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