Haplogroup
Prediction from Y
T. Whit Athey
A new
approach to predicting the Ychromosome haplogroup from a set of Y
Introduction
Many people have taken advantage of
the availability of reasonably priced Ychromosome testing of short tandem
repeats (STRs). The resulting data can
be useful in confirming genealogical relationships between two or more
males. The set of repeat values that is
obtained for a set of Ychromosome markers is called a haplotype.
There is also considerable interest
in determining the Ychromosome haplogroup,
a group or family of Ychromosomes related by descent. Y haplogroups are determined by the pattern
of single nucleotide polymorphisms
(SNPs), which can also be tested and determined directly. However, the process of determining the
haplogroup by direct testing of SNPs can sometimes be a lengthy process. Therefore, there is considerable interest in
predicting the haplogroup from a set of
One of the major
The disadvantage of this approach is
that if no prediction can be made, then the customer gets no information, even
if it is very clear that some haplogroups could be ruled out, or that the
haplotype is probably in one of a small number of possible haplogroups. Theoretically, the most likely haplogroups
could be provided to the customer using this approach, but this is not
currently done.
Another approach is based on the
allele frequencies for each haplogroup and how well a given test haplotype fits
the pattern of alleles in each haplogroup.
This approach is outlined below and it has been implemented on a web
site since October, 2004, being used by many people. It allows any number of the FTDNA set of 37
markers to be entered, and the program returns a “goodness of fit” score for 10
haplogroups (E3a, E3b, G, I1a, I1b, I1c, J2, N3, R1a, and R1b). More than 98% of people of West European
extraction fall into one of these 10 haplogroups. While the program is known as a “predictor”
program, it really just provides information of how well the given haplotype
fits the pattern of previously reported STR values for a haplogroup.
Nomenclature
In this paper, the order of
presentation of YSTR values is that traditionally employed by FTDNA. The 37 markers presently tested by FTDNA are
the only markers for which sufficient allele frequency data are available to
make the haplogroup prediction possible.
The 37 markers, ordered as per the FTDNA convention, may be seen at the
following web site:
http://www.ftdna.com/9markers.html
Rarely, in some haplotypes, there
are extra repeat values for markers such as DYS019 (also called DYS394) and
DYS464. These were ignored for purposes
of the method described in this paper.
Methods
Let your haplotype be represented by
the set of values, {w_{j}}. This
can represent the haplotype for a set of 12, 25, 37 or any arbitrary number of
markers up to 37. For example, we could
consider the set of values that represent what FTDNA calls the “Western Atlantic
Modal Haplotype” (WAMH):
{w_{j}} = {13, 24, 14, 11, 11, 14, 12, 12, 12, 13, 13, 16}
In this case the index j runs from 1
to 12.
Let f_{ij}(x) represent the
allele frequency at the jth marker for the ith haplogroup, where x represents the
value (repeat count) of the allele.
These allele frequencies are simply determined empirically from public
databases and published haplotypes.[2] f_{ij}(x) will form a table of values
where the rows are labeled with the repeat values and the columns are labeled
with the DYS marker names. Table 1
represents an example for the R1b haplogroup, using only the first 12 markers
for simplicity. In practice, there will
be many more columns of markers, 37 in the present implementation, and there
will also be more rows required for many of the other markers. There will be a table like this for each
haplogroup in the prediction program, the haplogroups being labeled with the
index i, and the markers being labeled with the index j.
In Table 1, the values in the column
labeled with DYS426, for example, show the frequency of occurrence of the
repeat values 10, 11, 12, 13, and 14, where we see that almost all (98%) R1b
haplotypes have a repeat value of 12, with small percentages for the other four
closest values. Note also that the great
majority of the table is “empty,” or that most cells contain a frequency of
zero (showing that no haplotype has been found yet with those repeat values on
those markers).
Next we compute for the test
haplotype, the “goodness of fit” parameter for the ith haplogroup. This calculation is straightforward, but
complicated. The approach first calculates,
for a given test haplotype, the following ratio for each marker:
f_{ij}(w_{j})/ f_{ij}(w_{i,max})
where the f represents the table of
allele frequencies. That is, for the jth
marker and the ith haplogroup, we calculate the frequency from the table for
the test haplotype’s repeat value for that marker, and divide by the frequency
of the modal value for that marker (in that particular haplogroup). As an example, let’s calculate this ratio for
the fourth marker (DYS391) in the haplogroup R1b for the following test
haplotype, which has a value for DYS391 of 10:
{w_{j}} = {13, 24, 14, 10,
11, 14, 12, 12, 13, 13, 13, 16}
We look at the column in Table 1
labeled with DYS391 and go down the column to the row corresponding to repeat
value of 10, and here we find the frequency of .318. We see that this is not the modal value for
this haplogroup—11 is the modal value.
For the denominator of the ratio we are calculating, we take the
frequency of the modal value—the frequency for a value of 11, which we see is
.628. Then our ratio becomes:
f_{ij}(w_{j})/ f_{ij}(w_{i,max})
= 0.318/0.628 = 0.506
The overall “goodness of fit”
parameter for that haplogroup, is simply the geometric mean[3]
of all of these ratios (one for each marker).
The calculation of the “goodness of fit” parameter is illustrated in
detail in Table 2 for the test
haplotype above and haplogroup R1b.
Table 1
Allele Frequencies for Haplogroup
R1b
R E P E A T 
DYS Marker Number 

393 
390 
019 
391 
385a 
385b 
426 
388 
439 
389a 
392 
389b 

7 
0.0% 
0.0% 
0.0% 
0.0% 
0.1% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
8 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
9 
0.0% 
0.0% 
0.0% 
0.4% 
0.1% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
10 
0.0% 
0.0% 
0.0% 
31.8% 
2.8% 
0.0% 
0.1% 
0.0% 
0.3% 
0.1% 
0.0% 
0.0% 
11 
0.0% 
0.0% 
0.0% 
62.8% 
89.7% 
1.6% 
0.5% 
0.3% 
14.6% 
0.4% 
0.0% 
0.0% 
12 
2.0% 
0.0% 
0.0% 
4.9% 
5.9% 
1.7% 
98.0% 
98.4% 
74.1% 
3.6% 
0.6% 
0.0% 
13 
95.4% 
0.0% 
0.5% 
0.1% 
0.5% 
8.7% 
1.0% 
1.1% 
9.5% 
85.8% 
90.2% 
0.1% 
14 
2.5% 
0.0% 
93.2% 
0.0% 
0.6% 
69.2% 
0.4% 
0.2% 
1.3% 
9.8% 
8.8% 
0.0% 
15 
0.0% 
0.0% 
5.7% 
0.0% 
0.3% 
16.5% 
0.0% 
0.0% 
0.1% 
0.3% 
0.5% 
5.0% 
16 
0.0% 
0.0% 
0.4% 
0.0% 
0.0% 
2.2% 
0.0% 
0.0% 
0.1% 
0.0% 
0.0% 
79.3% 
17 
0.0% 
0.0% 
0.1% 
0.0% 
0.0% 
0.1% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
13.8% 
18 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
1.6% 
19 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.1% 
0.0% 
0.0% 
0.2% 
20 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
21 
0.0% 
0.1% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
22 
0.0% 
1.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
23 
0.0% 
28.4% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
24 
0.0% 
55.2% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
25 
0.0% 
14.6% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
26 
0.0% 
0.7% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
0.0% 
Table 2

DYS
Marker Number 
Geom Mean 


393 
390 
019 
391 
385 a 
385 b 
426 
388 
439 
389 a 
392 
389 b 

Test Haplo type 
13 
24 
14 
10 
11 
14 
12 
12 
13 
13 
13 
16 

f_{ij}(w_{j}) 
.954 
.552 
.932 
.318 
.897 
.692 
.980 
.984 
.095 
.858 
.902 
.793 

f_{ij}(w_{i,max}) 
.954 
.552 
.932 
.628 
.897 
.692 
.980 
.984 
.741 
.858 
.902 
.793 

Ratio 
1.0 
1.0 
1.0 
.506 
1.0 
1.0 
1.0 
1.0 
.128 
1.0 
1.0 
1.0 
.796 














Example Calculation
Once the “goodness of fit” parameter
is obtained, we simply multiply by 100 to get the final “score” for the
haplogroup—in this case a score of about 80.
We would expect to get such a high score for a haplotype that was only
different from the modal haplotype at two markers. If you have the modal value for a marker in a
particular haplogroup, the fraction [f_{ij}(w_{j})/ f_{ij}(w_{i
max})] will equal 1.0. So, if you
have all of your marker values on the modal values for a haplogroup, the
geometric mean of all those ones will just be one (which when multiplied by 100
will yield a fitness score of 100).
As a practical computational matter,
it is more convenient to perform the calculation of the geometric mean by
instead taking the arithmetic mean of the logarithms of the ratios, and then
raising 10 to the resulting power. Using
this approach, the score for the ith haplogroup for a given haplotype can be
written as:
_{N }
{(1/N) x ∑ log [f_{ij}(w_{j})/
f_{ij}(w_{i,max})]},
F_{i} = 100 x 10 ^{j}
where N is the number of markers
considered.
A large fraction of allele frequencies
for any given haplogroup (those several repeat units off of the modal value)
will be zero, as we saw in Table 1 above.
If any of these zero values were actually used in the calculation,
finding a zero on any marker would result in the overall score for that
haplogroup being zero, regardless of how well all the other markers might
fit. Therefore, these zero allele
frequencies were set arbitrarily to 0.000001 (one chance in a million) so that
a very rare value would not totally dominate the final score. On the particular marker DYS455, the “zero”
values were set to 10^{8} rather than 10^{6}, because that
marker is fairly convincingly diagnostic for one haplogroup, I1a, and the value
for a “zero ratio” that is assigned in this case effectively weights DYS455
more highly than the others, at least for discordant values.
It is also possible to weight some
markers more heavily than others by simply counting them twice or more in the
calculation, but this has not been done in the present implementation. Presumably, it would be the slower mutating
markers that would be weighted more heavily, and these would tend to have a
sharp and tight distribution about the modal value, resulting in ratios for
nonmodal values that were very low anyway, effectively weighting more heavily
any slowmutating marker. The optimum
way to weight markers remains an open question.
Allele Frequencies
The approach to prediction of
haplogroups outlined above requires knowledge (or at least a good estimate) of
the allele frequencies for each haplogroup, which constitutes a major obstacle
to successful implementation. It was
only through the establishment of public YSTR databases, such as YSearch and
YBase, that calculation of the allele frequencies for several haplogroups became
possible. These public databases usually
have included a field for the haplogroup, which were obtained primarily from
the FTDNA/UAZ prediction algorithm.
Therefore, a major part of the implementation of the allele frequency
approach for haplogroup prediction, must include the development of a database
of haplotypes from members of single haplogroups.
In identifying and collecting
haplotypes for a single haplogroup, it has sometimes been possible to collect
haplotypes by searching the public databases using a minimal modal haplotype
for a haplogroup (obtained from published studies). This approach can identify haplotypes that
match the minimal search criteria, but which also contain 25 or 37 markers. The YSTR (minimal) haplotypes that have been
published (Behar et al. 2000; Behar et al. 2004; Bosch et al. 2001; Butler et
al. 2002; Capelli et al. 2003; Cinnioglu et al. 2004; DiGiacomo et al. 2004;
Kivisild et al. 2003; Rootsi et al. 2004) as belonging to a particular
haplogroup, confirmed by SNP testing, were also added to the database and these
contributed to the allele frequencies for those few markers.
For the special case of haplogroup
I1a, every haplotype so far identified as I1a, has had a DYS455 value of 8 (or
rarely, 7 or 9, but never 10 or higher).
This allowed a convenient method for identifying I1a haplotypes in the
databases.
When compiling a set of haplotypes
from one haplogroup for use in determining the allele frequencies, one is
likely to find that there are several haplotypes that have the same
surname. This is because a large
fraction of people who are tested for YSTR values are tested through a surname
project, and individuals tested may share a common ancestor within the last few
hundred years. Such haplotypes from the
same surname will likely be much more similar (or may even be identical) than
two haplotypes of different surnames.
Therefore, in compiling the database for determining the allele
frequencies, an effort was made to avoid including haplotypes from the same
surname, except when there were several differences. Within a surname project, the matching
haplotypes were compared and a single representative one was selected for the
database. Variant values for the cluster
of haplotypes were included as a single partial “haplotype” that contained only
the variant values and not the matching values.
In this way, the full extent of variation could be included without
overweighting the haplotypes in the cluster.
For some haplogroups such as N3,
there have been very few 37marker haplotypes reported. Therefore, the allele frequency distributions
for some of the markers are very rough.
If a new N3 haplotype is tested, it may have a value that has not been
previously reported, causing abnormally low scores to be reported for the N3
haplogroup. Some manual “smoothing” of
the allele frequency distributions at the edges was applied to help avoid this
problem. One method for such “edge
smoothing” uses a Gaussian curve fit to the existing data. However, many of the allele frequency
distributions are obviously not Gaussian.
If the approach is applied to each “tail” of the distribution
independently, however, the approximate frequencies at the extremes can be
estimated satisfactorily.
The haplogroup predictor algorithm
has been implemented in a webbased Excel program at the following web site:
http://www.hprg.com/hapest5/ [address changed July 2008 to URL shown]
The initial version of the program
is limited to the 10 most common haplogroups in
Results
Several tests were carried out using
the haplogroup predictor on sets of haplotypes with known or predicted
haplogroups. It is important to test the
program with haplotypes that were not used in determining the allele
frequencies. This constrains the extent
of such validation testing because nearly all of the available haplotypes were
used to determine the allele frequencies.
Recently, however, additional
haplotypes have been added to YSearch that were not available at the time of
compiling of the allele frequencies.
There were sufficient numbers of haplotypes for testing purposes only
for the most common haplogroups such as R1b and I1a.
Results From Testing R1b Haplotypes
The prediction algorithm was applied
to 101 haplotypes from YSearch where the haplogroup had been indicated as R1b. Probably, nearly all of these predicted
haplogroup assignments had been provided by FTDNA. All had been tested to 37 STR markers by
FTDNA, and none of the surnames associated with these haplotypes were among
those used to calculate the allele frequencies used in the predictor
program. Nearly all were recent
additions to YSearch where the submission occurred after the original
collection of haplotypes for the calculation of allele frequencies.
The scores from the haplogroup
prediction algorithm for the R1b set of haplotypes ranged from 40 to 85 with
one exception. This one exception
resulted in a score of 4 for R1b and raises questions about whether or not the
haplotype is really in R1b. The mean of
the scores is about 65. Figure 1 shows a
frequency histogram for the 101 scores.
In all but three of the 101 cases,
the secondhighest score was for Haplogroup J2, with the three other cases
having as secondhighest scores, scores for R1a. In a few cases, the score for Haplogroup N3
came close to being the secondhighest score.
In no case did the secondhighest score exceed 26, so there was no
overlap in the distribution of scores, except for the
Figure 1 Distribution of R1b Scores for
101 R1b Haplotypes
Table 3
Unusual Values for an R1b Haplotype

3 
0 1 
3 
4 
3 
3 9 2 
3 8 9 b 
4 
4 
4 4 

C A 2 b 

4 

Unusual Haplotype 
15 
15 
15 
11 
13 
12 
18 
8 
8 
21 
14 
14 
14 
14 
21 
20 
10 
Frequency In R1b (%) 
<1 
6 
<1 
<1 
1 
1 
2 
2 
<1 
<1 
13 
1 
<1 
<1 
<1 
<1 
<1 
Modal R1b 
13 
14 
11 
12 
12 
13 
16 
9 
10 
19 
15 
15 
17 
17 
23 

11 
It is instructive to examine the R1b
haplotype that gave the low score of 4, in order to understand which marker
values are contributing the most to the low score. Table 3 shows that this haplotype has several
unusual values for the R1b haplogroup.
If there were only a few values that
were off the modal values for R1b, one could still allow the possibility that
the haplotype is R1b. The pattern of
multiple discordant values, compared to the typical values of R1b, suggests
that this haplotype might have been mislabeled.
Results from Testing Fifty I1a
Haplotypes
50 haplotypes were identified on
YSearch that had a DYS455 repeat value of 7, 8, or 9 (generally considered to
indicate membership in Haplogroup I1a), all with different surnames, and all
with surnames different from the set of haplotypes used to compute the original
allele frequencies used in the predictor program. One haplotype had a value of 9 for DYS455 and
the other 49 had the value of 8. These
were mostly recent additions to YSearch.
The haplogroup prediction program was applied to each of these 50
haplotypes and the resulting scores for ten haplogroups were compiled.
The I1a scores for the 50 haplotypes
ranged from 31 to 89, with an average score of about 65. Only four of the haplotypes had scores less
than 50. Figure 2 shows the distribution
of scores.
In all but two cases, the score for
I1a was at least twice that for any other haplogroup. The haplogroup with the second highest score
was most often J2, with I1b, I1c, and G close behind. The scores for E3a, E3b, N3, R1a and R1b were
much smaller and did not exceed 7. The
single haplotype with the value of 9 on DYS455 got a rather low score of 34,
accurately reporting that this haplotype has unusual values compared to typical
I1a haplotype.
There is considerable overlap of the
allele frequency distribution on many of the DYS markers between I1a and
J2. However, the highest score observed
for Haplogroup J2 on any of these 50 haplotypes was 34, and the mean value was
about 23.
FTDNA does not estimate the
membership in the subgroups of Haplogroup I, but only predicts overall
Haplogroup I. In YSearch, the 50
haplotypes had been labeled (by the submitter) with a haplogroup in about half
of the cases. Four had been labeled with
“I1a,” implying that the submitter had information beyond what he may have
obtained from FTDNA (or perhaps from SNP testing), 25 had been labeled with “I”
(implying that those predictions came from FTDNA), and 21 had been
Figure 2
Distribution of
I1a Scores for 50 I1a Haplotypes
labeled as “Unknown.” In five of the “Unknown” cases, the submitter
confirmed that FTDNA had not predicted a haplogroup for his haplotype, and in
seven cases, the submitter replied that FTDNA had predicted I, but for various
reasons, he had not added that information to YSearch. In the remaining nine cases, the submitter
did not respond to an inquiry.
For all but five of the 50 haplotypes,
the haplogroup predictor program reported a score above 50 (one of the five
just missed with a score of 49) and would have been predicted I1a (not just I)
by the haplogroup predictor program.
Conclusion
The allelefrequency approach to haplogroup
prediction appears to provide a powerful and robust alternative to
geneticdistance approaches.
ElectronicDatabase Information
www.ysearch.org genetic genealogy database
www.ybase.org genetic genealogy database
haplogroup
predictor
References
Address for
correspondence: T.
[1] The
genetic distance is just the sum of the differences of the repeat values on
each marker.
[2] Note
that a substantial portion of the haplogroup identifications that are reported
by the contributor to YSearch and YBase probably came originally from the
haplogroup prediction algorithm by Family Tree
[3] The geometric mean of a set of N numbers is the Nth root of the product of the N numbers.