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Exercises using Familias[1]
Contents Exercise S1 Standard paternity case. Small example 3 Exercise S2. Paternity case. Mutation 4 Exercise S3 Cap paper challenge ("bone") 5 Exercise S4 Cap paper challenge ("grandson-grandfather") 6 Exercise S5 Standard paternity case. Essen-Möller 7 Exercise S6. Incest? 8 Exercise S7*. Mutation 10 Exercise S8* Mutation. Theoretical, requires some knowledge of probability
11 Exercise S9. Paternity case with mutation 12 Exercise S10. Sisters? 12 Exercise S11 Silent allele? 13 Exercise S12* Theta-correction. Theoretical 14 Exercise S13 Cap paper challenge ("grandson-grandfather continued") 14 Exercise S14 Further input and output options 14
The present document contains exercises for Familias. For these exercises
we will be using Familias 2.0 which can be downloaded from
http://familias.name/download.html. (Actually, this version is also called
1,97. However, there are only small changes compared to the previous
version familias 1-81.) Some suggested solutions appear in this document .
There are also some videos available. Input files used in the exercises
are here. There is little overlap between the present exercises and the
previous, appearing in the manual. In some cases, answers are given with
ridiculously many digits. This is done since the exercises also serve to
demonstrate that the program calculates correctly.[2] Exercises marked with a star (*) are more theoretical. Questions regarding
theoretical calculations, can also be skipped if the focus is on Familias.
Exercise S1 Standard paternity case. Small example
The purpose of this exercise is to consider the simplest possible paternity
case. Figure 1[3] shows a mother (undisputed), an alleged father (AF) and a
child. We consider . H1: The alleged father (AF) is the real father. (The mother is
undisputed.)
. H2: The alleged father and the child are unrelated. (The mother is
undisputed.) [pic] a) Consider first only one one autosomal locus, called S1, with alleles A,
B and C, see Figure 1. The allele frequencies are [pic] Explain why the
likelihood ratio is[pic]. How do you interpret the LR?
b) Calculate the LR using Familias.
c) There is a second autosomal locus, called S2, with alleles a, b, c and d
with allele frequencies 0.1, 0.1, 0.1 and 0.7, respectively. See Figure
1. Calculate the LR for this marker by hand. Calculate the likelihood
ratio for the two first markers using Familias.
d) It can be shown that the likelihood ratio for two first markers is
[pic]Use this to verify the Familias answer.
e) Generate a report using the Report option. Save the report file. The
report includes all input and all output. Check that the report file is
correct. In particular check that the LR for markers S1 and S2 as well as
the combined likelihood ratio is correct.
f) Save the Familias file. Exit Familias.
g) Start Familias and read the previously saved file.
h) We next consider theta-correction ([pic]-correction). For simplicity we
will only use the first marker, S1. The [pic]- parameter is called
kinship parameter in Familias and is set using the Options button in
Familias. Set the kinship parameter to[pic]=0,02. Calculate the LR for
the first marker S1. To get calculations for selected markers only, in
this case S1, use the Systems included button. Check that your answer
coincide with the following theoretical result
[pic] i) Discuss the assumptions underlying the calculations of this exercise. Exercise S2. Paternity case. Mutation
We consider a motherless paternity case, see Figure 2, with one marker,
VWA: |Allele |14 |
|D3S1358 | |
|D21S11 | |
|D18S51 | |
|D7S820 | |
|D16S539 | |
|CSF1PO | |
|F13B | |
|LPL | |
|TOTAL | | a) One of the markers, D7S820, gives a very large LR, namely 11189. What do
you think is the reason for this large LR? What is the combined LR if
marker D7S820 is removed?
[pic] Exercise S4 Cap paper challenge ("grandson-grandfather")
Two individuals, GF and GS, are submitted to the laboratory for testing. We
consider the hypotheses
. H1: GF is the grandfather of GS.
. H2: The individuals GF and GS are unrelated.
Figure 4 shows the pedigree corresponding to H1 for the first marker
(D3S1358). a) Enter the data manually into Familias and calculate the LR for the first
marker shown in Figure 4. The allele frequencies are 14: 0,122;
15:0,258;17:0,197
b) Calculate the LR based on all markers. Read input from the file
ExS4.txt.
c) For the discussion: Formulate a conclusion. In the CAP exercise it was
stated that GF and GS share the same Y-haplotype and that the frequency
of this haplotype is 0.0025. Can this information be used? [pic] Exercise S5 Standard paternity case. Essen-Möller
We revisit Exercise S1. Consider the hypotheses . H1: The alleged father (AF) is the real father. The mother is
undisputed.
. H2: The alleged father and the child are unrelated. The mother is
undisputed. Rather than calculating the LR we will now calculate the Essen-Möller index
W defined as the probability of H1 conditional on the genotypic data.
Assume apriori that the hypotheses H1 and H2 are apriori equally likely.
Then it can be shown that [pic] a) Recall that LR=20 for the first marker. Calculate W.
b) Recall that LR=200 for two markers. Calculate W.
c) In Familias, W is obtained pressing Probabilities. Use Familias to
calculate W for the two above cases.
d) For the discussion: Do you prefer LR or W?
Exercise S6. Incest?
Consider the following hypotheses . H1: AF, the father of mother (undisputed), is the father also of her
child.
. H2: An unrelated man is the father of the child. Figure 5 shows the pedigree corresponding to hypothesis H1. The allele
frequencies are [pic]
a) Use Familias to calculate the LR. Check that your result coincides with
the theoretical [pic] Does the incest influence the result LR in this
particular case?
b) The defense claims that one should rather consider the following three
hypotheses
. H1: AF, the father of mother, is the father also of her child.
. H2: An unrelated man is the father of child.
. H3: The brother of mother is the father of the child. See Figure 6. The LR can be calculated in several ways depending on the choice of the
reference. Use H2 as the reference and use Familias to calculate the LRs.
In other words, calculate
[pic]
Check that[pic]
c) When there are more than two hypotheses, as above, some prefer to rather
calculate posterior probabilities for the hypotheses. Assume that each of
the three hypotheses are equally likely and calculate the posterior
probabilities
[pic]
[pic]
[pic] Exercise S7*. Mutation
In this exercise, which extends on Exercise S2, we will try the different
mutation models.
Throughout we consider data from the system VWA: |Allele |14 |15 |16 |17 |18 |
|Mother |A1A2 |A1A2 |A2A3 |A2A3 |A2A3 |
|Sister 1 |A2A3 |A2A3 |A3A4 |A3A4 |A3A4 |
|Sister 2 |A2A3 |A2A3 |A1A3 |A1A3 |A1A3 | a) What is the LR comparing the full sisters-alternative compared to the
half-sisters-alternative?
b) For the discussion: The LR in this case does not give rise to a clear
conclusion. How many, which, further markers should be used?
Exercise S11 Silent allele? See Figure 8. This is a paternity case where there is suspicion of a silent
allele. Include a silent allele frequency of 0.05, and calculate the LR
using Familias. The allele frequencies of A and [pic]
B are both 0.1
Exercise S12* Theta-correction. Theoretical
Verify theoretically the formula in Exercise S1 h). Exercise S13 Cap paper challenge ("grandson-grandfather continued")
This exercise expands on the previous Exercise S4 by introducing theta
correction: Calculate the LR based on all markers. To save time you can
read input from the file ExS4.txt and introduce a theta (kinship-parameter)
of 0.02. (Hint: This is done in the pedigree window and in Familias 2.0 you
should press the Options button.)
Exercise S14 Further input and output options
A practical way to start work with Familias is to begin by reading a
Familias file containing the relevant database. Sometimes it is, however,
of interest to read and write databases and case data and this will be the
topic below. a) Read input from the file ExS3.txt.
b) Write the data base from the 'General DNA data' window. Call the output
file database.txt
c) Write the case data from the 'Case Related DNA Data'. Call the output
file casedata.txt.
d) Open a new, blank, project in Familias.
e) Read database.txt
f) Read casedata.txt
g) Define the pedigrees, see Exercise S3, and calculate the LR once more.
-----------------------
[1] Thore Egeland, Sept 28, 2012
Norwegian University of Life Sciences
P.O Box 5003
N-1432 Aas Norway
Thore.Egeland@umb.no
http://arken.umb.no/~theg/alcala
[2] More complete validation appears in "Validation of software for
calculating the likelihood ratio for parentage and kinship", Drábek, FSI:
Genetics, Volume 3, Issue 2, Pages 112-118, (2008).
[3] All figures are made using the R-package paramlink available from
http://cran.r-project.org/ -----------------------
father -/- mother A1/A2 sister 1 A2/A3 sister 2 A2/A3 Figure 7. H1 and H2 (right) father 1 -/- mother A1/A2 father 2 -/- sister 1 A2/A3 sister 2 A2/A3