3 Analysis of Population Structure
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3.3.2 Formal Tests for Admixture Under a Population Tree-Model
Once we have some proposed demographic model/s, we can start estimating
demographic parameters in these models. An alternative, but not mutually exclusive,
way to proceed is to construct formal tests of these models. The proposed model is
used as a null model to make predictions, and then these predictions are compared
to the observed data in order to test if the data is consistent with the model. A
recent suite of tests along these lines is the 3-population test, the 4-population test
(Reich et al. 2009), and the D-test (Green et al. 2010). These have been successfully
applied to test for admixture among human populations as well as for identifying a
significant level of admixture from archaic humans (Neandertals and Denisovans)
among human populations (Green et al. 2010; Reich et al. 2010). These methods,
collectively referred to as f -statistics (in contrast to Wright’s F-statistics), relate
the expected covariances in allele frequencies between not only 2 but also 3 and 4
populations in a bifurcating population phylogeny with the possibility of punctual
admixture events.
The f 3 statistic, or 3-population test, is computed as the product (p X − p A )
(p X − p B ), where p X , p A , and p B are the allele frequencies at each locus in
population A, B, and X. The expected value of this product is positive under a
tree model, but the estimate from data can be negative under certain admixture
scenarios (which violate the tree model), and negative f 3 -statistics can only occur
due to admixture events.
The f 4 statistic, or 4-population test, is computed as the product (p A − p B )
(p X − p Y ), where p A , p B , p X , and p Y are the allele frequencies at each locus in
population A, B, X, and Y. This product is expected to be 0 if the 4 populations
are related by an unrooted phylogeny of the form (A, B), (X, Y) without admixture.
Violations of this assumption can create (significantly) positive or negative values
where the sign of the statistic contains information on the direction of the admixture.
The D-test is a version of the f 4 statistic with a denominator that includes a
term for heterozygosity. Jackknife or bootstrap permutation tests of chromosomes
or blocks of the genome can be used to assess statistical uncertainty and perform
hypothesis tests using these statistics (Reich et al. 2009).
We illustrate these methods by performing the D-test on our data (Table 3.1).
Using San as the outgroup, we see that the single-tree hypothesis with the smallest
deviation from D = 0 has the Mozabite and the French as the closest related
populations. However, the negative D-value for this tree suggests gene flow from
the Yoruba into the Mozabite. This result is consistent with the Mozabite having
ancestry related to both Yoruba and the French with more gene flow from the
French than from the Yoruba. This result closely mirrors the analysis based on
F ST , and it is (supposedly) robust to effects of genetic drift (e.g., from different
effective population sizes in the different populations), which could impact F ST
results. However, we cannot rule out alternative models without a more detailed
model of genetic drift in the population history model.
63
3.3.2 Formal Tests for Admixture Under a Population Tree-Model
Once we have some proposed demographic model/s, we can start estimating
demographic parameters in these models. An alternative, but not mutually exclusive,
way to proceed is to construct formal tests of these models. The proposed model is
used as a null model to make predictions, and then these predictions are compared
to the observed data in order to test if the data is consistent with the model. A
recent suite of tests along these lines is the 3-population test, the 4-population test
(Reich et al. 2009), and the D-test (Green et al. 2010). These have been successfully
applied to test for admixture among human populations as well as for identifying a
significant level of admixture from archaic humans (Neandertals and Denisovans)
among human populations (Green et al. 2010; Reich et al. 2010). These methods,
collectively referred to as f -statistics (in contrast to Wright’s F-statistics), relate
the expected covariances in allele frequencies between not only 2 but also 3 and 4
populations in a bifurcating population phylogeny with the possibility of punctual
admixture events.
The f 3 statistic, or 3-population test, is computed as the product (p X − p A )
(p X − p B ), where p X , p A , and p B are the allele frequencies at each locus in
population A, B, and X. The expected value of this product is positive under a
tree model, but the estimate from data can be negative under certain admixture
scenarios (which violate the tree model), and negative f 3 -statistics can only occur
due to admixture events.
The f 4 statistic, or 4-population test, is computed as the product (p A − p B )
(p X − p Y ), where p A , p B , p X , and p Y are the allele frequencies at each locus in
population A, B, X, and Y. This product is expected to be 0 if the 4 populations
are related by an unrooted phylogeny of the form (A, B), (X, Y) without admixture.
Violations of this assumption can create (significantly) positive or negative values
where the sign of the statistic contains information on the direction of the admixture.
The D-test is a version of the f 4 statistic with a denominator that includes a
term for heterozygosity. Jackknife or bootstrap permutation tests of chromosomes
or blocks of the genome can be used to assess statistical uncertainty and perform
hypothesis tests using these statistics (Reich et al. 2009).
We illustrate these methods by performing the D-test on our data (Table 3.1).
Using San as the outgroup, we see that the single-tree hypothesis with the smallest
deviation from D = 0 has the Mozabite and the French as the closest related
populations. However, the negative D-value for this tree suggests gene flow from
the Yoruba into the Mozabite. This result is consistent with the Mozabite having
ancestry related to both Yoruba and the French with more gene flow from the
French than from the Yoruba. This result closely mirrors the analysis based on
F ST , and it is (supposedly) robust to effects of genetic drift (e.g., from different
effective population sizes in the different populations), which could impact F ST
results. However, we cannot rule out alternative models without a more detailed
model of genetic drift in the population history model.