def windowed_tajima_d(pos, ac, size=None, start=None, stop=None, step=None, windows=None, fill=np.nan): """Calculate the value of Tajima's D in windows over a single chromosome/contig. 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. size : int, optional The window size (number of bases). start : int, optional The position at which to start (1-based). stop : int, optional The position at which to stop (1-based). step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. windows : array_like, int, shape (n_windows, 2), optional Manually specify the windows to use as a sequence of (window_start, window_stop) positions, using 1-based coordinates. Overrides the size/start/stop/step parameters. fill : object, optional The value to use where a window is completely inaccessible. Returns ------- D : ndarray, float, shape (n_windows,) Tajima's D. windows : ndarray, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions, using 1-based coordinates. counts : ndarray, int, shape (n_windows,) Number of variants in each window. 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] >>> D, windows, counts = allel.stats.windowed_tajima_d( ... pos, ac, size=10, start=1, stop=31 ... ) >>> D array([ 0.59158014, 2.93397641, 6.12372436]) >>> windows array([[ 1, 10], [11, 20], [21, 31]]) >>> counts array([3, 4, 2]) """ # check inputs if not isinstance(pos, SortedIndex): pos = SortedIndex(pos, copy=False) if not hasattr(ac, "count_segregating"): ac = AlleleCountsArray(ac, copy=False) # assume number of chromosomes sampled is constant for all variants n = ac.sum(axis=1).max() # calculate constants a1 = np.sum(1 / np.arange(1, n)) 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) # locate segregating variants is_seg = ac.is_segregating() # calculate mean pairwise difference mpd = mean_pairwise_difference(ac, fill=0) # define statistic to compute for each window # noinspection PyPep8Naming def statistic(w_is_seg, w_mpd): S = np.count_nonzero(w_is_seg) pi = np.sum(w_mpd) d = pi - (S / a1) d_stdev = np.sqrt((e1 * S) + (e2 * S * (S - 1))) wD = d / d_stdev return wD D, windows, counts = windowed_statistic( pos, values=(is_seg, mpd), statistic=statistic, size=size, start=start, stop=stop, step=step, windows=windows, fill=fill, ) return D, windows, counts
def windowed_watterson_theta(pos, ac, size=None, start=None, stop=None, step=None, windows=None, is_accessible=None, fill=np.nan): """Calculate the value of Watterson's estimator in windows over a single chromosome/contig. 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. size : int, optional The window size (number of bases). start : int, optional The position at which to start (1-based). stop : int, optional The position at which to stop (1-based). step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. windows : array_like, int, shape (n_windows, 2), optional Manually specify the windows to use as a sequence of (window_start, window_stop) positions, using 1-based coordinates. Overrides the size/start/stop/step parameters. is_accessible : array_like, bool, shape (len(contig),), optional Boolean array indicating accessibility status for all positions in the chromosome/contig. fill : object, optional The value to use where a window is completely inaccessible. Returns ------- theta_hat_w : ndarray, float, shape (n_windows,) Watterson's estimator (theta hat per base). windows : ndarray, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions, using 1-based coordinates. n_bases : ndarray, int, shape (n_windows,) Number of (accessible) bases in each window. counts : ndarray, int, shape (n_windows,) Number of variants in each window. 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, windows, n_bases, counts = allel.windowed_watterson_theta( ... pos, ac, size=10, start=1, stop=31 ... ) >>> theta_hat_w array([0.10909091, 0.16363636, 0.04958678]) >>> windows array([[ 1, 10], [11, 20], [21, 31]]) >>> n_bases array([10, 10, 11]) >>> counts array([3, 4, 2]) """ # flake8: noqa # 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) # locate segregating variants is_seg = ac.is_segregating() # count segregating variants in windows S, windows, counts = windowed_statistic(pos, is_seg, statistic=np.count_nonzero, size=size, start=start, stop=stop, step=step, windows=windows, fill=0) # 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)) # absolute value of Watterson's theta theta_hat_w_abs = S / a1 # theta per base theta_hat_w, n_bases = per_base(theta_hat_w_abs, windows=windows, is_accessible=is_accessible, fill=fill) return theta_hat_w, windows, n_bases, counts
def windowed_watterson_theta( pos, ac, size=None, start=None, stop=None, step=None, windows=None, is_accessible=None, fill=np.nan ): """Calculate the value of Watterson's estimator in windows over a single chromosome/contig. 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. size : int, optional The window size (number of bases). start : int, optional The position at which to start (1-based). stop : int, optional The position at which to stop (1-based). step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. windows : array_like, int, shape (n_windows, 2), optional Manually specify the windows to use as a sequence of (window_start, window_stop) positions, using 1-based coordinates. Overrides the size/start/stop/step parameters. is_accessible : array_like, bool, shape (len(contig),), optional Boolean array indicating accessibility status for all positions in the chromosome/contig. fill : object, optional The value to use where a window is completely inaccessible. Returns ------- theta_hat_w : ndarray, float, shape (n_windows,) Watterson's estimator (theta hat per base). windows : ndarray, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions, using 1-based coordinates. n_bases : ndarray, int, shape (n_windows,) Number of (accessible) bases in each window. counts : ndarray, int, shape (n_windows,) Number of variants in each window. 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, windows, n_bases, counts = allel.stats.windowed_watterson_theta( ... pos, ac, size=10, start=1, stop=31 ... ) >>> theta_hat_w array([ 0.10909091, 0.16363636, 0.04958678]) >>> windows array([[ 1, 10], [11, 20], [21, 31]]) >>> n_bases array([10, 10, 11]) >>> counts array([3, 4, 2]) """ # flake8: noqa # 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) # locate segregating variants is_seg = ac.is_segregating() # count segregating variants in windows S, windows, counts = windowed_statistic( pos, is_seg, statistic=np.count_nonzero, size=size, start=start, stop=stop, step=step, windows=windows, fill=0 ) # 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)) # absolute value of Watterson's theta theta_hat_w_abs = S / a1 # theta per base theta_hat_w, n_bases = per_base(theta_hat_w_abs, windows=windows, is_accessible=is_accessible, fill=fill) return theta_hat_w, windows, n_bases, counts
def windowed_tajima_d(pos, ac, size=None, start=None, stop=None, step=None, windows=None, min_sites=3): """Calculate the value of Tajima's D in windows over a single chromosome/contig. 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. size : int, optional The window size (number of bases). start : int, optional The position at which to start (1-based). stop : int, optional The position at which to stop (1-based). step : int, optional The distance between start positions of windows. If not given, defaults to the window size, i.e., non-overlapping windows. windows : array_like, int, shape (n_windows, 2), optional Manually specify the windows to use as a sequence of (window_start, window_stop) positions, using 1-based coordinates. Overrides the size/start/stop/step parameters. 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. windows : ndarray, int, shape (n_windows, 2) The windows used, as an array of (window_start, window_stop) positions, using 1-based coordinates. counts : ndarray, int, shape (n_windows,) Number of variants in each window. 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, 20, 22, 25, 27] >>> D, windows, counts = allel.windowed_tajima_d(pos, ac, size=20, step=10, start=1, stop=31) >>> D array([1.36521524, 4.22566622]) >>> windows array([[ 1, 20], [11, 31]]) >>> counts array([6, 6]) """ # check inputs if not isinstance(pos, SortedIndex): pos = SortedIndex(pos, copy=False) if not hasattr(ac, 'count_segregating'): ac = AlleleCountsArray(ac, copy=False) # assume number of chromosomes sampled is constant for all variants n = ac.sum(axis=1).max() # calculate constants a1 = np.sum(1 / np.arange(1, n)) 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) # locate segregating variants is_seg = ac.is_segregating() # calculate mean pairwise difference mpd = mean_pairwise_difference(ac, fill=0) # define statistic to compute for each window # noinspection PyPep8Naming def statistic(w_is_seg, w_mpd): S = np.count_nonzero(w_is_seg) if S < min_sites: return np.nan pi = np.sum(w_mpd) d = pi - (S / a1) d_stdev = np.sqrt((e1 * S) + (e2 * S * (S - 1))) wD = d / d_stdev return wD D, windows, counts = windowed_statistic(pos, values=(is_seg, mpd), statistic=statistic, size=size, start=start, stop=stop, step=step, windows=windows, fill=np.nan) return D, windows, counts