Familias
is a program for computing probabilities for pedigrees. We assume one has
measured the alleles of two or more persons at some loci, and that the
frequencies and other properties of these alleles in the general population are
known. The likelihoods of different pedigrees can then be computed. If a prior
distribution on the possible pedigrees is given, the posterior is output. The
program can even generate lists of possible pedigrees, based on user input.
The data
can be input into the program
interactively and saved to a file. This file can then be loaded later. It is
also possible to read a database of allele systems and furthermore the data for
a specific case. Complete details on how this is done are provided in the
manual available from http:\\www.nr.no\familias
.
At the end,
a report giving an overview of the computation may be generated.
A standard use of the program will
consist of the following steps:
The
easiest use for the program is for standard paternity cases. However, here we
present a more complex example. A woman M has 3 sons S1, S2, and S3, and the
question is if a putative father PF is the father of all, some, or none of
these sons. DNA data is available for S1, S2, S3, and PF. Data from 8 loci is
given. In all loci, all alleles have frequency 0.05. The alleles observed in
the data are numbered 1,2,3,4. With this notation, S1, S2, S3 and PF have
observations given in the table below:
Locus |
S1 |
S2 |
S3 |
PF |
1 |
1,2 |
3,4 |
3,4 |
1,3 |
2 |
1,2 |
3 |
1,2 |
2,3 |
3 |
1,2 |
3,4 |
1,2 |
1,4 |
4 |
1,2 |
3,4 |
3,4 |
1,4 |
5 |
1,2 |
3,4 |
3 |
1,3 |
6 |
1 |
1,2 |
3 |
1,3 |
7 |
1,2 |
1,2 |
3,4 |
2,3 |
8 |
1,2 |
2,3 |
3,4 |
2,3 |
Let us
start with entering the general allele information. Click on the icon looking
like a rolled-up document, and the “General DNA Data” form appears. This form
gives an overview of the allele systems entered. To enter a new system, click
on “Add”. The “Allele system” form appears. Each of the alleles in the system
must be entered by entering a name and a frequency in the lowest fields,
followed by clicking “Add”. Fa,ilias 1.6 requires allele frequencies to sum to
1. It is convenient to add an extra allele for each system to secure that this
property holds, otherwise familias will scale the frequencies to add to 1. Note
that the tab button may be useful. When the four alleles 1,2,3,4 and an extra
allel, called, say, ‘Extra’, have been entered, click on OK, and the system
appears in the “General DNA Data” form. Continue with the other 7 systems. At
this point, it may be a good idea to save the current information entered to a
file. This is done by clicking on the floppy disc icon.
We
continue with entering the relevant persons. Start by clicking on the yellow
and green face icon. The “Persons” form appears. Write in “S1” in the “Person”
field, check “Male”, and “Is Child”. Checking the “Is Child” box guarantees
that when pedigrees are later generated, none are generated where this person
has children. The “Year of Birth” box may be left open; if a year is given, it
is only used to influence the set of pedigrees later generated. Click “Add”,
and go on to enter S2, S3, M, and PF in a similar fashion. Note the following
trick: If you enter Year of Births for M and PF that are less than 12 years
apart, no pedigrees will later be generated where one of these is a parent of
the other.
To enter
the known relations between M and her three sons, use the “Known Relations”
form, which appears by clicking the icon with the red circle and square. We
then go on to the stage where the DNA data is entered. Click on the blue lab
dish icon. The “Case-Related DNA Data” form appears. To enter data for a
person, double-click on that person. Each observation must be entered by
writing in, or choosing, the system name, and the two allele names, followed by
clicking “Add”. If only one allele has been observed for a person in a system,
that allele must be entered twice. Click “OK” when all information for this
person has been entered. You can always go back and add or remove data later.
After you have added your data, it is again smart to save the work you have
done to some file, using the “Save as” choice from the “File” menu.
We are
now ready to generate the relevant pedigrees for which we would like
likelihoods computed.
We start
by clicking on the icon with the multicolored rings, and the “Pedigrees” form
appears. One way to generate the pedigrees is to do it manually, using the
“Add” button on the “Pedigrees” form. It produces a form called “Pedigree”,
where the relationships can be entered. Extra persons needed to define specific
relationships can be entered by clicking on the “Persons” button on the form.
To avoid this manual work, we can instead use the “Generate” button on the
“Pedigrees” form. Click it, and keep the default settings of no extra males or
females. Eight pedigrees are generated, assuming you have entered the person
data as suggested above. To inspect a
pedigree, double-click on its line in the “Pedigrees” form. Note that the
number of possible pedigrees increases extremely fast with the number of extra
persons introduced. Even small numbers of extra persons can cause the program
to continue with computations for hours, and unfortunately, the only way to
stop it is to terminate the “familias” program. This is one reason why it is a
good idea to always save your data before you start the generating function.
To
compute probabilities (a prior and a posterior) for the generated set of
pedigrees, click on the “Probability” button on the “Pedigrees” form. The first
four fields have to do with how the prior is computed. The default parameters
will generate a flat prior, where all pedigrees have the same prior
probability. Reducing the “Generations parameter” towards zero will reduce
prior probability of pedigrees with many generations, and “Max generations”
may, when different from 0, reduce the possible number of generations. Reducing
the “Inbreeding parameter” reduces the prior probability of inbred pedigrees,
and similarly with the “Promiscuity parameter”. If you click “No” in the “Use
case-specific DNA data”, only the prior will be computed. If you click “Yes”,
the posterior will be computed.
We leave
the box unchanged, and just click “OK”. The posteriors are computed, and we see
that the pedigree where PF is the father of S3, but not of S1 or S2, is the
most likely. Use the “Likel” button to study the relative likelihoods of the
pedigrees, and the “scale” button to scale all values in proportion to one
chosen pedigree.
To
generate a report, click the “Report” button on the “Pedigrees” form. A box
with the contents of the report appears. Note that the report will list the
pedigrees selected in the pedigree list. In order to print it out, you must
first save it to a file, using the “Save” button at the bottom of the “Report”
form. Then, the resulting file must be opened with a separate program, e.g.,
“Word”, and edited and/or written out from that program.