def tajima_d(ac, pos=None, start=None, stop=None):
"""Calculate the value of Tajima's D over a given region.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
pos : array_like, int, shape (n_items,), optional
Variant positions, using 1-based coordinates, in ascending order.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
Returns
-------
D : float
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()
>>> allel.stats.tajima_d(ac)
3.1445848780213814
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> allel.stats.tajima_d(ac, pos=pos, start=7, stop=25)
3.8779735196179366
"""
# check inputs
if not hasattr(ac, "count_segregating"):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if pos is not None and (start is not None or stop is not None):
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
loc = pos.locate_range(start, stop)
ac = ac[loc]
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# count segregating variants
S = ac.count_segregating()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate Watterson's theta (absolute value)
theta_hat_w_abs = S / a1
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# calculate theta_hat pi (sum differences over variants)
theta_hat_pi_abs = np.sum(mpd)
# N.B., both theta estimates are usually divided by the number of
# (accessible) bases but here we want the absolute difference
d = theta_hat_pi_abs - theta_hat_w_abs
# calculate the denominator (standard deviation)
a2 = np.sum(1 / (np.arange(1, n) ** 2))
b1 = (n + 1) / (3 * (n - 1))
b2 = 2 * (n ** 2 + n + 3) / (9 * n * (n - 1))
c1 = b1 - (1 / a1)
c2 = b2 - ((n + 2) / (a1 * n)) + (a2 / (a1 ** 2))
e1 = c1 / a1
e2 = c2 / (a1 ** 2 + a2)
d_stdev = np.sqrt((e1 * S) + (e2 * S * (S - 1)))
# finally calculate Tajima's D
D = d / d_stdev
return D
def tajima_d(ac, pos=None, start=None, stop=None, min_sites=3):
"""Calculate the value of Tajima's D over a given region.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
pos : array_like, int, shape (n_items,), optional
Variant positions, using 1-based coordinates, in ascending order.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
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 : float
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()
>>> allel.tajima_d(ac)
3.1445848780213814
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> allel.tajima_d(ac, pos=pos, start=7, stop=25)
3.8779735196179366
"""
# check inputs
if not hasattr(ac, 'count_segregating'):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if pos is not None and (start is not None or stop is not None):
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
loc = pos.locate_range(start, stop)
ac = ac[loc]
# count segregating variants
S = ac.count_segregating()
if S < min_sites:
return np.nan
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate Watterson's theta (absolute value)
theta_hat_w_abs = S / a1
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# calculate theta_hat pi (sum differences over variants)
theta_hat_pi_abs = np.sum(mpd)
# N.B., both theta estimates are usually divided by the number of
# (accessible) bases but here we want the absolute difference
d = theta_hat_pi_abs - theta_hat_w_abs
# calculate the denominator (standard deviation)
a2 = np.sum(1 / (np.arange(1, n)**2))
b1 = (n + 1) / (3 * (n - 1))
b2 = 2 * (n**2 + n + 3) / (9 * n * (n - 1))
c1 = b1 - (1 / a1)
c2 = b2 - ((n + 2) / (a1 * n)) + (a2 / (a1**2))
e1 = c1 / a1
e2 = c2 / (a1**2 + a2)
d_stdev = np.sqrt((e1 * S) + (e2 * S * (S - 1)))
# finally calculate Tajima's D
D = d / d_stdev
return D
def watterson_theta(pos, ac, start=None, stop=None, is_accessible=None):
"""Calculate the value of Watterson's estimator over a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
theta_hat_w : float
Watterson's estimator (theta hat per base).
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()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w = allel.stats.watterson_theta(pos, ac, start=1, stop=31)
>>> theta_hat_w
0.10557184750733138
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, "count_segregating"):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# count segregating variants
S = ac.count_segregating()
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate absolute value
theta_hat_w_abs = S / a1
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
theta_hat_w = theta_hat_w_abs / n_bases
return theta_hat_w
def watterson_theta(pos, ac, start=None, stop=None, is_accessible=None):
"""Calculate the value of Watterson's estimator over a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
theta_hat_w : float
Watterson's estimator (theta hat per base).
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()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w = allel.watterson_theta(pos, ac, start=1, stop=31)
>>> theta_hat_w
0.10557184750733138
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, 'count_segregating'):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# count segregating variants
S = ac.count_segregating()
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate absolute value
theta_hat_w_abs = S / a1
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1:stop])
theta_hat_w = theta_hat_w_abs / n_bases
return theta_hat_w
