# Introduction

Pedigrees have long been the backbone of statistical genetics to infer modes of inheritance for Mendelian disorders, and we’ll show later in the course that they can also be quite useful for understanding more complex traits. The first part of this assignment will focus on understanding basic pedigree analyses.

Secondly, we will examine Hardy-Weinberg equilibrium, which has historically been a means to understand alleles in a population and more recently been applied to high-throughput genotyping data for quality control.

# Problem 1

Use the pedigree shown in Figure 1 to answer the questions associated with problem 1.

(A) What is the likely form of inheritance for the trait shown on this pedigree?

(B) List the genotypes of individuals 1-5. If multiple genotypes per person are possible, list each.

(C) Assuming that the individual marked by * does not carry a causal allele, what is the probability that individual 5 will be a carrier of a causal allele?

# Problem 2

Use the pedigree shown in Figure 2 to answer the questions associated with problem 2.

(A) What is the likely form of inheritance for the trait shown on this pedigree?

(B) List the genotypes of individuals 1-5. If multiple genotypes per person are possible, list each.

(C) What is the probability that individual 5 will be a carrier of a causal allele?

(D) If individuals 2 and 3 were to have many more children, what are all of the possible genotypes of the offspring and in what proportion would they occur in?

# Problem 3

What genetic factors must be occurring for a Hardy-Weinberg equilibrium to exist?

# Problem 4

Suppose that an allele t occurs with a frequency of 0.9 in a population of Harvard students. Give the frequency of genotypes TT, Tt, and tt.

# Problem 5

Suppose that you get genotyping data for a particular variant in a cohort where 4000 individuals are genotypes for G/G, 1300 are genotyped for A/A, and 3700 are genotyped for A/G. Compute the Chi-squared statistic and p-value associated with whether this genotyped variant follows HWE. Interpret your summary statistic in the context of whether or not you believe that the variant was accurately genotyped.

# Problem 6

Suppose that you are studying a genetic disorder in homozygous recessives that causes death during the teenage years. If 10 in 10,000 newborn babies have the disease, what are the expected frequencies of the three genotypes in newborns, assuming the population is at Hardy-Weinberg equilibrium? Why is this assumption of Hardy-Weinberg equilibrium not strictly correct for this application?