarize the genotype and phenotype ratios of the offspring.
- What are the chances that any one of this couple’s children will have sickle cell disease?
- If this couple moved to an area where malaria was endemic, which of their children would be more likely to survive if infected with the parasite? Explain your answer.
In humans, ABO blood type results from multiple alleles: IA, IB, and iO. A few simple rules of blood type genetics are that:
- Two parents who are heterozygous for Type A blood and have sickle cell trait have children. Answer the following questions:
- What is the genotype of the parents? _____________________
- What are the genetic makeups of all the possible gametes they can produce:
- Complete the two-trait Punnett square to determine the frequency of the different phenotypes in the offspring. Note: Consider blood type and normal vs. mutant hemoglobin in the various phenotypes).
- Now try a different way of solving a two-trait cross. Because of Mendel’s second law of heredity (law of independent assortment), you can work with the blood type gene and the hemoglobin gene separately. Set up two one-trait crosses with the following parents: the mother is heterozygous for Type B blood and has sickle cell trait and the father has Type AB blood and also has the sickle cell trait.
- What are the chances that a child of this couple will have Type B blood and sickle cell trait?
- What are the chances that a child will have Type AB blood and will not have sickle cell disease?
- What are the chances that a child will have Type B blood and sickle cell disease?
- What are the chances that a child will have Type B blood and normal hemoglobin?
- The following pedigree traces sickle cell disease through three generations of a family. Use the pedigree to answer the following questions:
- What is the genotype of the father in the first generation? _____
- What is the genotype of the daughter in the second generation? _____
- What is the genotype of individual 3 in the second generation? How do you know?
- If the couple in the second generation has another child, what are the chances the child will have the following:
- Sickle cell disease _______
- Sickle cell trait _______
- Normal hemoglobin _______
- If the entire family moves to an area where malaria is endemic, four of the five males in the pedigree will have a genetic advantage over the other individuals in the family. Explain why this is.
- The following pedigree traces sickle cell disease through four generations of a family living in New York City. Use the pedigree to answer the following questions.
- What is the genotype of the mother in the first generation? _____
- What are the possible genotypes of the father in the first generation? ____________
- What can you say about the genotype of all the children of the couple in the first generation? Explain your answer.
- Regarding your answer to 6c, based on where the family resides, why would this genotype be considered a disadvantage?
- What are the genotypes of the parents in the third generation? Explain how you know.
- What is the possible genotype (or genotypes) of the mother in the second generation?
- If the couple in the third generation has another child, what are the child’s chances of the following?
- Having sickle cell disease _________
- Having sickle cell trait ________
- Being homozygous for normal RBCs ________
- The following pedigree traces sickle cell disease through four generations of a family living in the highlands of eastern Africa. Use the pedigree to answer the following questions:
- What are the genotypes of the following individuals?
- Individual 1: _________
- Individual 2: _________
- Individual 7: _________
- Individual 10: _________
- Individual 13: _________
- Individual 17: _________
- If individuals 13 and 14 have another child, what are the chances that the child will have sickle cell disease?
- If the same couple has three more children, what are the chances that all three children will have sickle cell disease? Show your work.
- Based on where the family lives, does the sickle cell trait off a genetic advantage? Explain.
- If individuals 8 and 9 have four more children, what are the chances that two of the children will be homozygous for normal RBCs? Explain why.
- Imagine that you are a genetic counselor, and a couple planning to start a family comes to you for information. Jerome was married before, and he and his first wife have a daughter with sickle cell disease. The brother of his current wife, Michaela, died of complications from sickle cell disease, but neither of her parents had the disease.
- Draw a pedigree representing this family. Be sure to clearly label Jerome and Michaela.
- What is the probability that Jerome and Michaela will have a baby with sickle cell disease? Note that neither Jerome nor Michaela has sickle cell disease. Explain/show your work.
- Natasha and Demarcus are planning on having children. Each has a sister with sickle cell disease. Neither Natasha nor Demarcus nor any of their parents have the disease, and none of them have been tested to see if they carry the sickle cell trait.
- Draw a pedigree representing this family. Be sure to clearly label Natasha and Demarcus.
- Based on this incomplete information, calculate the probability that, if this couple, has a child, the child will have sickle cell disease. Show your work.