PHG 519/EPI 516/BIOSTAT 516
Homework 5
Due 10:30am, Thursday, November 10
Two locus heterogeneity: Consider a disease that can be caused by either of two different
unlinked loci, each with a completely penetrant dominant disease allele. Use the following
notation:
Disease locus 1: alleles D and d
Disease locus 2: alleles T and t
Marker locus: alleles A and a
P(recombination between the marker locus and disease locus 1) = 0
P(recombination between the marker locus and disease locus 2) = ½
For the following two families, derive the likelihood assuming a single (common) locus is
segregating. We are interested in determining whether the marker locus is linked to the
disease locus, i.e. can we determine the truth that =0 when there is heterogeneity that is
ignored.
Segregating Locus 1 ONLY
Aa
Aa
Segregating Locus 2 ONLY
aa
aa
Aa
Aa
Aa
aa
aa
aa
1) The first family has the disease due to locus 1 and the second family has the disease due to
locus 2. However, make the false assumption that only one disease locus, disease locus 1,
is segregating in both pedigrees. Based on this assumption, determine the disease
genotypes and their phase with the marker genotypes.
2) Based on your results in (1), which of the offspring would be classified as recombinants (with
respect to the disease gene and the marker) and which would be classified as nonrecombinants?
3) Write the likelihood for each pedigree in terms of the recombination fraction . Denote these
by L1 and L2. Note that the only unknown parameter in these likelihoods is , since we are
assuming a single autosomal dominant locus controls the disease.
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4) The overall likelihood is equal to L= L1 x L2. Compute the LOD score for each of the
following values of  for testing H0: =1/2.

0
0.1
0.2
0.3
0.4
0.5
LOD
5) Is the maximum-likelihood estimate of  closest to 0, 0.1, 0.2, 0.3, 0.4, or ½? Explain.
6) Do these data suggest tight linkage between the marker and the disease locus? What is the
“moral” of this example? (Remember the “truth” as given at the beginning of the problem.)
7) Now suppose you use a genetic model of heterogeneity. In particular, assume a fraction, ,
segregate at a locus that is linked to marker locus and a fraction (1-) segregate at another
locus that is not linked to the marker. Write the likelihoods under this model.
8) Explain how to use (7) to test for linkage under the model that allows for the possibility of
heterogeneity.
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