def weir_cockerham_fst(g, subpops, max_allele=None, blen=None):
"""Compute the variance components from the analyses of variance of
allele frequencies according to 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.
max_allele : int, optional
The highest allele index to consider.
blen : int, optional
Block length to use for chunked computation.
Returns
-------
a : ndarray, float, shape (n_variants, n_alleles)
Component of variance between populations.
b : ndarray, float, shape (n_variants, n_alleles)
Component of variance between individuals within populations.
c : ndarray, float, shape (n_variants, n_alleles)
Component of variance between gametes within individuals.
Examples
--------
Calculate variance components from some genotype data::
>>> import allel
>>> g = [[[0, 0], [0, 0], [1, 1], [1, 1]],
... [[0, 1], [0, 1], [0, 1], [0, 1]],
... [[0, 0], [0, 0], [0, 0], [0, 0]],
... [[0, 1], [1, 2], [1, 1], [2, 2]],
... [[0, 0], [1, 1], [0, 1], [-1, -1]]]
>>> subpops = [[0, 1], [2, 3]]
>>> a, b, c = allel.weir_cockerham_fst(g, subpops)
>>> a
array([[ 0.5 , 0.5 , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , -0.125, -0.125],
[-0.375, -0.375, 0. ]])
>>> b
array([[ 0. , 0. , 0. ],
[-0.25 , -0.25 , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0.125 , 0.25 ],
[ 0.41666667, 0.41666667, 0. ]])
>>> c
array([[0. , 0. , 0. ],
[0.5 , 0.5 , 0. ],
[0. , 0. , 0. ],
[0.125 , 0.25 , 0.125 ],
[0.16666667, 0.16666667, 0. ]])
Estimate the parameter theta (a.k.a., Fst) for each variant
and each allele individually::
>>> fst = a / (a + b + c)
>>> fst
array([[ 1. , 1. , nan],
[ 0. , 0. , nan],
[ nan, nan, nan],
[ 0. , -0.5, -0.5],
[-1.8, -1.8, nan]])
Estimate Fst for each variant individually (averaging over alleles)::
>>> fst = (np.sum(a, axis=1) /
... (np.sum(a, axis=1) + np.sum(b, axis=1) + np.sum(c, axis=1)))
>>> fst
array([ 1. , 0. , nan, -0.4, -1.8])
Estimate Fst averaging over all variants and alleles::
>>> fst = np.sum(a) / (np.sum(a) + np.sum(b) + np.sum(c))
>>> fst
-4.36809058868914e-17
Note that estimated Fst values may be negative.
"""
# check inputs
if not hasattr(g, 'shape') or not hasattr(g, 'ndim'):
g = GenotypeArray(g, copy=False)
if g.ndim != 3:
raise ValueError('g must have three dimensions')
if g.shape[2] != 2:
raise NotImplementedError('only diploid genotypes are supported')
# determine highest allele index
if max_allele is None:
max_allele = g.max()
# compute in chunks to avoid loading big arrays into memory
blen = get_blen_array(g, blen)
n_variants = g.shape[0]
shape = (n_variants, max_allele + 1)
a = np.zeros(shape, dtype='f8')
b = np.zeros(shape, dtype='f8')
c = np.zeros(shape, dtype='f8')
for i in range(0, n_variants, blen):
j = min(n_variants, i + blen)
gb = g[i:j]
ab, bb, cb = _weir_cockerham_fst(gb, subpops, max_allele)
a[i:j] = ab
b[i:j] = bb
c[i:j] = cb
return a, b, c
def mendel_errors(parent_genotypes, progeny_genotypes):
"""Locate genotype calls not consistent with Mendelian transmission of
alleles.
Parameters
----------
parent_genotypes : array_like, int, shape (n_variants, 2, 2)
Genotype calls for the two parents.
progeny_genotypes : array_like, int, shape (n_variants, n_progeny, 2)
Genotype calls for the progeny.
Returns
-------
me : ndarray, int, shape (n_variants, n_progeny)
Count of Mendel errors for each progeny genotype call.
Examples
--------
The following are all consistent with Mendelian transmission. Note that a
value of 0 is returned for missing calls::
>>> import allel
>>> import numpy as np
>>> genotypes = np.array([
... # aa x aa -> aa
... [[0, 0], [0, 0], [0, 0], [-1, -1], [-1, -1], [-1, -1]],
... [[1, 1], [1, 1], [1, 1], [-1, -1], [-1, -1], [-1, -1]],
... [[2, 2], [2, 2], [2, 2], [-1, -1], [-1, -1], [-1, -1]],
... # aa x ab -> aa or ab
... [[0, 0], [0, 1], [0, 0], [0, 1], [-1, -1], [-1, -1]],
... [[0, 0], [0, 2], [0, 0], [0, 2], [-1, -1], [-1, -1]],
... [[1, 1], [0, 1], [1, 1], [0, 1], [-1, -1], [-1, -1]],
... # aa x bb -> ab
... [[0, 0], [1, 1], [0, 1], [-1, -1], [-1, -1], [-1, -1]],
... [[0, 0], [2, 2], [0, 2], [-1, -1], [-1, -1], [-1, -1]],
... [[1, 1], [2, 2], [1, 2], [-1, -1], [-1, -1], [-1, -1]],
... # aa x bc -> ab or ac
... [[0, 0], [1, 2], [0, 1], [0, 2], [-1, -1], [-1, -1]],
... [[1, 1], [0, 2], [0, 1], [1, 2], [-1, -1], [-1, -1]],
... # ab x ab -> aa or ab or bb
... [[0, 1], [0, 1], [0, 0], [0, 1], [1, 1], [-1, -1]],
... [[1, 2], [1, 2], [1, 1], [1, 2], [2, 2], [-1, -1]],
... [[0, 2], [0, 2], [0, 0], [0, 2], [2, 2], [-1, -1]],
... # ab x bc -> ab or ac or bb or bc
... [[0, 1], [1, 2], [0, 1], [0, 2], [1, 1], [1, 2]],
... [[0, 1], [0, 2], [0, 0], [0, 1], [0, 1], [1, 2]],
... # ab x cd -> ac or ad or bc or bd
... [[0, 1], [2, 3], [0, 2], [0, 3], [1, 2], [1, 3]],
... ])
>>> me = allel.mendel_errors(genotypes[:, :2], genotypes[:, 2:])
>>> me
array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]])
The following are cases of 'non-parental' inheritance where one or two
alleles are found in the progeny that are not present in either parent.
Note that the number of errors may be 1 or 2 depending on the number of
non-parental alleles::
>>> genotypes = np.array([
... # aa x aa -> ab or ac or bb or cc
... [[0, 0], [0, 0], [0, 1], [0, 2], [1, 1], [2, 2]],
... [[1, 1], [1, 1], [0, 1], [1, 2], [0, 0], [2, 2]],
... [[2, 2], [2, 2], [0, 2], [1, 2], [0, 0], [1, 1]],
... # aa x ab -> ac or bc or cc
... [[0, 0], [0, 1], [0, 2], [1, 2], [2, 2], [2, 2]],
... [[0, 0], [0, 2], [0, 1], [1, 2], [1, 1], [1, 1]],
... [[1, 1], [0, 1], [1, 2], [0, 2], [2, 2], [2, 2]],
... # aa x bb -> ac or bc or cc
... [[0, 0], [1, 1], [0, 2], [1, 2], [2, 2], [2, 2]],
... [[0, 0], [2, 2], [0, 1], [1, 2], [1, 1], [1, 1]],
... [[1, 1], [2, 2], [0, 1], [0, 2], [0, 0], [0, 0]],
... # ab x ab -> ac or bc or cc
... [[0, 1], [0, 1], [0, 2], [1, 2], [2, 2], [2, 2]],
... [[0, 2], [0, 2], [0, 1], [1, 2], [1, 1], [1, 1]],
... [[1, 2], [1, 2], [0, 1], [0, 2], [0, 0], [0, 0]],
... # ab x bc -> ad or bd or cd or dd
... [[0, 1], [1, 2], [0, 3], [1, 3], [2, 3], [3, 3]],
... [[0, 1], [0, 2], [0, 3], [1, 3], [2, 3], [3, 3]],
... [[0, 2], [1, 2], [0, 3], [1, 3], [2, 3], [3, 3]],
... # ab x cd -> ae or be or ce or de
... [[0, 1], [2, 3], [0, 4], [1, 4], [2, 4], [3, 4]],
... ])
>>> me = allel.mendel_errors(genotypes[:, :2], genotypes[:, 2:])
>>> me
array([[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 2, 2],
[1, 1, 1, 2],
[1, 1, 1, 2],
[1, 1, 1, 2],
[1, 1, 1, 1]])
The following are cases of 'hemi-parental' inheritance, where progeny
appear to have inherited two copies of an allele found only once in one of
the parents::
>>> genotypes = np.array([
... # aa x ab -> bb
... [[0, 0], [0, 1], [1, 1], [-1, -1]],
... [[0, 0], [0, 2], [2, 2], [-1, -1]],
... [[1, 1], [0, 1], [0, 0], [-1, -1]],
... # ab x bc -> aa or cc
... [[0, 1], [1, 2], [0, 0], [2, 2]],
... [[0, 1], [0, 2], [1, 1], [2, 2]],
... [[0, 2], [1, 2], [0, 0], [1, 1]],
... # ab x cd -> aa or bb or cc or dd
... [[0, 1], [2, 3], [0, 0], [1, 1]],
... [[0, 1], [2, 3], [2, 2], [3, 3]],
... ])
>>> me = allel.mendel_errors(genotypes[:, :2], genotypes[:, 2:])
>>> me
array([[1, 0],
[1, 0],
[1, 0],
[1, 1],
[1, 1],
[1, 1],
[1, 1],
[1, 1]])
The following are cases of 'uni-parental' inheritance, where progeny
appear to have inherited both alleles from a single parent::
>>> genotypes = np.array([
... # aa x bb -> aa or bb
... [[0, 0], [1, 1], [0, 0], [1, 1]],
... [[0, 0], [2, 2], [0, 0], [2, 2]],
... [[1, 1], [2, 2], [1, 1], [2, 2]],
... # aa x bc -> aa or bc
... [[0, 0], [1, 2], [0, 0], [1, 2]],
... [[1, 1], [0, 2], [1, 1], [0, 2]],
... # ab x cd -> ab or cd
... [[0, 1], [2, 3], [0, 1], [2, 3]],
... ])
>>> me = allel.mendel_errors(genotypes[:, :2], genotypes[:, 2:])
>>> me
array([[1, 1],
[1, 1],
[1, 1],
[1, 1],
[1, 1],
[1, 1]])
"""
# setup
parent_genotypes = GenotypeArray(parent_genotypes)
progeny_genotypes = GenotypeArray(progeny_genotypes)
check_ploidy(parent_genotypes.ploidy, 2)
check_ploidy(progeny_genotypes.ploidy, 2)
# transform into per-call allele counts
max_allele = max(parent_genotypes.max(), progeny_genotypes.max())
parent_gc = parent_genotypes.to_allele_counts(max_allele=max_allele, dtype='i1')
progeny_gc = progeny_genotypes.to_allele_counts(max_allele=max_allele, dtype='i1')
# detect nonparental and hemiparental inheritance by comparing allele
# counts between parents and progeny
max_progeny_gc = parent_gc.clip(max=1).sum(axis=1)
max_progeny_gc = max_progeny_gc[:, np.newaxis, :]
me = (progeny_gc - max_progeny_gc).clip(min=0).sum(axis=2)
# detect uniparental inheritance by finding cases where no alleles are
# shared between parents, then comparing progeny allele counts to each
# parent
p1_gc = parent_gc[:, 0, np.newaxis, :]
p2_gc = parent_gc[:, 1, np.newaxis, :]
# find variants where parents don't share any alleles
is_shared_allele = (p1_gc > 0) & (p2_gc > 0)
no_shared_alleles = ~np.any(is_shared_allele, axis=2)
# find calls where progeny genotype is identical to one or the other parent
me[no_shared_alleles &
(np.all(progeny_gc == p1_gc, axis=2) |
np.all(progeny_gc == p2_gc, axis=2))] = 1
# retrofit where either or both parent has a missing call
me[np.any(parent_genotypes.is_missing(), axis=1)] = 0
return me
def weir_cockerham_fst(g, subpops, max_allele=None, chunked=False, blen=None):
"""Compute the variance components from the analyses of variance of
allele frequencies according to 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.
max_allele : int, optional
The highest allele index to consider.
chunked : bool, optional
If True, use a block-wise implementation to avoid loading the entire
input array into memory.
blen : int, optional
Block length to use for chunked implementation.
Returns
-------
a : ndarray, float, shape (n_variants, n_alleles)
Component of variance between populations.
b : ndarray, float, shape (n_variants, n_alleles)
Component of variance between individuals within populations.
c : ndarray, float, shape (n_variants, n_alleles)
Component of variance between gametes within individuals.
Examples
--------
Calculate variance components from some genotype data::
>>> import allel
>>> g = [[[0, 0], [0, 0], [1, 1], [1, 1]],
... [[0, 1], [0, 1], [0, 1], [0, 1]],
... [[0, 0], [0, 0], [0, 0], [0, 0]],
... [[0, 1], [1, 2], [1, 1], [2, 2]],
... [[0, 0], [1, 1], [0, 1], [-1, -1]]]
>>> subpops = [[0, 1], [2, 3]]
>>> a, b, c = allel.stats.weir_cockerham_fst(g, subpops)
>>> a
array([[ 0.5 , 0.5 , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0. , 0. ],
[ 0. , -0.125, -0.125],
[-0.375, -0.375, 0. ]])
>>> b
array([[ 0. , 0. , 0. ],
[-0.25 , -0.25 , 0. ],
[ 0. , 0. , 0. ],
[ 0. , 0.125 , 0.25 ],
[ 0.41666667, 0.41666667, 0. ]])
>>> c
array([[ 0. , 0. , 0. ],
[ 0.5 , 0.5 , 0. ],
[ 0. , 0. , 0. ],
[ 0.125 , 0.25 , 0.125 ],
[ 0.16666667, 0.16666667, 0. ]])
Estimate the parameter theta (a.k.a., Fst) for each variant
and each allele individually::
>>> fst = a / (a + b + c)
>>> fst
array([[ 1. , 1. , nan],
[ 0. , 0. , nan],
[ nan, nan, nan],
[ 0. , -0.5, -0.5],
[-1.8, -1.8, nan]])
Estimate Fst for each variant individually (averaging over alleles)::
>>> fst = (np.sum(a, axis=1) /
... (np.sum(a, axis=1) + np.sum(b, axis=1) + np.sum(c, axis=1)))
>>> fst
array([ 1. , 0. , nan, -0.4, -1.8])
Estimate Fst averaging over all variants and alleles::
>>> fst = np.sum(a) / (np.sum(a) + np.sum(b) + np.sum(c))
>>> fst
-4.3680905886891398e-17
Note that estimated Fst values may be negative.
"""
# check inputs
if not hasattr(g, 'shape') or not hasattr(g, 'ndim'):
g = GenotypeArray(g, copy=False)
if g.ndim != 3:
raise ValueError('g must have three dimensions')
if g.shape[2] != 2:
raise NotImplementedError('only diploid genotypes are supported')
# determine highest allele index
if max_allele is None:
max_allele = g.max()
if chunked:
# use a block-wise implementation
blen = get_blen_array(g, blen)
n_variants = g.shape[0]
shape = (n_variants, max_allele + 1)
a = np.zeros(shape, dtype='f8')
b = np.zeros(shape, dtype='f8')
c = np.zeros(shape, dtype='f8')
for i in range(0, n_variants, blen):
j = min(n_variants, i+blen)
gb = g[i:j]
ab, bb, cb = _weir_cockerham_fst(gb, subpops, max_allele)
a[i:j] = ab
b[i:j] = bb
c[i:j] = cb
else:
a, b, c = _weir_cockerham_fst(g, subpops, max_allele)
return a, b, c
