def moving_weir_cockerham_fst(g,
subpops,
size,
start=0,
stop=None,
step=None,
max_allele=None):
"""Estimate average Fst in moving windows over a single chromosome/contig,
following the method of Weir and Cockerham (1984).
Parameters
----------
g : array_like, int, shape (n_variants, n_samples, ploidy)
Genotype array.
subpops : sequence of sequences of ints
Sample indices for each subpopulation.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
max_allele : int, optional
The highest allele index to consider.
Returns
-------
fst : ndarray, float, shape (n_windows,)
Average Fst in each window.
"""
# calculate per-variant values
a, b, c = weir_cockerham_fst(g, subpops, max_allele=max_allele)
# compute the numerator and denominator in moving windows
num = moving_statistic(a,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
den = moving_statistic(a + b + c,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
# calculate fst in each window
fst = num / den
return fst
def blockwise_weir_cockerham_fst(g, subpops, blen, max_allele=None):
"""Estimate average Fst and standard error using the block-jackknife.
Parameters
----------
g : array_like, int, shape (n_variants, n_samples, ploidy)
Genotype array.
subpops : sequence of sequences of ints
Sample indices for each subpopulation.
blen : int
Block size (number of variants).
max_allele : int, optional
The highest allele index to consider.
Returns
-------
fst : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
"""
# calculate per-variant values
a, b, c = weir_cockerham_fst(g, subpops, max_allele=max_allele)
# calculate overall estimate
a_sum = np.nansum(a)
b_sum = np.nansum(b)
c_sum = np.nansum(c)
fst = a_sum / (a_sum + b_sum + c_sum)
# compute the numerator and denominator within each block
num_bsum = moving_statistic(a, statistic=np.nansum, size=blen)
den_bsum = moving_statistic(a + b + c, statistic=np.nansum, size=blen)
# calculate the statistic values in each block
vb = num_bsum / den_bsum
# estimate standard error
_, se, vj = jackknife((num_bsum, den_bsum),
statistic=lambda n, d: np.sum(n) / np.sum(d))
return fst, se, vb, vj
def average_weir_cockerham_fst(g, subpops, blen, max_allele=None):
"""Estimate average Fst and standard error using the block-jackknife.
Parameters
----------
g : array_like, int, shape (n_variants, n_samples, ploidy)
Genotype array.
subpops : sequence of sequences of ints
Sample indices for each subpopulation.
blen : int
Block size (number of variants).
max_allele : int, optional
The highest allele index to consider.
Returns
-------
fst : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
"""
# calculate per-variant values
a, b, c = weir_cockerham_fst(g, subpops, max_allele=max_allele)
# calculate overall estimate
a_sum = np.nansum(a)
b_sum = np.nansum(b)
c_sum = np.nansum(c)
fst = a_sum / (a_sum + b_sum + c_sum)
# compute the numerator and denominator within each block
num_bsum = moving_statistic(a, statistic=np.nansum, size=blen)
den_bsum = moving_statistic(a + b + c, statistic=np.nansum, size=blen)
# calculate the statistic values in each block
vb = num_bsum / den_bsum
# estimate standard error
_, se, vj = jackknife((num_bsum, den_bsum),
statistic=lambda n, d: np.sum(n) / np.sum(d))
return fst, se, vb, vj
def moving_patterson_fst(ac1, ac2, size, start=0, stop=None, step=None):
"""Estimate average Fst in moving windows over a single chromosome/contig,
following the method of Patterson (2012).
Parameters
----------
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the second population.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
fst : ndarray, float, shape (n_windows,)
Average Fst in each window.
"""
# calculate per-variant values
num, den = patterson_fst(ac1, ac2)
# compute the numerator and denominator in moving windows
num_sum = moving_statistic(num,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
den_sum = moving_statistic(den,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
# calculate fst in each window
fst = num_sum / den_sum
return fst
def moving_haplotype_diversity(h, size, start=0, stop=None, step=None):
"""Estimate haplotype diversity in moving windows.
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
hd : ndarray, float, shape (n_windows,)
Haplotype diversity.
"""
hd = moving_statistic(values=h, statistic=haplotype_diversity, size=size, start=start, stop=stop, step=step)
return hd
def moving_haplotype_diversity(h, size, start=0, stop=None, step=None):
"""Estimate haplotype diversity in moving windows.
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
hd : ndarray, float, shape (n_windows,)
Haplotype diversity.
"""
hd = moving_statistic(values=h,
statistic=haplotype_diversity,
size=size,
start=start,
stop=stop,
step=step)
return hd
def blockwise_patterson_fst(ac1, ac2, blen):
"""Estimate average Fst between two populations and standard error using
the block-jackknife.
Parameters
----------
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the second population.
blen : int
Block size (number of variants).
Returns
-------
fst : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
"""
# calculate per-variant values
num, den = patterson_fst(ac1, ac2)
# calculate overall estimate
fst = np.nansum(num) / np.nansum(den)
# compute the numerator and denominator within each block
num_bsum = moving_statistic(num, statistic=np.nansum, size=blen)
den_bsum = moving_statistic(den, statistic=np.nansum, size=blen)
# calculate the statistic values in each block
vb = num_bsum / den_bsum
# estimate standard error
_, se, vj = jackknife((num_bsum, den_bsum),
statistic=lambda n, d: np.sum(n) / np.sum(d))
return fst, se, vb, vj
def average_patterson_fst(ac1, ac2, blen):
"""Estimate average Fst between two populations and standard error using
the block-jackknife.
Parameters
----------
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the second population.
blen : int
Block size (number of variants).
Returns
-------
fst : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
"""
# calculate per-variant values
num, den = patterson_fst(ac1, ac2)
# calculate overall estimate
fst = np.nansum(num) / np.nansum(den)
# compute the numerator and denominator within each block
num_bsum = moving_statistic(num, statistic=np.nansum, size=blen)
den_bsum = moving_statistic(den, statistic=np.nansum, size=blen)
# calculate the statistic values in each block
vb = num_bsum / den_bsum
# estimate standard error
_, se, vj = jackknife((num_bsum, den_bsum),
statistic=lambda n, d: np.sum(n) / np.sum(d))
return fst, se, vb, vj
def moving_tajima_d(ac, size, start=0, stop=None, step=None, min_sites=3):
"""Calculate the value of Tajima's D in moving windows of `size` variants.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
min_sites : int, optional
Minimum number of segregating sites for which to calculate a value. If
there are fewer, np.nan is returned. Defaults to 3.
Returns
-------
d : ndarray, float, shape (n_windows,)
Tajima's D.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> D = allel.moving_tajima_d(ac, size=4, step=2)
>>> D
array([0.1676558 , 2.01186954, 5.70029703])
"""
d = moving_statistic(values=ac,
statistic=tajima_d,
size=size,
start=start,
stop=stop,
step=step,
min_sites=min_sites)
return d
def moving_weir_cockerham_fst(g, subpops, size, start=0, stop=None, step=None, max_allele=None):
"""Estimate average Fst in moving windows over a single chromosome/contig,
following the method of Weir and Cockerham (1984).
Parameters
----------
g : array_like, int, shape (n_variants, n_samples, ploidy)
Genotype array.
subpops : sequence of sequences of ints
Sample indices for each subpopulation.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
max_allele : int, optional
The highest allele index to consider.
Returns
-------
fst : ndarray, float, shape (n_windows,)
Average Fst in each window.
"""
# calculate per-variant values
a, b, c = weir_cockerham_fst(g, subpops, max_allele=max_allele)
# compute the numerator and denominator in moving windows
num = moving_statistic(a, statistic=np.nansum, size=size, start=start, stop=stop, step=step)
den = moving_statistic(a + b + c, statistic=np.nansum, size=size, start=start, stop=stop, step=step)
# calculate fst in each window
fst = num / den
return fst
def moving_patterson_fst(ac1, ac2, size, start=0, stop=None, step=None):
"""Estimate average Fst in moving windows over a single chromosome/contig,
following the method of Patterson (2012).
Parameters
----------
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the second population.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
fst : ndarray, float, shape (n_windows,)
Average Fst in each window.
"""
# calculate per-variant values
num, den = patterson_fst(ac1, ac2)
# compute the numerator and denominator in moving windows
num_sum = moving_statistic(num, statistic=np.nansum, size=size, start=start, stop=stop, step=step)
den_sum = moving_statistic(den, statistic=np.nansum, size=size, start=start, stop=stop, step=step)
# calculate fst in each window
fst = num_sum / den_sum
return fst
def moving_tajima_d(ac, size, start=0, stop=None, step=None):
"""Calculate the value of Tajima's D in moving windows of `size` variants.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
d : ndarray, float, shape (n_windows,)
Tajima's D.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> D = allel.stats.moving_tajima_d(ac, size=3)
>>> D
array([ 0.59158014, 1.89305645, 5.79748537])
"""
d = moving_statistic(values=ac,
statistic=tajima_d,
size=size,
start=start,
stop=stop,
step=step)
return d
def moving_garud_h(h, size, start=0, stop=None, step=None):
"""Compute the H1, H12, H123 and H2/H1 statistics for detecting signatures
of soft sweeps, as defined in Garud et al. (2015), in moving windows,
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
h1 : ndarray, float, shape (n_windows,)
H1 statistics (sum of squares of haplotype frequencies).
h12 : ndarray, float, shape (n_windows,)
H12 statistics (sum of squares of haplotype frequencies, combining
the two most common haplotypes into a single frequency).
h123 : ndarray, float, shape (n_windows,)
H123 statistics (sum of squares of haplotype frequencies, combining
the three most common haplotypes into a single frequency).
h2_h1 : ndarray, float, shape (n_windows,)
H2/H1 statistics, indicating the "softness" of a sweep.
"""
gh = moving_statistic(values=h,
statistic=garud_h,
size=size,
start=start,
stop=stop,
step=step)
h1 = gh[:, 0]
h12 = gh[:, 1]
h123 = gh[:, 2]
h2_h1 = gh[:, 3]
return h1, h12, h123, h2_h1
def moving_tajima_d(ac, size, start=0, stop=None, step=None):
"""Calculate the value of Tajima's D in moving windows of `size` variants.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
D : ndarray, float, shape (n_windows,)
Tajima's D.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> D = allel.stats.moving_tajima_d(ac, size=3)
>>> D
array([ 0.59158014, 1.89305645, 5.79748537])
"""
D = moving_statistic(values=ac, statistic=tajima_d, size=size, start=start, stop=stop, step=step)
return D
def moving_garud_h(h, size, start=0, stop=None, step=None):
"""Compute the H1, H12, H123 and H2/H1 statistics for detecting signatures
of soft sweeps, as defined in Garud et al. (2015), in moving windows,
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
h1 : ndarray, float, shape (n_windows,)
H1 statistics (sum of squares of haplotype frequencies).
h12 : ndarray, float, shape (n_windows,)
H12 statistics (sum of squares of haplotype frequencies, combining
the two most common haplotypes into a single frequency).
h123 : ndarray, float, shape (n_windows,)
H123 statistics (sum of squares of haplotype frequencies, combining
the three most common haplotypes into a single frequency).
h2_h1 : ndarray, float, shape (n_windows,)
H2/H1 statistics, indicating the "softness" of a sweep.
"""
gh = moving_statistic(values=h, statistic=garud_h, size=size, start=start,
stop=stop, step=step)
h1 = gh[:, 0]
h12 = gh[:, 1]
h123 = gh[:, 2]
h2_h1 = gh[:, 3]
return h1, h12, h123, h2_h1
def average_patterson_d(aca, acb, acc, acd, blen):
"""Estimate D(A, B; C, D) and standard error using the block-jackknife.
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.
blen : int
Block size (number of variants).
Returns
-------
d : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
z : float
Z-score (number of standard errors from zero).
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
Notes
-----
See Patterson (2012), main text and Appendix A.
See Also
--------
allel.stats.admixture.patterson_d
"""
# calculate per-variant values
num, den = patterson_d(aca, acb, acc, acd)
# N.B., nans can occur if any of the populations have completely missing
# genotype calls at a variant (i.e., allele number is zero). Here we
# assume that is rare enough to be negligible.
# calculate overall estimate
d_avg = np.nansum(num) / np.nansum(den)
# compute the numerator and denominator within each block
num_bsum = moving_statistic(num, statistic=np.nansum, size=blen)
den_bsum = moving_statistic(den, statistic=np.nansum, size=blen)
# calculate the statistic values in each block
vb = num_bsum / den_bsum
# estimate standard error
_, se, vj = jackknife((num_bsum, den_bsum),
statistic=lambda n, d: np.sum(n) / np.sum(d))
# compute Z score
z = d_avg / se
return d_avg, se, z, vb, vj
def average_patterson_f3(acc, aca, acb, blen, normed=True):
"""Estimate F3(C; A, B) and standard error using the block-jackknife.
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).
blen : int
Block size (number of variants).
normed : bool, optional
If False, use un-normalised f3 values.
Returns
-------
f3 : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
z : float
Z-score (number of standard errors from zero).
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
Notes
-----
See Patterson (2012), main text and Appendix A.
See Also
--------
allel.stats.admixture.patterson_f3
"""
# calculate per-variant values
T, B = patterson_f3(acc, aca, acb)
# N.B., nans can occur if any of the populations have completely missing
# genotype calls at a variant (i.e., allele number is zero). Here we
# assume that is rare enough to be negligible.
# calculate overall value of statistic
if normed:
f3 = np.nansum(T) / np.nansum(B)
else:
f3 = np.nanmean(T)
# calculate value of statistic within each block
if normed:
T_bsum = moving_statistic(T, statistic=np.nansum, size=blen)
B_bsum = moving_statistic(B, statistic=np.nansum, size=blen)
vb = T_bsum / B_bsum
_, se, vj = jackknife((T_bsum, B_bsum),
statistic=lambda t, b: np.sum(t) / np.sum(b))
else:
vb = moving_statistic(T, statistic=np.nanmean, size=blen)
_, se, vj = jackknife(vb, statistic=np.mean)
# compute Z score
z = f3 / se
return f3, se, z, vb, vj
def moving_patterson_d(aca,
acb,
acc,
acd,
size,
start=0,
stop=None,
step=None):
"""Estimate D(A, B; C, D) in moving windows.
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.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
Returns
-------
d : ndarray, float, shape (n_windows,)
Estimated value of the statistic in each window.
"""
# calculate per-variant values
num, den = patterson_d(aca, acb, acc, acd)
# N.B., nans can occur if any of the populations have completely missing
# genotype calls at a variant (i.e., allele number is zero). Here we
# assume that is rare enough to be negligible.
# compute the numerator and denominator within each window
num_sum = moving_statistic(num,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
den_sum = moving_statistic(den,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
# calculate the statistic values in each block
d = num_sum / den_sum
return d
def moving_patterson_f3(acc,
aca,
acb,
size,
start=0,
stop=None,
step=None,
normed=True):
"""Estimate F3(C; A, B) in moving windows.
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).
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
step : int, optional
The number of variants between start positions of windows. If not
given, defaults to the window size, i.e., non-overlapping windows.
normed : bool, optional
If False, use un-normalised f3 values.
Returns
-------
f3 : ndarray, float, shape (n_windows,)
Estimated value of the statistic in each window.
"""
# calculate per-variant values
T, B = patterson_f3(acc, aca, acb)
# calculate value of statistic within each block
if normed:
T_bsum = moving_statistic(T,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
B_bsum = moving_statistic(B,
statistic=np.nansum,
size=size,
start=start,
stop=stop,
step=step)
f3 = T_bsum / B_bsum
else:
f3 = moving_statistic(T,
statistic=np.nanmean,
size=size,
start=start,
stop=stop,
step=step)
return f3
def blockwise_patterson_f3(acc, aca, acb, blen, normed=True):
"""Estimate F3(C; A, B) and standard error using the block-jackknife.
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).
blen : int
Block size (number of variants).
normed : bool, optional
If False, use un-normalised f3 values.
Returns
-------
f3 : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
z : float
Z-score (number of standard errors from zero).
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
Notes
-----
See Patterson (2012), main text and Appendix A.
See Also
--------
allel.stats.admixture.patterson_f3
"""
# calculate per-variant values
T, B = patterson_f3(acc, aca, acb)
# N.B., nans can occur if any of the populations have completely missing
# genotype calls at a variant (i.e., allele number is zero). Here we
# assume that is rare enough to be negligible.
# calculate overall value of statistic
if normed:
f3 = np.nansum(T) / np.nansum(B)
else:
f3 = np.nanmean(T)
# calculate value of statistic within each block
if normed:
T_bsum = moving_statistic(T, statistic=np.nansum, size=blen)
B_bsum = moving_statistic(B, statistic=np.nansum, size=blen)
vb = T_bsum / B_bsum
_, se, vj = jackknife((T_bsum, B_bsum),
statistic=lambda t, b: np.sum(t) / np.sum(b))
else:
vb = moving_statistic(T, statistic=np.nanmean, size=blen)
_, se, vj = jackknife(vb, statistic=np.mean)
# compute Z score
z = f3 / se
return f3, se, z, vb, vj
def blockwise_patterson_d(aca, acb, acc, acd, blen):
"""Estimate D(A, B; C, D) and standard error using the block-jackknife.
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.
blen : int
Block size (number of variants).
Returns
-------
d : float
Estimated value of the statistic using all data.
se : float
Estimated standard error.
z : float
Z-score (number of standard errors from zero).
vb : ndarray, float, shape (n_blocks,)
Value of the statistic in each block.
vj : ndarray, float, shape (n_blocks,)
Values of the statistic from block-jackknife resampling.
Notes
-----
See Patterson (2012), main text and Appendix A.
See Also
--------
allel.stats.admixture.patterson_d
"""
# calculate per-variant values
num, den = patterson_d(aca, acb, acc, acd)
# N.B., nans can occur if any of the populations have completely missing
# genotype calls at a variant (i.e., allele number is zero). Here we
# assume that is rare enough to be negligible.
# calculate overall estimate
d = np.nansum(num) / np.nansum(den)
# compute the numerator and denominator within each block
num_bsum = moving_statistic(num, statistic=np.nansum, size=blen)
den_bsum = moving_statistic(den, statistic=np.nansum, size=blen)
# calculate the statistic values in each block
vb = num_bsum / den_bsum
# estimate standard error
_, se, vj = jackknife((num_bsum, den_bsum),
statistic=lambda n, d: np.sum(n) / np.sum(d))
# compute Z score
z = d / se
return d, se, z, vb, vj
def plot_moving_haplotype_frequencies(pos,
h,
size,
start=0,
stop=None,
n=None,
palette='Paired',
singleton_color='w',
ax=None):
"""Plot haplotype frequencies in moving windows over the genome.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
n : int, optional
Color only the `n` most frequent haplotypes (by default, all
non-singleton haplotypes are colored).
palette : string, optional
A Seaborn palette name.
singleton_color : string, optional
Color to paint singleton haplotypes.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
Returns
-------
ax : axes
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns
# setup figure
if ax is None:
fig, ax = plt.subplots()
# compute haplotype frequencies
# N.B., here we use a haplotype rank data structure to enable the use of
# pcolormesh() which is a lot faster than any other type of plotting
# function
hr = moving_hfs_rank(h, size=size, start=start, stop=stop)
# truncate to n most common haplotypes
if n:
hr[hr > n] = 0
# compute window start and stop positions
windows = moving_statistic(pos,
statistic=lambda v: (v[0], v[-1]),
size=size,
start=start,
stop=stop)
# create color map
colors = [singleton_color] + sns.color_palette(palette, n_colors=hr.max())
cmap = mpl.colors.ListedColormap(colors)
# draw colors
x = np.append(windows[:, 0], windows[-1, -1])
y = np.arange(h.shape[1] + 1)
ax.pcolormesh(x, y, hr.T, cmap=cmap)
# tidy up
ax.set_xlim(windows[0, 0], windows[-1, -1])
ax.set_ylim(0, h.shape[1])
ax.set_ylabel('haplotype count')
ax.set_xlabel('position (bp)')
return ax
def plot_moving_haplotype_frequencies(
pos, h, size, start=0, stop=None, n=None, palette="Paired", singleton_color="w", ax=None
):
"""Plot haplotype frequencies in moving windows over the genome.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
size : int
The window size (number of variants).
start : int, optional
The index at which to start.
stop : int, optional
The index at which to stop.
n : int, optional
Color only the `n` most frequent haplotypes (by default, all
non-singleton haplotypes are colored).
palette : string, optional
A Seaborn palette name.
singleton_color : string, optional
Color to paint singleton haplotypes.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
Returns
-------
ax : axes
"""
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns
# setup figure
if ax is None:
fig, ax = plt.subplots()
# compute haplotype frequencies
# N.B., here we use a haplotype rank data structure to enable the use of
# pcolormesh() which is a lot faster than any other type of plotting
# function
hr = moving_hfs_rank(h, size=size, start=start, stop=stop)
# truncate to n most common haplotypes
if n:
hr[hr > n] = 0
# compute window start and stop positions
windows = moving_statistic(pos, statistic=lambda x: (x[0], x[-1]), size=size, start=start, stop=stop)
# create color map
colors = [singleton_color] + sns.color_palette(palette, n_colors=hr.max())
cmap = mpl.colors.ListedColormap(colors)
# draw colors
x = np.append(windows[:, 0], windows[-1, -1])
y = np.arange(h.shape[1] + 1)
ax.pcolormesh(x, y, hr.T, cmap=cmap)
# tidy up
ax.set_xlim(windows[0, 0], windows[-1, -1])
ax.set_ylim(0, h.shape[1])
ax.set_ylabel("haplotype count")
ax.set_xlabel("position (bp)")
return ax