def patterson_f3(acc, aca, acb):
"""Unbiased estimator for F3(C; A, B), the three-population test for
admixture in population C.
Parameters
----------
acc : array_like, int, shape (n_variants, 2)
Allele counts for the test population (C).
aca : array_like, int, shape (n_variants, 2)
Allele counts for the first source population (A).
acb : array_like, int, shape (n_variants, 2)
Allele counts for the second source population (B).
Returns
-------
T : ndarray, float, shape (n_variants,)
Un-normalized f3 estimates per variant.
B : ndarray, float, shape (n_variants,)
Estimates for heterozygosity in population C.
Notes
-----
See Patterson (2012), main text and Appendix A.
For un-normalized f3 statistics, ignore the `B` return value.
To compute the f3* statistic, which is normalized by heterozygosity in
population C to remove numerical dependence on the allele frequency
spectrum, compute ``np.sum(T) / np.sum(B)``.
"""
# check inputs
aca = AlleleCountsArray(aca, copy=False)
assert aca.shape[1] == 2, 'only biallelic variants supported'
acb = AlleleCountsArray(acb, copy=False)
assert acb.shape[1] == 2, 'only biallelic variants supported'
acc = AlleleCountsArray(acc, copy=False)
assert acc.shape[1] == 2, 'only biallelic variants supported'
check_dim0_aligned(aca, acb, acc)
# compute allele number and heterozygosity in test population
sc = acc.sum(axis=1)
hc = h_hat(acc)
# compute sample frequencies for the alternate allele
a = aca.to_frequencies()[:, 1]
b = acb.to_frequencies()[:, 1]
c = acc.to_frequencies()[:, 1]
# compute estimator
T = ((c - a) * (c - b)) - (hc / sc)
B = 2 * hc
return T, B
def patterson_f3(acc, aca, acb):
"""Unbiased estimator for F3(C; A, B), the three-population test for
admixture in population C.
Parameters
----------
acc : array_like, int, shape (n_variants, 2)
Allele counts for the test population (C).
aca : array_like, int, shape (n_variants, 2)
Allele counts for the first source population (A).
acb : array_like, int, shape (n_variants, 2)
Allele counts for the second source population (B).
Returns
-------
T : ndarray, float, shape (n_variants,)
Un-normalized f3 estimates per variant.
B : ndarray, float, shape (n_variants,)
Estimates for heterozygosity in population C.
Notes
-----
See Patterson (2012), main text and Appendix A.
For un-normalized f3 statistics, ignore the `B` return value.
To compute the f3* statistic, which is normalized by heterozygosity in
population C to remove numerical dependence on the allele frequency
spectrum, compute ``np.sum(T) / np.sum(B)``.
"""
# check inputs
aca = AlleleCountsArray(aca, copy=False)
assert aca.shape[1] == 2, 'only biallelic variants supported'
acb = AlleleCountsArray(acb, copy=False)
assert acb.shape[1] == 2, 'only biallelic variants supported'
acc = AlleleCountsArray(acc, copy=False)
assert acc.shape[1] == 2, 'only biallelic variants supported'
check_dim0_aligned(aca, acb, acc)
# compute allele number and heterozygosity in test population
sc = acc.sum(axis=1)
hc = h_hat(acc)
# compute sample frequencies for the alternate allele
a = aca.to_frequencies()[:, 1]
b = acb.to_frequencies()[:, 1]
c = acc.to_frequencies()[:, 1]
# compute estimator
T = ((c - a) * (c - b)) - (hc / sc)
B = 2 * hc
return T, B
def patterson_d(aca, acb, acc, acd):
"""Unbiased estimator for D(A, B; C, D), the normalised four-population
test for admixture between (A or B) and (C or D), also known as the
"ABBA BABA" test.
Parameters
----------
aca : array_like, int, shape (n_variants, 2),
Allele counts for population A.
acb : array_like, int, shape (n_variants, 2)
Allele counts for population B.
acc : array_like, int, shape (n_variants, 2)
Allele counts for population C.
acd : array_like, int, shape (n_variants, 2)
Allele counts for population D.
Returns
-------
num : ndarray, float, shape (n_variants,)
Numerator (un-normalised f4 estimates).
den : ndarray, float, shape (n_variants,)
Denominator.
Notes
-----
See Patterson (2012), main text and Appendix A.
For un-normalized f4 statistics, ignore the `den` return value.
"""
# check inputs
aca = AlleleCountsArray(aca, copy=False)
assert aca.shape[1] == 2, 'only biallelic variants supported'
acb = AlleleCountsArray(acb, copy=False)
assert acb.shape[1] == 2, 'only biallelic variants supported'
acc = AlleleCountsArray(acc, copy=False)
assert acc.shape[1] == 2, 'only biallelic variants supported'
acd = AlleleCountsArray(acd, copy=False)
assert acd.shape[1] == 2, 'only biallelic variants supported'
check_dim0_aligned(aca, acb, acc, acd)
# compute sample frequencies for the alternate allele
a = aca.to_frequencies()[:, 1]
b = acb.to_frequencies()[:, 1]
c = acc.to_frequencies()[:, 1]
d = acd.to_frequencies()[:, 1]
# compute estimator
num = (a - b) * (c - d)
den = (a + b - (2 * a * b)) * (c + d - (2 * c * d))
return num, den
def patterson_d(aca, acb, acc, acd):
"""Unbiased estimator for D(A, B; C, D), the normalised four-population
test for admixture between (A or B) and (C or D), also known as the
"ABBA BABA" test.
Parameters
----------
aca : array_like, int, shape (n_variants, 2),
Allele counts for population A.
acb : array_like, int, shape (n_variants, 2)
Allele counts for population B.
acc : array_like, int, shape (n_variants, 2)
Allele counts for population C.
acd : array_like, int, shape (n_variants, 2)
Allele counts for population D.
Returns
-------
num : ndarray, float, shape (n_variants,)
Numerator (un-normalised f4 estimates).
den : ndarray, float, shape (n_variants,)
Denominator.
Notes
-----
See Patterson (2012), main text and Appendix A.
For un-normalized f4 statistics, ignore the `den` return value.
"""
# check inputs
aca = AlleleCountsArray(aca, copy=False)
assert aca.shape[1] == 2, 'only biallelic variants supported'
acb = AlleleCountsArray(acb, copy=False)
assert acb.shape[1] == 2, 'only biallelic variants supported'
acc = AlleleCountsArray(acc, copy=False)
assert acc.shape[1] == 2, 'only biallelic variants supported'
acd = AlleleCountsArray(acd, copy=False)
assert acd.shape[1] == 2, 'only biallelic variants supported'
check_dim0_aligned(aca, acb, acc, acd)
# compute sample frequencies for the alternate allele
a = aca.to_frequencies()[:, 1]
b = acb.to_frequencies()[:, 1]
c = acc.to_frequencies()[:, 1]
d = acd.to_frequencies()[:, 1]
# compute estimator
num = (a - b) * (c - d)
den = (a + b - (2 * a * b)) * (c + d - (2 * c * d))
return num, den
def patterson_f2(aca, acb):
"""Unbiased estimator for F2(A, B), the branch length between populations
A and B.
Parameters
----------
aca : array_like, int, shape (n_variants, 2)
Allele counts for population A.
acb : array_like, int, shape (n_variants, 2)
Allele counts for population B.
Returns
-------
f2 : ndarray, float, shape (n_variants,)
Notes
-----
See Patterson (2012), Appendix A.
"""
# check inputs
aca = AlleleCountsArray(aca, copy=False)
assert aca.shape[1] == 2, 'only biallelic variants supported'
acb = AlleleCountsArray(acb, copy=False)
assert acb.shape[1] == 2, 'only biallelic variants supported'
check_dim0_aligned(aca, acb)
# compute allele numbers
sa = aca.sum(axis=1)
sb = acb.sum(axis=1)
# compute heterozygosities
ha = h_hat(aca)
hb = h_hat(acb)
# compute sample frequencies for the alternate allele
a = aca.to_frequencies()[:, 1]
b = acb.to_frequencies()[:, 1]
# compute estimator
x = ((a - b)**2) - (ha / sa) - (hb / sb)
return x
def patterson_f2(aca, acb):
"""Unbiased estimator for F2(A, B), the branch length between populations
A and B.
Parameters
----------
aca : array_like, int, shape (n_variants, 2)
Allele counts for population A.
acb : array_like, int, shape (n_variants, 2)
Allele counts for population B.
Returns
-------
f2 : ndarray, float, shape (n_variants,)
Notes
-----
See Patterson (2012), Appendix A.
"""
# check inputs
aca = AlleleCountsArray(aca, copy=False)
assert aca.shape[1] == 2, 'only biallelic variants supported'
acb = AlleleCountsArray(acb, copy=False)
assert acb.shape[1] == 2, 'only biallelic variants supported'
check_dim0_aligned(aca, acb)
# compute allele numbers
sa = aca.sum(axis=1)
sb = acb.sum(axis=1)
# compute heterozygosities
ha = h_hat(aca)
hb = h_hat(acb)
# compute sample frequencies for the alternate allele
a = aca.to_frequencies()[:, 1]
b = acb.to_frequencies()[:, 1]
# compute estimator
x = ((a - b) ** 2) - (ha / sa) - (hb / sb)
return x
