"""
Allele frequency calculations.
See also the examples at:
- http://nbviewer.ipython.org/github/alimanfoo/anhima/blob/master/examples/af.ipynb
""" # noqa
from __future__ import division, print_function, unicode_literals, \
absolute_import
# third party dependencies
import numpy as np
# internal dependencies
import anhima
def _check_genotypes(genotypes):
"""
Internal function to check the genotypes input argument meets
expectations.
"""
genotypes = np.asarray(genotypes)
assert genotypes.ndim >= 2
if genotypes.ndim == 2:
# assume haploid, add ploidy dimension
genotypes = genotypes[..., np.newaxis]
return genotypes
[docs]def is_variant(genotypes):
"""Find variants with at least one non-reference allele observation.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
is_variant : ndarray, bool
An array of shape (n_variants,) where an element is True if there
are at least `min_ac` non-reference alleles found for the corresponding
variant.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# aggregate over samples and ploidy dimensions
out = np.sum(genotypes > 0, axis=(1, 2)) >= 1
return out
[docs]def count_variant(genotypes):
"""Count variants with at least one non-reference allele observed.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
min_ac : int, optional
The minimum number of non-reference alleles required to consider
variant.
Returns
-------
n : int
The number of variants.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
return np.count_nonzero(is_variant(genotypes))
[docs]def is_non_variant(genotypes):
"""Find variants with no non-reference alleles.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
is_non_variant : ndarray, bool
An array of shape (n_variants,) where an element is True if there
are no non-reference alleles found for the corresponding variant.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# aggregate over samples and ploidy dimensions
out = np.all(genotypes <= 0, axis=(1, 2))
return out
[docs]def count_non_variant(genotypes):
"""Count variants with no non-reference alleles.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
n : int
The number of variants.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
return np.count_nonzero(is_non_variant(genotypes))
[docs]def is_singleton(genotypes, allele=1):
"""Find variants with only a single instance of `allele` observed.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
The allele to find singletons of.
Returns
-------
is_singleton : ndarray, bool
An array of shape (n_variants,) where an element is True if there
is a single instance of `allele` observed.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants, but note this function checks for a
specific `allele`.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# aggregate over samples and ploidy dimensions
out = np.sum(genotypes == allele, axis=(1, 2)) == 1
return out
[docs]def count_singletons(genotypes, allele=1):
"""Count variants with only a single instance of `allele` observed.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
The allele to find singletons of.
Returns
-------
n : int
The number of variants.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants, but note this function checks for a
specific `allele`.
"""
return np.count_nonzero(is_singleton(genotypes, allele))
[docs]def is_doubleton(genotypes, allele=1):
"""Find variants with only two instances of `allele` observed.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
The allele to find doubletons of.
Returns
-------
is_doubleton : ndarray, bool
An array of shape (n_variants,) where an element is True if there
are exactly two instances of `allele` observed.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants, but note this function checks for a
specific `allele`.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# aggregate over samples and ploidy dimensions
out = np.sum(genotypes == allele, axis=(1, 2)) == 2
return out
[docs]def count_doubletons(genotypes, allele=1):
"""Count variants with only two instances of `allele` observed.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
The allele to find doubletons of.
Returns
-------
n : int
The number of variants.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants, but note this function checks for a
specific `allele`.
"""
return np.count_nonzero(is_doubleton(genotypes, allele))
[docs]def allele_number(genotypes):
"""Count the number of non-missing allele calls per variant.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
an : ndarray, int
An array of shape (n_variants,) counting the total number of
non-missing alleles observed.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# aggregate over samples and ploidy dimensions
an = np.sum(genotypes >= 0, axis=(1, 2))
return an
[docs]def allele_count(genotypes, allele=1):
"""Calculate number of observations of the given allele per variant.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
The allele to count.
Returns
-------
ac : ndarray, int
An array of shape (n_variants,) counting the number of
times the given `allele` was observed.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants, but note that this function
calculates the frequency of a specific `allele`.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# aggregate over samples and ploidy dimensions
ac = np.sum(genotypes == allele, axis=(1, 2))
return ac
[docs]def allele_frequency(genotypes, allele=1):
"""Calculate frequency of the given allele per variant.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
The allele to calculate the frequency of.
Returns
-------
an : ndarray, int
An array of shape (n_variants,) counting the total number of
non-missing alleles observed.
ac : ndarray, int
An array of shape (n_variants,) counting the number of
times the given `allele` was observed.
af : ndarray, float
An array of shape (n_variants,) containing the allele frequency.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants, but note that this function
calculates the frequency of a specific `allele`.
"""
# count non-missing alleles
an = allele_number(genotypes)
# count alleles
ac = allele_count(genotypes, allele=allele)
# calculate allele frequency, accounting for missingness
err = np.seterr(invalid='ignore')
af = np.where(an > 0, ac / an, 0)
np.seterr(**err)
return an, ac, af
[docs]def allele_counts(genotypes, alleles=None):
"""Calculate allele counts per variant.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
alleles : sequence of ints, optional
The alleles to count. If not specified, all alleles will be counted.
Returns
-------
ac : ndarray, int
An array of shape (n_variants, n_alleles) counting the number of
times the given `alleles` were observed.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check input
genotypes = _check_genotypes(genotypes)
# determine number of variants
n_variants = genotypes.shape[0]
# if alleles not specified, count all alleles
if alleles is None:
m = np.amax(genotypes)
alleles = range(m+1)
# count alleles
ac = np.zeros((n_variants, len(alleles)), dtype='i4')
for i, allele in enumerate(alleles):
np.sum(genotypes == allele, axis=(1, 2), out=ac[:, i])
return ac
[docs]def allele_frequencies(genotypes, alleles=None):
"""Calculate allele frequencies per variant.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
alleles : sequence of ints, optional
The alleles to calculate the frequency of. If not specified, all
alleles will be counted.
Returns
-------
an : ndarray, int
An array of shape (n_variants,) counting the total number of
non-missing alleles observed.
ac : ndarray, int
An array of shape (n_variants, n_alleles) counting the number of
times the given `alleles` were observed.
af : ndarray, float
An array of shape (n_variants, n_alleles) containing the allele
frequencies.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# count non-missing alleles
an = allele_number(genotypes)[:, np.newaxis]
# count alleles
ac = allele_counts(genotypes, alleles=alleles)
# calculate allele frequencies, accounting for missingness
err = np.seterr(invalid='ignore')
af = np.where(an > 0, ac / an, 0)
np.seterr(**err)
return an, ac, af
[docs]def allelism(genotypes):
"""Determine the number of distinct alleles found for each variant.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
n : ndarray, int
An array of shape (n_variants,) where an element holds the allelism
of the corresponding variant.
See Also
--------
max_allele
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# calculate allele counts
ac = allele_counts(genotypes)
# count alleles present
n = np.sum(ac > 0, axis=1)
return n
[docs]def is_non_segregating(genotypes, allele=None):
"""Find non-segregating variants (fixed for a single allele).
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
If given, find variants fixed with respect to `allele`. Otherwise
find variants fixed for any allele.
Returns
-------
is_non_segregating : ndarray, bool
An array of shape (n_variants,) where an element is True if all
genotype calls for the corresponding variant are either missing or
equal to the same allele.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
if allele is None:
# count distinct alleles
n_alleles = allelism(genotypes)
# find fixed variants
out = n_alleles == 1
else:
# find fixed variants with respect to a specific allele
out = np.all((genotypes < 0) | (genotypes == allele), axis=(1, 2))
return out
[docs]def count_non_segregating(genotypes, allele=None):
"""Count non-segregating variants.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
allele : int, optional
If given, find variants fixed with respect to `allele`.
Returns
-------
n : int
The number of variants.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
return np.count_nonzero(is_non_segregating(genotypes, allele=allele))
[docs]def is_segregating(genotypes):
"""Find segregating variants (where more than one allele is observed).
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
is_segregating : ndarray, bool
An array of shape (n_variants,) where an element is True if more
than one allele is found for the given variant.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
# check inputs
genotypes = _check_genotypes(genotypes)
# count distinct alleles
n_alleles = allelism(genotypes)
# find segregating variants
out = n_alleles > 1
return out
[docs]def count_segregating(genotypes):
"""Count segregating variants.
Parameters
----------
genotypes : array_like
An array of shape (n_variants, n_samples, ploidy) where each
element of the array is an integer corresponding to an allele index
(-1 = missing, 0 = reference allele, 1 = first alternate allele,
2 = second alternate allele, etc.).
Returns
-------
n : int
The number of variants.
Notes
-----
Applicable to polyploid genotype calls.
Applicable to multiallelic variants.
"""
return np.count_nonzero(is_segregating(genotypes))
[docs]def maximum_likelihood_ancestry(genotypes, qa, qb, filter_size=0):
"""Given alternate allele frequencies in two populations `qa` and `qb`,
predict the ancestry for a set of `genotypes`.
Parameters
----------
genotypes : array_like
An array of diploid genotype calls of shape (n_variants, n_samples,
2) where each element of the array is an integer corresponding to an
allele index (-1 = missing, 0 = reference allele, 1 = first alternate
allele, 2 = second alternate allele, etc.).
qa : array_like, float
A 1-dimensional array of shape (n_variants, ) containing alternate
allele frequencies for population A.
qb : array_like, float
A 1-dimensional array of shape (n_variants, ) containing alternate
allele frequencies for population B.
filter_size : int, optional
Sum likelihoods in a moving window of size `filter_size`.
Returns
-------
ancestry : ndarray, int, shape (n_variants, n_samples)
An array containing the ancestry predictions, where 0 = AA (both
alleles derive from population A), 1 = AB (hybrid ancestry) and 2 =
BB (both alleles derive from population B), and -1 = ambiguous (models
are equally likely).
confidence : ndarray, float, shape (n_variants, n_samples)
The confidence in the ancestry prediction (natural logarithm of the
likelihood ratio for the two most likely models).
Notes
-----
Where allele frequencies are similar between populations A and B,
ancestry predictions will have low confidence, because different ancestry
models will have similar likelihoods. Greater confidence will be obtained by
filtering variants to select those where the difference in allele
frequencies is greater. E.g.::
>>> flt = np.abs(qa - qb) > .5
>>> genotypes_flt = genotypes[flt]
>>> qa_flt = qa[flt]
>>> qb_flt = qb[flt]
>>> ancestry, confidence = maximum_likelihood_ancestry(genotypes_flt, qa_flt, qb_flt)
""" # noqa
# check inputs
genotypes = _check_genotypes(genotypes)
# require biallelic genotypes
assert np.amax(genotypes) < 2
n_variants, n_samples, ploidy = genotypes.shape
# require diploid genotypes
assert ploidy == 2
qa = np.asarray(qa)
qb = np.asarray(qb)
assert qa.ndim == qb.ndim == 1
assert n_variants == qa.shape[0] == qb.shape[0]
# calculate reference allele frequencies, assuming biallelic variants
pa = 1 - qa
pb = 1 - qb
# work around zero frequencies which cause problems when calculating logs
pa[pa == 0] = np.exp(-250)
qa[qa == 0] = np.exp(-250)
pb[pb == 0] = np.exp(-250)
qb[qb == 0] = np.exp(-250)
# calculate likelihoods
logpa = np.log(pa)
logqa = np.log(qa)
logpb = np.log(pb)
logqb = np.log(qb)
# set up likelihoods array
n_models = 3
n_gn_states = 3
log_likelihoods = np.empty((n_variants, n_samples, n_models, n_gn_states),
dtype='f8')
# probability of genotype (e.g., 0 = hom ref) given model (e.g., 0 = aa)
log_likelihoods[:, :, 0, 0] = (2 * logpa)[:, np.newaxis]
log_likelihoods[:, :, 1, 0] = (np.log(2) + logpa + logqa)[:, np.newaxis]
log_likelihoods[:, :, 2, 0] = (2 * logqa)[:, np.newaxis]
log_likelihoods[:, :, 0, 1] = (logpa + logpb)[:, np.newaxis]
log_likelihoods[:, :, 1, 1] = (np.logaddexp(logpa + logqb,
logqa + logpb)[:, np.newaxis])
log_likelihoods[:, :, 2, 1] = (logqa + logqb)[:, np.newaxis]
log_likelihoods[:, :, 0, 2] = (2 * logpb)[:, np.newaxis]
log_likelihoods[:, :, 1, 2] = (np.log(2) + logpb + logqb)[:, np.newaxis]
log_likelihoods[:, :, 2, 2] = (2 * logqb)[:, np.newaxis]
# transform genotypes for convenience
gn = anhima.gt.as_012(genotypes)
# calculate actual model likelihoods for each genotype call
model_likelihoods = np.empty((n_variants, n_samples, n_models), dtype='f8')
model_likelihoods.fill(-250)
for model in 0, 1, 2:
for gn_state in 0, 1, 2:
model_likelihoods[:, :, model][gn == gn_state] = \
log_likelihoods[:, :, model, gn_state][gn == gn_state]
# optionally combine likelihoods in a moving window
if filter_size:
model_likelihoods = np.apply_along_axis(np.convolve,
0,
model_likelihoods,
np.ones((filter_size,)))
# remove edges
model_likelihoods = \
model_likelihoods[filter_size//2:-1*(filter_size//2), ...]
# predict ancestry as model with highest likelihood
ancestry = np.argmax(model_likelihoods, axis=2)
# calculate confidence by comparing first and second most likely models
model_likelihoods.sort(axis=2)
confidence = model_likelihoods[:, :, 2] - model_likelihoods[:, :, 1]
# recind prediction where confidence is zero (models are equally likely)
ancestry[confidence == 0] = -1
return ancestry, confidence