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fws.py
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fws.py
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import numpy as np
import pandas as pd
import statsmodels.api as sm
# see: https://stackoverflow.com/questions/71109838/numpy-typing-with-specific-shape-and-datatype
import numpy.typing as npt
from typing import Annotated, Literal, TypeVar
DType = TypeVar("DType", bound=np.generic)
ArrayNxNx2 = Annotated[npt.NDArray[DType], Literal["N", "N", 2]]
# Define a dummy decorator for the case where numba isn't available:
# the decorated function will fall back to the pure python implementation.
try:
from numba import njit
except ImportError:
def njit(*args, **kwargs):
return lambda f: f
# __all__ defines the list of functions that will be publicly available
__all__ = ["fws"]
def fws(
a: ArrayNxNx2, # n_sites x n_samples x 2 array of allele depths (AD)
input: str = "AD",
) -> np.array:
"""
Calculate Fws for each sample in a population, from an array of biallelic allele depth or genotype information
Parameters
----------
a : ArrayNxNx2
numpy.array with shape: (n_sites x n_samples x 2) containing allele depth (AD)
or genotype (GT) information at biallelic sites for each sample.
input: str = "AD" [| "GT"]
specifies what the contents of `a` are - either the allele depth for each allele
for each sample at each site (the default), or diploid genotype calls.
Returns
-------
np.array[float]
An array of fws values, in the same order as the samples in the input
"""
if input == "AD":
maf_func = maf_from_AD
elif input == "GT":
maf_func = maf_from_GT
else:
raise Exception("Unknown input type: please use one of \"AD\" or \"GT\"")
# Calculate population-level minor allele frequency (MAF)
pop_maf = maf_func(a)
# Bin the population-level MAFs and calculate mean population-level expected heterozygosity per bin
bin_indices = get_bin_indices(pop_maf)
pop_mafs_binned = [pop_maf[b] for b in bin_indices]
pop_exphet_binned = [np.nanmean(exphet_from_maf(x)) for x in pop_mafs_binned]
# Then perform the sample-level calculation of Fws
fws = np.zeros(a.shape[1])
# For every sample
for i in range(a.shape[1]):
# calculate sample-level MAF
samp_maf = maf_func(a[:,[i],:])
# bin the sample-level MAFs using the population bin indices
samp_maf_binned = [samp_maf[b] for b in bin_indices]
# and calculate sample-level expected heterozygosity
samp_exp_het_binned = [np.nanmean(exphet_from_maf(x)) for x in samp_maf_binned]
# Get an index such that there are no nans in either pop or sample vector
non_nan_index = ~np.isnan(pop_exphet_binned) & ~np.isnan(samp_exp_het_binned)
x = [het for het,idx in zip(pop_exphet_binned, non_nan_index) if idx]
y = [het for het,idx in zip(samp_exp_het_binned, non_nan_index) if idx]
# then fit the linear regression: samp_exp_het_binned ~ pop_exp_het_binned.
# The code below doesn't fit an intercept, so it is constrained to be 0
model = sm.OLS(y, x)
slope = model.fit().params[0]
# Fiddle the fws value a little, depending on the regression
if slope < 0:
f = np.nan
elif slope > 1:
f = 0
else:
f = 1-slope
# and add it to the list to be returned
fws[i] = f
return fws
@njit()
def maf_from_AD(
AD: ArrayNxNx2, # n_sites x n_samples x 2 array of allele depths (AD)
) -> np.array: # 1d array of minor allele frequencies, len(n_sites)
# We will populate this array with mafs
mafs = np.zeros(AD.shape[0], dtype=np.float64)
# For every site
for i in range(AD.shape[0]):
# Initiate a vector a per-sample AFs to calculate mean MAF from
AFs = np.zeros(AD.shape[1], dtype=np.float64)
# For every sample
for j in range(AD.shape[1]):
ad1 = AD[i,j,0]
ad2 = AD[i,j,1]
# skip sites with missing data
if ad1 < 0 or ad2 < 0 or np.isnan(ad1) or np.isnan(ad2):
AFs[j] = np.nan
continue
if (ad1 + ad2) == 0:
AFs[j] = np.nan
continue
else:
AFs[j] = ad1 / (ad1 + ad2)
# Calculate maf from this site's average AFs
mafs[i] = np.nanmean(AFs)
if mafs[i] > 0.5:
mafs[i] = 1 - mafs[i]
return mafs
# TO DO - check all sites are biallelic?
# - sort out the dtype of GT
@njit
def maf_from_GT(
GT: ArrayNxNx2 # n_sites x n_samples x 2 array of genotypes (GT)
) -> np.array: # 1d array of minor allele frequencies, len(n_sites)
# We will populate this array with mafs
mafs = np.zeros(GT.shape[0], dtype=np.float64)
# We will use this value to make a look up array of the correct length
max_GT = int(np.nanmax(GT))
# For every site
for i in range(GT.shape[0]):
# Initiate an array of zeroed counts of each allele
AC = np.zeros((max_GT+1), dtype=np.int64)
# For every sample
for j in range(GT.shape[1]):
# skip missing data
if GT[i,j,0] < 0 or GT[i,j,1] < 0 or np.isnan(GT[i,j,0]) or np.isnan(GT[i,j,1]):
continue
gt1 = int(GT[i,j,0])
gt2 = int(GT[i,j,1])
# add a one for each allele present to the array
AC[gt1] += 1
AC[gt2] += 1
# if there is only missing data at this site, set maf to nan and continue to the next site]
if np.sum(AC) == 0:
mafs[i] = np.nan
continue
# If we sort (and reverse) the array, the frequency we calculate below will always be < 0.5 because
# the lower allele count is AC[1]. This means we don't have to check for AF > 0.5
AC.sort()
AC = np.flip(AC)
# calculate maf as lowest allele count / total allele count (this assume a mono or biallelic site)
maf = AC[1] / (AC[0] + AC[1])
mafs[i] = maf
return mafs
# Calculate expected heterozygosity from minor allele frequency
def exphet_from_maf(
mafs: np.ndarray, # a 1d array of floats which are minor allele frequencies
) -> np.ndarray: # the operation is vectorised so the lenth of the output is the same as len(mafs)
# expected heterozygosity is the same as 1 - sum(expected homozygosity for each allele):
# exp_het = 1 - (((1-mafs)**2) + mafs**2)
# or, equivalently, for a biallelic site: 2 * p * q (like in the Hardy-Weinberg equation):
exp_het = 2 * (1-mafs) * mafs
return exp_het
# Given a 1d array of minor allele frequencies, return the indices which will place them in 10 equally-spaced bins in [0,0.5]
def get_bin_indices(
mafs: np.ndarray, # a 1d array of mafs
) -> list[np.ndarray]: # a list of indices for binning the maf array
bin_boundaries = np.linspace(0, 0.5, 11) # [0.05,0.10,0.15,0.20,..,0.45,0.50]
bins = pd.cut(mafs, bins=bin_boundaries, include_lowest = True) # splits mafs into the bins whose boundaries are defined above
bin_indices = [np.where(bins == b)[0] for b in bins.categories] # a (length = len(mafs)) list of indices which places mafs into the 10 bins defined above
return bin_indices