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PhiManip

Module for manipulating population frequency spectra phi, such as population splittings and admixture.

check_xx(xx)

Check whether the input xx is monotonically increasing from 0 to 1.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies.

 required

Raises:

Type Description
ValueError

If xx does not start at 0, end at 1, or is not monotonically increasing.
Source code in dadi/PhiManip.py 
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def check_xx(xx):
    """
    Check whether the input xx is monotonically increasing from 0 to 1.

    Args:
        xx (array): One-dimensional grid of frequencies.

    Raises:
        ValueError: If xx does not start at 0, end at 1, or is not monotonically increasing.
    """
    if not xx[0] == 0 and xx[1] == 1:
        raise ValueError('Input xx argument does not run from 0 to 1.'
                         'Have you passed in an incorrect argument?')
    if not numpy.all(numpy.diff(xx) >= 0):
        raise ValueError('Input xx argument is not monotonically increasing. '
                         'Have you passed in an incorrect argument?')

filter_pops(phi, xx, tokeep)

Filter phi to keep only certain populations.

Returns new phi with len(tokeep) populations.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original populations.

 required
xx array

Mapping of points in phi to frequencies in population to be removed.

 required
tokeep list

List of population numbers to keep, numbering from 1.

 required

Returns:

Name Type Description
phi array

The updated phi array with only the specified populations.
Source code in dadi/PhiManip.py 
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def filter_pops(phi, xx, tokeep):
    """
    Filter phi to keep only certain populations.

    Returns new phi with len(tokeep) populations.

    Args:
        phi (array): Phi corresponding to original populations.
        xx (array): Mapping of points in phi to frequencies in population to be removed.
        tokeep (list): List of population numbers to keep, numbering from 1.

    Returns:
        phi (array): The updated phi array with only the specified populations.
    """
    toremove = list(range(1, phi.ndim+1))
    for pop_ii in tokeep:
        toremove.remove(pop_ii)
    for pop_ii in sorted(toremove)[::-1]:
        phi = remove_pop(phi, xx, pop_ii)
    return phi

phi_1D(xx, nu=1.0, theta0=1.0, gamma=0, h=0.5, theta=None, beta=1, deme_ids=None)

Compute a one-dimensional phi for a constant-sized population with genic selection.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
nu float

Size of this population, relative to the reference population size Nref.

 1.0
theta0 float

Scaled mutation rate, equal to 4*Nref * u, where u is the mutation event rate per generation for the simulated locus and Nref is the reference population size.

 1.0
gamma float

Scaled selection coefficient, equal to 2*Nref * s, where s is the selective advantage.

 0
h float

Dominance coefficient. If A is the selected allele, the aa has fitness 1, aA has fitness 1+2sh, and AA has fitness 1+2s. h = 0.5 corresponds to genic selection.

 0.5
theta float

Deprecated in favor of distinct nu and theta0 arguments, for consistency with Integration functions.

 None
beta float

Scaling factor for selection.

 1
deme_ids list

Sequence of strings representing the names of demes.

 None

Returns:

Name Type Description
phi array

A new phi array.
Source code in dadi/PhiManip.py 
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def phi_1D(xx, nu=1.0, theta0=1.0, gamma=0, h=0.5, theta=None, beta=1, deme_ids=None):
    """
    Compute a one-dimensional phi for a constant-sized population with genic selection.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        nu (float): Size of this population, relative to the reference population size Nref.
        theta0 (float): Scaled mutation rate, equal to 4*Nref * u, where u is the mutation 
            event rate per generation for the simulated locus and Nref is the reference 
            population size.
        gamma (float): Scaled selection coefficient, equal to 2*Nref * s, where s is the
            selective advantage.
        h (float): Dominance coefficient. If A is the selected allele, the aa has fitness 1,
            aA has fitness 1+2sh, and AA has fitness 1+2s. h = 0.5 corresponds to genic selection.
        theta (float, optional): Deprecated in favor of distinct nu and theta0 arguments, for 
            consistency with Integration functions.
        beta (float): Scaling factor for selection.
        deme_ids (list, optional): Sequence of strings representing the names of demes.

    Returns:
        phi (array): A new phi array.
    """
    Demes.cache = [Demes.Initiation(nu, deme_ids=deme_ids)]

    if theta is not None:
        raise ValueError('The parameter theta has been deprecated in favor of '
                         'parameters nu and theta0, for consistency with the '
                         'Integration functions.')

    if h == 0.5:
        return phi_1D_genic(xx, nu, theta0, gamma, beta=beta)

    # Eqn 1 from Williamson, Fledel-Alon, Bustamante _Genetics_ 168:463 (2004).

    # Modified to incorporate fact that for beta != 1, we get a term of 
    # 4*beta/(beta+1)^2 in V. This can be implemented by rescaling gamma
    # and rescaling the final phi.
    gamma = gamma * 4.*beta/(beta+1.)**2

    # Our final result is of the form 
    # exp(Q) * int_0_x exp(-Q) / int_0_1 exp(-Q)

    # For large negative gamma, exp(-Q) becomes numerically infinite.
    # To work around this, we can adjust Q in both the top and bottom
    # integrals by the same factor. We choose to make that factor the 
    # maximum of -Q, which is -2*gamma.
    Qadjust = 0
    # For negative gamma, the maximum of -Q is -2*gamma.
    if gamma < 0 and numpy.isinf(numpy.exp(-2*gamma)):
        Qadjust = -2*gamma

    # For large positive gamma, the prefactor exp(Q) becomes numerically
    # infinite, while the numerator becomes very small. To work around this,
    # we'll can pull the prefactor into the numerator integral.

    # Evaluate the denominator integral.
    integrand = lambda xi: numpy.exp(-4*gamma*h*xi - 2*gamma*(1-2*h)*xi**2
                                     - Qadjust)
    int0, eps = scipy.integrate.quad(integrand, 0, 1, epsabs=0,
                                     points=numpy.linspace(0,1,41))

    ints = numpy.empty(len(xx))
    # Evaluate the numerator integrals
    if gamma < 0:
        # In this case, the prefactor is not divergent, so we can evaluate
        # the numerator as before, using the Qadjust if necessary.
        for ii,q in enumerate(xx):
            val, eps = scipy.integrate.quad(integrand, q, 1, epsabs=0,
                                            points=numpy.linspace(q,1,41))
            ints[ii] = val
        phi = numpy.exp(4*gamma*h*xx + 2*gamma*(1-2*h)*xx**2)*ints/int0
    else:
        # In this case, the prefactor may be divergent, so we do the integral
        # with the prefactor pulled inside
        integrand = lambda xi, q: numpy.exp(-4*gamma*h*(xi-q) -
                                            2*gamma*(1-2*h)*(xi**2-q**2))
        for ii,q in enumerate(xx):
            val, eps = scipy.integrate.quad(integrand, q, 1, args=(q,))
            ints[ii] = val
        phi = ints/int0

    # Protect from division by zero errors
    phi[1:-1] *= 1./(xx[1:-1]*(1-xx[1:-1]))
    # Technically, phi diverges at 0. This kludge lets us do numerics
    # sensibly.
    phi[0] = phi[1]
    # I used Mathematica to calculate the proper limit for x goes to 1.
    # But if we've adjusted the denominator integrand, then that limit doesn't
    # hold. We only need to do that in cases of strong negative selection,
    # when phi near 1 should be almost zero anyways. So we'll just ensure
    # that it is at least monotonically decreasing.
    if Qadjust == 0:
        phi[-1] = 1./int0
    else:
        phi[-1] = min(phi[-1], phi[-2])

    return phi * nu*theta0 * 4.*beta/(beta+1.)**2

phi_1D_X(xx, nu=1.0, theta0=1.0, gamma=0, h=0.5, beta=1, alpha=1)

Compute a one-dimensional phi for a constant-sized population with genic selection.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
nu float

Size of this population, relative to the reference population size Nref.

 1.0
theta0 float

Scaled mutation rate, equal to 4*Nref * u, where u is the mutation event rate per generation for the simulated locus and Nref is the reference population size.

 1.0
gamma float

Scaled selection coefficient, equal to 2*Nref * s, where s is the selective advantage.

 0
h float

Dominance coefficient. If A is the selected allele, the aa has fitness 1, aA has fitness 1+2sh, and AA has fitness 1+2s. Male carriers have fitness 1+2s. h = 0.5 corresponds to genic selection.

 0.5
beta float

Scaling factor for selection.

 1
alpha float

Additional scaling factor for selection.

 1

Returns:

Name Type Description
phi array

A new phi array.
Source code in dadi/PhiManip.py 
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def phi_1D_X(xx, nu=1.0, theta0=1.0, gamma=0, h=0.5, beta=1, alpha=1):
    """
    Compute a one-dimensional phi for a constant-sized population with genic selection.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        nu (float): Size of this population, relative to the reference population size Nref.
        theta0 (float): Scaled mutation rate, equal to 4*Nref * u, where u is the mutation 
            event rate per generation for the simulated locus and Nref is the reference 
            population size.
        gamma (float): Scaled selection coefficient, equal to 2*Nref * s, where s is the
            selective advantage.
        h (float): Dominance coefficient. If A is the selected allele, the aa has fitness 1,
            aA has fitness 1+2sh, and AA has fitness 1+2s. Male carriers have fitness 1+2s.
            h = 0.5 corresponds to genic selection.
        beta (float): Scaling factor for selection.
        alpha (float): Additional scaling factor for selection.

    Returns:
        phi (array): A new phi array.
    """
    Kv = (2.*beta+4.)*(beta+1.)/(9.*beta)
    Km1 = 4./3. * gamma*(0.5+h)
    Km2 = 4./3.*gamma*(1.-2.*h)
    g1 = Km1/Kv
    g2 = Km2/Kv

    # First we evaluate the relevant integrals.
    ints = numpy.empty(len(xx))
    integrand = lambda xi: numpy.exp(-2*g1*xi - g2*xi**2)
    val, eps = scipy.integrate.quad(integrand, 0, 1)
    int0 = val
    for ii,q in enumerate(xx):
        val, eps = scipy.integrate.quad(integrand, q, 1)
        ints[ii] = val

    phi = numpy.exp(2*g1*xx + g2*xx**2)*ints/int0
    # Protect from division by zero errors
    if xx[0] == 0 and xx[-1] == 1:
        phi[1:-1] *= 1./(xx[1:-1]*(1-xx[1:-1]))
    else:
        phi *= 1./(xx*(1-xx))

    if xx[0] == 0:
        # Technically, phi diverges at 0. This fixes lets us do numerics
        # sensibly.
        phi[0] = phi[1]
    if xx[-1] == 1:
        # I used Mathematica to check that this was the proper limit.
        phi[-1] = 1./int0
    return phi * nu*theta0 * 1./Kv * 2./(1.+2.*beta)*(1./(1.+alpha) + beta)

phi_1D_genic(xx, nu=1.0, theta0=1.0, gamma=0, theta=None, beta=1)

Compute a one-dimensional phi for a constant-sized population with genic selection.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
nu float

Size of this population, relative to the reference population size Nref.

 1.0
theta0 float

Scaled mutation rate, equal to 4*Nref * u, where u is the mutation event rate per generation for the simulated locus and Nref is the reference population size.

 1.0
gamma float

Scaled selection coefficient, equal to 2*Nref * s, where s is the selective advantage.

 0
theta float

Deprecated in favor of distinct nu and theta0 arguments, for consistency with Integration functions.

 None
beta float

Scaling factor for selection.

 1

Returns:

Name Type Description
phi array

A new phi array.
Source code in dadi/PhiManip.py 
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def phi_1D_genic(xx, nu=1.0, theta0=1.0, gamma=0, theta=None, beta=1):
    """
    Compute a one-dimensional phi for a constant-sized population with genic selection.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        nu (float): Size of this population, relative to the reference population size Nref.
        theta0 (float): Scaled mutation rate, equal to 4*Nref * u, where u is the mutation 
            event rate per generation for the simulated locus and Nref is the reference 
            population size.
        gamma (float): Scaled selection coefficient, equal to 2*Nref * s, where s is the
            selective advantage.
        theta (float, optional): Deprecated in favor of distinct nu and theta0 arguments, for 
            consistency with Integration functions.
        beta (float): Scaling factor for selection.

    Returns:
        phi (array): A new phi array.
    """

    if theta is not None:
        raise ValueError('The parameter theta has been deprecated in favor of '
                         'parameters nu and theta0, for consistency with the '
                         'Integration functions.')
    if gamma == 0:
        return phi_1D_snm(xx, nu, theta0, beta=beta)

    # Beta effectively re-scales gamma.
    gamma = gamma * 4.*beta/(beta+1.)**2

    exp = numpy.exp
    # Protect from warnings on division by zero
    if xx[0] == 0 and xx[-1] == 1:
        phi = 0*xx
        if gamma > -300:
            phi[1:-1] = 1./(xx[1:-1]*(1-xx[1:-1]))\
                    * (1-exp(-2*gamma*(1-xx[1:-1])))/(1-exp(-2*gamma))
        else:
            # Avoid overflow issues for very negative gammas
            phi[1:-1] = 1./(xx[1:-1]*(1-xx[1:-1])) * exp(2*gamma*xx[1:-1])
    else:
        if gamma > -300:
            phi = 1./(xx*(1-xx)) * (1-exp(-2*gamma*(1-xx)))/(1-exp(-2*gamma))
        else:
            phi = 1./(xx*(1-xx)) * exp(2*gamma*xx)

    if xx[0] == 0:
        phi[0] = phi[1]
    if xx[-1] == 1:
        if gamma < 300:
            limit = 2*gamma * exp(2*gamma)/(exp(2*gamma)-1)
        else:
            limit = 2*gamma
        phi[-1] = limit
    return phi * nu*theta0 * 4.*beta/(beta+1.)**2

phi_1D_snm(xx, nu=1.0, theta0=1.0, theta=None, beta=1)

Compute the standard neutral one-dimensional probability density.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
nu float

Size of this population, relative to the reference population size Nref.

 1.0
theta0 float

Scaled mutation rate, equal to 4*Nref * u, where u is the mutation event rate per generation for the simulated locus and Nref is the reference population size.

 1.0
theta float

Deprecated in favor of distinct nu and theta0 arguments, for consistency with Integration functions.

 None
beta float

Scaling factor for selection.

 1

Returns:

Name Type Description
phi array

A new phi array.
Source code in dadi/PhiManip.py 
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def phi_1D_snm(xx, nu=1.0, theta0=1.0, theta=None, beta=1):
    """
    Compute the standard neutral one-dimensional probability density.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        nu (float): Size of this population, relative to the reference population size Nref.
        theta0 (float): Scaled mutation rate, equal to 4*Nref * u, where u is the mutation 
            event rate per generation for the simulated locus and Nref is the reference 
            population size.
        theta (float, optional): Deprecated in favor of distinct nu and theta0 arguments, for 
            consistency with Integration functions.
        beta (float): Scaling factor for selection.

    Returns:
        phi (array): A new phi array.
    """

    if theta is not None:
        raise ValueError('The parameter theta has been deprecated in favor of '
                         'parameters nu and theta0, for consistency with the '
                         'Integration functions.')
    # Protect from division by zero errors
    if xx[0] == 0:
        phi = 0*xx
        phi[1:] = nu*theta0/xx[1:]
        phi[0] = phi[1]
    else:
        phi = nu*theta0/xx
    return phi * 4.*beta/(beta+1.)**2

phi_1D_to_2D(xx, phi_1D, deme_ids=None)

Implement a one-to-two population split.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
phi_1D array

Initial probability density.

 required
deme_ids list

Sequence of strings representing the names of demes after split.

 None

Returns:

Name Type Description
phi_2D array

A new two-dimensional phi array.
Source code in dadi/PhiManip.py 
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def phi_1D_to_2D(xx, phi_1D, deme_ids=None):
    """
    Implement a one-to-two population split.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        phi_1D (array): Initial probability density.
        deme_ids (list, optional): Sequence of strings representing the names of demes after split.

    Returns:
        phi_2D (array): A new two-dimensional phi array.
    """
    check_xx(xx)

    Demes.cache.append(Demes.Split(proportions=[1], deme_ids=deme_ids))

    pts = len(xx)
    phi_2D = numpy.zeros((pts, pts))
    for ii in range(1, pts-1):
        phi_2D[ii,ii] = phi_1D[ii] * 2/(xx[ii+1]-xx[ii-1])
    return phi_2D

phi_2D_admix_1_into_2(phi, f, xx, yy)

Admix population 1 into population 2.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 2 populations.

 required
f float

Fraction of updated population 2 to be derived from population 1. A fraction 1-f will be derived from the original population 2.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_2D_admix_1_into_2(phi, f, xx,yy):
    """
    Admix population 1 into population 2.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 2 populations.
        f (float): Fraction of updated population 2 to be derived from population 1. 
            A fraction 1-f will be derived from the original population 2.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.

    Returns:
        phi (array): The updated phi array.
    """
    # This is just like the the split_admix situation, but we're splitting into
    # a population with zz=yy. We could do this by creating a xx by yy by yy
    # array, then integrating out the second population. That's a big waste of
    # memory, however.
    Demes.cache.append(Demes.Pulse(sources=[1], dest=2, proportions=[f]))
    lower_z_index, upper_z_index, frac_lower, frac_upper, norm \
            = _two_pop_admixture_intermediates(phi, f, xx,yy,yy)

    # Basically, we're splitting into a third zz population, then integrating
    # over yy to be left with the two populations we care about.
    lower_cont = frac_lower*norm
    upper_cont = frac_upper*norm
    idx_j = numpy.arange(phi.shape[1])
    for ii in range(phi.shape[0]):
        phi_int = numpy.zeros((phi.shape[1], phi.shape[1]))
        # Use fancy indexing to avoid the commented out loop.
        #for jj in range(len(yy)):
        #    phi_int[jj, upper_z_index[ii,jj]] += frac_upper[ii,jj]*norm[ii,jj]
        #    phi_int[jj, lower_z_index[ii,jj]] += frac_lower[ii,jj]*norm[ii,jj]
        phi_int[idx_j, lower_z_index[ii]] = lower_cont[ii]
        phi_int[idx_j, upper_z_index[ii]] += upper_cont[ii]
        phi[ii] = Numerics.trapz(phi_int, yy, axis=0)

    return phi

phi_2D_admix_2_into_1(phi, f, xx, yy)

Admix population 2 into population 1.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 2 populations.

 required
f float

Fraction of updated population 1 to be derived from population 2. A fraction 1-f will be derived from the original population 1.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_2D_admix_2_into_1(phi, f, xx,yy):
    """
    Admix population 2 into population 1.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 2 populations.
        f (float): Fraction of updated population 1 to be derived from population 2. 
            A fraction 1-f will be derived from the original population 1.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.

    Returns:
        phi (array): The updated phi array.
    """
    # Note that it's 1-f here since f now denotes the fraction coming from
    # population 2.
    Demes.cache.append(Demes.Pulse(sources=[2], dest=1, proportions=[f]))
    lower_z_index, upper_z_index, frac_lower, frac_upper, norm \
            = _two_pop_admixture_intermediates(phi, 1-f, xx,yy,xx)

    idx_i = numpy.arange(phi.shape[0])
    lower_cont = frac_lower*norm
    upper_cont = frac_upper*norm
    for jj in range(len(yy)):
        phi_int = numpy.zeros((len(xx), len(xx)))
        phi_int[idx_i, lower_z_index[:,jj]] = lower_cont[:,jj]
        phi_int[idx_i, upper_z_index[:,jj]] = upper_cont[:,jj]
        phi[:,jj] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_2D_to_3D_admix(phi, f1, xx, yy, zz, deme_ids=None)

Create population 3 admixed from populations 1 and 2.

Returns a 3D sfs of shape (len(xx),len(yy),len(zz))

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 2 populations.

 required
f1 float

Fraction of population 3 derived from population 1. A fraction 1-f1 will be derived from population 2.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Frequency mapping that will be used along population 3 axis.

 required
deme_ids list

Sequence of strings representing the names of demes after split.

 None

Returns:

Name Type Description
phi_3D array

A new three-dimensional phi array.
Source code in dadi/PhiManip.py 
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def phi_2D_to_3D_admix(phi, f1, xx,yy,zz, deme_ids=None):
    """
    Create population 3 admixed from populations 1 and 2.

    Returns a 3D sfs of shape (len(xx),len(yy),len(zz))

    Args:
        phi (array): Phi corresponding to original 2 populations.
        f1 (float): Fraction of population 3 derived from population 1. A fraction 1-f1
            will be derived from population 2.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Frequency mapping that will be used along population 3 axis.
        deme_ids (list, optional): Sequence of strings representing the names of demes after split.

    Returns:
        phi_3D (array): A new three-dimensional phi array.
    """
    Demes.cache.append(Demes.Split(proportions=[f1, 1-f1], deme_ids=deme_ids))

    lower_z_index, upper_z_index, frac_lower, frac_upper, norm \
            = _two_pop_admixture_intermediates(phi, f1, xx,yy,zz)


    # Assemble our result.
    # This uses numpy's fancy indexing. It is much, much faster than an
    # explicit loop.
    # See the numpy-discussion post "Numpy Advanced Indexing Question" by
    # Robert Kern on July 16, 2008
    # http://projects.scipy.org/pipermail/numpy-discussion/2008-July/035776.html
    idx_i = numpy.arange(len(xx))[:,numpy.newaxis]
    idx_j = numpy.arange(len(yy))[numpy.newaxis,:]

    phi_3D = numpy.zeros((len(xx), len(yy), len(zz)))
    phi_3D[idx_i, idx_j, lower_z_index] = frac_lower*norm
    phi_3D[idx_i, idx_j, upper_z_index] += frac_upper*norm

    return phi_3D

phi_2D_to_3D_split_1(xx, phi_2D, deme_ids=None)

Split population 1 into populations 1 and 3.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
phi_2D array

Initial probability density.

 required
deme_ids list

Sequence of strings representing the names of demes after split.

 None

Returns:

Name Type Description
phi_2D_to_3D_admix array

A new three-dimensional phi array.
Source code in dadi/PhiManip.py 
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def phi_2D_to_3D_split_1(xx, phi_2D, deme_ids=None):
    """
    Split population 1 into populations 1 and 3.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        phi_2D (array): Initial probability density.
        deme_ids (list, optional): Sequence of strings representing the names of demes after split.

    Returns:
        phi_2D_to_3D_admix (array): A new three-dimensional phi array.
    """
    check_xx(xx)

    return phi_2D_to_3D_admix(phi_2D,1,xx,xx,xx, deme_ids)

phi_2D_to_3D_split_2(xx, phi_2D, deme_ids=None)

Split population 2 into populations 2 and 3.

Parameters:

Name Type Description Default
xx array

One-dimensional grid of frequencies upon which phi is defined.

 required
phi_2D array

Initial probability density.

 required
deme_ids list

Sequence of strings representing the names of demes after split.

 None

Returns:

Name Type Description
phi_2D_to_3D_admix array

A new three-dimensional phi array.
Source code in dadi/PhiManip.py 
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def phi_2D_to_3D_split_2(xx, phi_2D, deme_ids=None):
    """
    Split population 2 into populations 2 and 3.

    Args:
        xx (array): One-dimensional grid of frequencies upon which phi is defined.
        phi_2D (array): Initial probability density.
        deme_ids (list, optional): Sequence of strings representing the names of demes after split.

    Returns:
        phi_2D_to_3D_admix (array): A new three-dimensional phi array.
    """
    check_xx(xx)

    return phi_2D_to_3D_admix(phi_2D,0,xx,xx,xx, deme_ids)

phi_3D_admix_1_and_2_into_3(phi, f1, f2, xx, yy, zz)

Admix populations 1 and 2 into population 3.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 3 populations.

 required
f1 float

Fraction of updated population 3 to be derived from population 1.

required
f2 float

Fraction of updated population 3 to be derived from population 2. A fraction (1-f1-f2) will be derived from the original pop 3.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_3D_admix_1_and_2_into_3(phi, f1,f2, xx,yy,zz):
    """
    Admix populations 1 and 2 into population 3.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 3 populations.
        f1 (float): Fraction of updated population 3 to be derived from population 1. 
        f2 (float): Fraction of updated population 3 to be derived from population 2. 
            A fraction (1-f1-f2) will be derived from the original pop 3.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[1,2], dest=3, proportions=[f1,f2]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _three_pop_admixture_intermediates(phi, f1,f2, xx,yy,zz, zz)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    # Basically, we're splitting into a fourth ww population, then integrating
    # over zz to be left with the two populations we care about.
    idx_k = numpy.arange(phi.shape[2])
    for ii in range(phi.shape[0]):
        for jj in range(phi.shape[1]):
            phi_int = numpy.zeros((phi.shape[2], phi.shape[2]))
            phi_int[idx_k, lower_w_index[ii,jj]] = lower_cont[ii,jj]
            phi_int[idx_k, upper_w_index[ii,jj]] = upper_cont[ii,jj]
            phi[ii,jj] = Numerics.trapz(phi_int, zz, axis=0)

    return phi

phi_3D_admix_1_and_3_into_2(phi, f1, f3, xx, yy, zz)

Admix populations 1 and 3 into population 2.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 3 populations.

 required
f1 float

Fraction of updated population 2 to be derived from population 1.

required
f3 float

Fraction of updated population 2 to be derived from population 3. A fraction (1-f1-f3) will be derived from the original pop 2.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_3D_admix_1_and_3_into_2(phi, f1,f3, xx,yy,zz):
    """
    Admix populations 1 and 3 into population 2.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 3 populations.
        f1 (float): Fraction of updated population 2 to be derived from population 1. 
        f3 (float): Fraction of updated population 2 to be derived from population 3. 
            A fraction (1-f1-f3) will be derived from the original pop 2.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[1,3], dest=2, proportions=[f1,f3]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _three_pop_admixture_intermediates(phi, f1,1-f1-f3, xx,yy,zz, yy)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    # Basically, we're splitting into a fourth ww population, then integrating
    # over yy to be left with the two populations we care about.
    idx_j = numpy.arange(phi.shape[1])
    for ii in range(phi.shape[0]):
        for kk in range(phi.shape[2]):
            phi_int = numpy.zeros((phi.shape[1], phi.shape[1]))
            phi_int[idx_j, lower_w_index[ii,:,kk]] = lower_cont[ii,:,kk]
            phi_int[idx_j, upper_w_index[ii,:,kk]] = upper_cont[ii,:,kk]
            phi[ii,:,kk] = Numerics.trapz(phi_int, yy, axis=0)

    return phi

phi_3D_admix_2_and_3_into_1(phi, f2, f3, xx, yy, zz)

Admix populations 2 and 3 into population 1.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 3 populations.

 required
f2 float

Fraction of updated population 1 to be derived from population 2.

required
f3 float

Fraction of updated population 1 to be derived from population 3. A fraction (1-f2-f3) will be derived from the original pop 1.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_3D_admix_2_and_3_into_1(phi, f2,f3, xx,yy,zz):
    """
    Admix populations 2 and 3 into population 1.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 3 populations.
        f2 (float): Fraction of updated population 1 to be derived from population 2. 
        f3 (float): Fraction of updated population 1 to be derived from population 3. 
            A fraction (1-f2-f3) will be derived from the original pop 1.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[2,3], dest=1, proportions=[f2,f3]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _three_pop_admixture_intermediates(phi, 1-f2-f3,f2, xx,yy,zz, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    # Basically, we're splitting into a fourth ww population, then integrating
    # over yy to be left with the two populations we care about.
    idx_i = numpy.arange(phi.shape[0])
    for jj in range(phi.shape[1]):
        for kk in range(phi.shape[2]):
            phi_int = numpy.zeros((phi.shape[0], phi.shape[0]))
            phi_int[idx_i, lower_w_index[:,jj,kk]] = lower_cont[:,jj,kk]
            phi_int[idx_i, upper_w_index[:,jj,kk]] = upper_cont[:,jj,kk]
            phi[:,jj,kk] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_3D_to_4D(phi, f1, f2, xx, yy, zz, aa, deme_ids=None)

Create population 4 from populations 1, 2, and 3.

Returns a 4D sfs of shape (len(xx),len(yy),len(zz),len(aa))

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 3 populations.

 required
f1 float

Fraction of population 4 derived from population 1.

 required
f2 float

Fraction of population 4 derived from population 2. A fraction 1-f1-f2 will be derived from population 3.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Frequency mapping that will be used along population 4 axis.

 required
deme_ids list

Sequence of strings representing the names of demes after split.

 None

Returns:

Name Type Description
phi_4D array

A new four-dimensional phi array.
Source code in dadi/PhiManip.py 
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def phi_3D_to_4D(phi, f1,f2, xx,yy,zz,aa, deme_ids=None):
    """
    Create population 4 from populations 1, 2, and 3.

    Returns a 4D sfs of shape (len(xx),len(yy),len(zz),len(aa))

    Args:
        phi (array): Phi corresponding to original 3 populations.
        f1 (float): Fraction of population 4 derived from population 1.
        f2 (float): Fraction of population 4 derived from population 2.
            A fraction 1-f1-f2 will be derived from population 3.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Frequency mapping that will be used along population 4 axis.
        deme_ids (list, optional): Sequence of strings representing the names of demes after split.

    Returns:
        phi_4D (array): A new four-dimensional phi array.
    """
    Demes.cache.append(Demes.Split(proportions=[f1, f2, 1-f1-f2], deme_ids=deme_ids))

    lower_z_index, upper_z_index, frac_lower, frac_upper, norm \
            = _three_pop_admixture_intermediates(phi, f1, f2, xx,yy,zz, aa)

    # Assemble our result.
    # This uses numpy's fancy indexing. It is much, much faster than an
    # explicit loop.
    # See the numpy-discussion post "Numpy Advanced Indexing Question" by
    # Robert Kern on July 16, 2008
    # http://projects.scipy.org/pipermail/numpy-discussion/2008-July/035776.html
    idx_i = numpy.arange(len(xx))[:,nuax,nuax]
    idx_j = numpy.arange(len(yy))[nuax,:,nuax]
    idx_k = numpy.arange(len(zz))[nuax,nuax,:]

    phi_4D = numpy.zeros((len(xx), len(yy), len(zz), len(aa)))
    phi_4D[idx_i, idx_j, idx_k, lower_z_index] = frac_lower*norm
    phi_4D[idx_i, idx_j, idx_k, upper_z_index] += frac_upper*norm

    return phi_4D

phi_4D_admix_into_1(phi, f2, f3, f4, xx, yy, zz, aa)

Admix populations 2, 3, and 4 into population 1.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 4 populations.

 required
f2 float

Fraction of updated population 1 to be derived from population 2.

required
f3 float

Fraction of updated population 1 to be derived from population 3.

required
f4 float

Fraction of updated population 1 to be derived from population 4. A fraction (1-f2-f3-f4) will be derived from the original pop 1.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_4D_admix_into_1(phi, f2,f3,f4, xx,yy,zz,aa):
    """
    Admix populations 2, 3, and 4 into population 1.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 4 populations.
        f2 (float): Fraction of updated population 1 to be derived from population 2. 
        f3 (float): Fraction of updated population 1 to be derived from population 3. 
        f4 (float): Fraction of updated population 1 to be derived from population 4. 
            A fraction (1-f2-f3-f4) will be derived from the original pop 1.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[2,3,4], dest=1, proportions=[f2,f3,f4]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _four_pop_admixture_intermediates(phi, 1-f2-f3-f4,f2,f3, xx,yy,zz,aa, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    # Basically, we're splitting into a fifth bb population, then integrating
    # over xx to be left with the two populations we care about.
    idx_i = numpy.arange(phi.shape[0])
    for jj in range(phi.shape[1]):
        for kk in range(phi.shape[2]):
            for ll in range(phi.shape[3]):
                phi_int = numpy.zeros((phi.shape[0], phi.shape[0]))
                phi_int[idx_i, lower_w_index[:,jj,kk,ll]] = lower_cont[:,jj,kk,ll]
                phi_int[idx_i, upper_w_index[:,jj,kk,ll]] = upper_cont[:,jj,kk,ll]
                phi[:,jj,kk,ll] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_4D_admix_into_2(phi, f1, f3, f4, xx, yy, zz, aa)

Admix populations 1,3, and 4 into population 2.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 4 populations.

 required
f1 float

Fraction of updated population 2 to be derived from population 1.

required
f3 float

Fraction of updated population 2 to be derived from population 3.

required
f4 float

Fraction of updated population 2 to be derived from population 4. A fraction (1-f1-f3-f4) will be derived from the original pop 2.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_4D_admix_into_2(phi, f1,f3,f4, xx,yy,zz,aa):
    """
    Admix populations 1,3, and 4 into population 2.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 4 populations.
        f1 (float): Fraction of updated population 2 to be derived from population 1. 
        f3 (float): Fraction of updated population 2 to be derived from population 3. 
        f4 (float): Fraction of updated population 2 to be derived from population 4. 
            A fraction (1-f1-f3-f4) will be derived from the original pop 2.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[1,3,4], dest=2, proportions=[f1, f3, f4]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _four_pop_admixture_intermediates(phi, f1,1-f1-f3-f4,f3, xx,yy,zz,aa, yy)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_j = numpy.arange(phi.shape[1])
    for ii in range(phi.shape[0]):
        for kk in range(phi.shape[2]):
            for ll in range(phi.shape[3]):
                phi_int = numpy.zeros((phi.shape[1], phi.shape[1]))
                phi_int[idx_j, lower_w_index[ii,:,kk,ll]] = lower_cont[ii,:,kk,ll]
                phi_int[idx_j, upper_w_index[ii,:,kk,ll]] = upper_cont[ii,:,kk,ll]
                phi[ii,:,kk,ll] = Numerics.trapz(phi_int, yy, axis=0)

    return phi

phi_4D_admix_into_3(phi, f1, f2, f4, xx, yy, zz, aa)

Admix populations 1,2, and 4 into population 3.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 4 populations.

 required
f1 float

Fraction of updated population 3 to be derived from population 1.

required
f2 float

Fraction of updated population 3 to be derived from population 2.

required
f4 float

Fraction of updated population 3 to be derived from population 4. A fraction (1-f1-f2-f4) will be derived from the original pop 3.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_4D_admix_into_3(phi, f1,f2,f4, xx,yy,zz,aa):
    """
    Admix populations 1,2, and 4 into population 3.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 4 populations.
        f1 (float): Fraction of updated population 3 to be derived from population 1. 
        f2 (float): Fraction of updated population 3 to be derived from population 2. 
        f4 (float): Fraction of updated population 3 to be derived from population 4. 
            A fraction (1-f1-f2-f4) will be derived from the original pop 3.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[1,2,4], dest=3, proportions=[f1, f2, f4]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _four_pop_admixture_intermediates(phi, f1,f2,1-f1-f2-f4, xx,yy,zz,aa, yy)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_k = numpy.arange(phi.shape[2])
    for ii in range(phi.shape[0]):
        for jj in range(phi.shape[1]):
            for ll in range(phi.shape[3]):
                phi_int = numpy.zeros((phi.shape[2], phi.shape[2]))
                phi_int[idx_k, lower_w_index[ii,jj,:,ll]] = lower_cont[ii,jj,:,ll]
                phi_int[idx_k, upper_w_index[ii,jj,:,ll]] = upper_cont[ii,jj,:,ll]
                phi[ii,jj,:,ll] = Numerics.trapz(phi_int, zz, axis=0)

    return phi

phi_4D_admix_into_4(phi, f1, f2, f3, xx, yy, zz, aa)

Admix populations 1,2, and 3 into population 4.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 4 populations.

 required
f1 float

Fraction of updated population 4 to be derived from population 1.

required
f2 float

Fraction of updated population 4 to be derived from population 2.

required
f3 float

Fraction of updated population 4 to be derived from population 3. A fraction (1-f1-f2-f3) will be derived from the original pop 4.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_4D_admix_into_4(phi, f1,f2,f3, xx,yy,zz,aa):
    """
    Admix populations 1,2, and 3 into population 4.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 4 populations.
        f1 (float): Fraction of updated population 4 to be derived from population 1. 
        f2 (float): Fraction of updated population 4 to be derived from population 2. 
        f3 (float): Fraction of updated population 4 to be derived from population 3. 
            A fraction (1-f1-f2-f3) will be derived from the original pop 4.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.

    Returns:
        phi (array): The updated phi array.
    """
    Demes.cache.append(Demes.Pulse(sources=[1,2,3], dest=1, proportions=[f1, f2, f3]))
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _four_pop_admixture_intermediates(phi, f1,f2,f3, xx,yy,zz,aa, yy)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_l = numpy.arange(phi.shape[3])
    for ii in range(phi.shape[0]):
        for jj in range(phi.shape[1]):
            for kk in range(phi.shape[2]):
                phi_int = numpy.zeros((phi.shape[3], phi.shape[3]))
                phi_int[idx_l, lower_w_index[ii,jj,kk,:]] = lower_cont[ii,jj,kk,:]
                phi_int[idx_l, upper_w_index[ii,jj,kk,:]] = upper_cont[ii,jj,kk,:]
                phi[ii,jj,kk,:] = Numerics.trapz(phi_int, aa, axis=0)

    return phi

phi_4D_to_5D(phi, f1, f2, f3, xx, yy, zz, aa, bb, deme_ids=None)

Create population 5 from populations 1, 2, 3, and 4.

Returns a 5D sfs of shape (len(xx),len(yy),len(zz),len(aa),len(bb))

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 4 populations.

 required
f1 float

Fraction of population 5 derived from population 1.

 required
f2 float

Fraction of population 5 derived from population 2.

 required
f3 float

Fraction of population 5 derived from population 3. A fraction 1-f1-f2-f3 will be derived from population 4.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required
bb array

Frequency mapping that will be used along population 5 axis.

 required
deme_ids list

Sequence of strings representing the names of demes after split.

 None

Returns:

Name Type Description
phi_5D array

A new five-dimensional phi array.
Source code in dadi/PhiManip.py 
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def phi_4D_to_5D(phi, f1,f2,f3, xx,yy,zz,aa,bb, deme_ids=None):
    """
    Create population 5 from populations 1, 2, 3, and 4.

    Returns a 5D sfs of shape (len(xx),len(yy),len(zz),len(aa),len(bb))

    Args:
        phi (array): Phi corresponding to original 4 populations.
        f1 (float): Fraction of population 5 derived from population 1.
        f2 (float): Fraction of population 5 derived from population 2.
        f3 (float): Fraction of population 5 derived from population 3.
            A fraction 1-f1-f2-f3 will be derived from population 4.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.
        bb (array): Frequency mapping that will be used along population 5 axis.
        deme_ids (list, optional): Sequence of strings representing the names of demes after split.

    Returns:
        phi_5D (array): A new five-dimensional phi array.
    """
    Demes.cache.append(Demes.Split(proportions=[f1, f2, f3, 1-f1-f2-f3], deme_ids=deme_ids))

    lower_z_index, upper_z_index, frac_lower, frac_upper, norm \
            = _four_pop_admixture_intermediates(phi, f1,f2,f3, xx,yy,zz,aa, bb)

    # Assemble our result.
    # This uses numpy's fancy indexing. It is much, much faster than an
    # explicit loop.
    # See the numpy-discussion post "Numpy Advanced Indexing Question" by
    # Robert Kern on July 16, 2008
    # http://projects.scipy.org/pipermail/numpy-discussion/2008-July/035776.html
    idx_i = numpy.arange(len(xx))[:,nuax,nuax,nuax]
    idx_j = numpy.arange(len(yy))[nuax,:,nuax,nuax]
    idx_k = numpy.arange(len(zz))[nuax,nuax,:,nuax]
    idx_l = numpy.arange(len(aa))[nuax,nuax,nuax,:]

    phi_5D = numpy.zeros((len(xx), len(yy), len(zz), len(aa), len(bb)))
    phi_5D[idx_i, idx_j, idx_k, idx_l, lower_z_index] = frac_lower*norm
    phi_5D[idx_i, idx_j, idx_k, idx_l, upper_z_index] += frac_upper*norm

    return phi_5D

phi_5D_admix_into_1(phi, f2, f3, f4, f5, xx, yy, zz, aa, bb)

Admix populations 2, 3, 4, and 5 into population 1.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 5 populations.

 required
f2 float

Fraction of updated population 1 to be derived from population 2.

required
f3 float

Fraction of updated population 1 to be derived from population 3.

required
f4 float

Fraction of updated population 1 to be derived from population 4.

required
f5 float

Fraction of updated population 1 to be derived from population 5. A fraction (1-f2-f3-f4-f5) will be derived from the original pop 1.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required
bb array

Mapping of points in phi to frequencies in population 5.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_5D_admix_into_1(phi, f2,f3,f4,f5, xx,yy,zz,aa,bb):
    """
    Admix populations 2, 3, 4, and 5 into population 1.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 5 populations.
        f2 (float): Fraction of updated population 1 to be derived from population 2. 
        f3 (float): Fraction of updated population 1 to be derived from population 3. 
        f4 (float): Fraction of updated population 1 to be derived from population 4. 
        f5 (float): Fraction of updated population 1 to be derived from population 5. 
            A fraction (1-f2-f3-f4-f5) will be derived from the original pop 1.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.
        bb (array): Mapping of points in phi to frequencies in population 5.

    Returns:
        phi (array): The updated phi array.
    """
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _five_pop_admixture_intermediates(phi, 1-f2-f3-f4-f5,f2,f3,f4, xx,yy,zz,aa,bb, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_i = numpy.arange(phi.shape[0])
    for jj in range(phi.shape[1]):
        for kk in range(phi.shape[2]):
            for ll in range(phi.shape[3]):
                for mm in range(phi.shape[4]):
                    phi_int = numpy.zeros((phi.shape[0], phi.shape[0]))
                    phi_int[idx_i, lower_w_index[:,jj,kk,ll,mm]] = lower_cont[:,jj,kk,ll,mm]
                    phi_int[idx_i, upper_w_index[:,jj,kk,ll,mm]] = upper_cont[:,jj,kk,ll,mm]
                    phi[:,jj,kk,ll,mm] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_5D_admix_into_2(phi, f1, f3, f4, f5, xx, yy, zz, aa, bb)

Admix populations 1, 3, 4, and 5 into population 2.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 5 populations.

 required
f1 float

Fraction of updated population 2 to be derived from population 1.

required
f3 float

Fraction of updated population 2 to be derived from population 3.

required
f4 float

Fraction of updated population 2 to be derived from population 4.

required
f5 float

Fraction of updated population 2 to be derived from population 5. A fraction (1-f1-f3-f4-f5) will be derived from the original pop 2.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required
bb array

Mapping of points in phi to frequencies in population 5.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_5D_admix_into_2(phi, f1,f3,f4,f5, xx,yy,zz,aa,bb):
    """
    Admix populations 1, 3, 4, and 5 into population 2.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 5 populations.
        f1 (float): Fraction of updated population 2 to be derived from population 1. 
        f3 (float): Fraction of updated population 2 to be derived from population 3. 
        f4 (float): Fraction of updated population 2 to be derived from population 4. 
        f5 (float): Fraction of updated population 2 to be derived from population 5. 
            A fraction (1-f1-f3-f4-f5) will be derived from the original pop 2.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.
        bb (array): Mapping of points in phi to frequencies in population 5.

    Returns:
        phi (array): The updated phi array.
    """
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _five_pop_admixture_intermediates(phi, f1, 1-f1-f3-f4-f5,f3,f4, xx,yy,zz,aa,bb, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_j = numpy.arange(phi.shape[1])
    for ii in range(phi.shape[0]):
        for kk in range(phi.shape[2]):
            for ll in range(phi.shape[3]):
                for mm in range(phi.shape[4]):
                    phi_int = numpy.zeros((phi.shape[1], phi.shape[1]))
                    phi_int[idx_j, lower_w_index[ii,:,kk,ll,mm]] = lower_cont[ii,:,kk,ll,mm]
                    phi_int[idx_j, upper_w_index[ii,:,kk,ll,mm]] = upper_cont[ii,:,kk,ll,mm]
                    phi[ii,:,kk,ll,mm] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_5D_admix_into_3(phi, f1, f2, f4, f5, xx, yy, zz, aa, bb)

Admix populations 1, 2, 4, and 5 into population 3.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 5 populations.

 required
f1 float

Fraction of updated population 3 to be derived from population 1.

required
f2 float

Fraction of updated population 3 to be derived from population 2.

required
f4 float

Fraction of updated population 3 to be derived from population 4.

required
f5 float

Fraction of updated population 3 to be derived from population 5. A fraction (1-f1-f2-f4-f5) will be derived from the original pop 3.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required
bb array

Mapping of points in phi to frequencies in population 5.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_5D_admix_into_3(phi, f1,f2,f4,f5, xx,yy,zz,aa,bb):
    """
    Admix populations 1, 2, 4, and 5 into population 3.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 5 populations.
        f1 (float): Fraction of updated population 3 to be derived from population 1. 
        f2 (float): Fraction of updated population 3 to be derived from population 2. 
        f4 (float): Fraction of updated population 3 to be derived from population 4. 
        f5 (float): Fraction of updated population 3 to be derived from population 5. 
            A fraction (1-f1-f2-f4-f5) will be derived from the original pop 3.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.
        bb (array): Mapping of points in phi to frequencies in population 5.

    Returns:
        phi (array): The updated phi array.
    """
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _five_pop_admixture_intermediates(phi, f1, f2, 1-f1-f2-f4-f5,f4, xx,yy,zz,aa,bb, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_k = numpy.arange(phi.shape[2])
    for ii in range(phi.shape[0]):
        for jj in range(phi.shape[1]):
            for ll in range(phi.shape[3]):
                for mm in range(phi.shape[4]):
                    phi_int = numpy.zeros((phi.shape[2], phi.shape[2]))
                    phi_int[idx_k, lower_w_index[ii,jj,:,ll,mm]] = lower_cont[ii,jj,:,ll,mm]
                    phi_int[idx_k, upper_w_index[ii,jj,:,ll,mm]] = upper_cont[ii,jj,:,ll,mm]
                    phi[ii,jj,:,ll,mm] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_5D_admix_into_4(phi, f1, f2, f3, f5, xx, yy, zz, aa, bb)

Admix populations 1, 2, 3, and 5 into population 4.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 5 populations.

 required
f1 float

Fraction of updated population 4 to be derived from population 1.

required
f2 float

Fraction of updated population 4 to be derived from population 2.

required
f3 float

Fraction of updated population 4 to be derived from population 3.

required
f5 float

Fraction of updated population 4 to be derived from population 5. A fraction (1-f1-f2-f3-f5) will be derived from the original pop 4.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required
bb array

Mapping of points in phi to frequencies in population 5.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_5D_admix_into_4(phi, f1,f2,f3,f5, xx,yy,zz,aa,bb):
    """
    Admix populations 1, 2, 3, and 5 into population 4.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 5 populations.
        f1 (float): Fraction of updated population 4 to be derived from population 1. 
        f2 (float): Fraction of updated population 4 to be derived from population 2. 
        f3 (float): Fraction of updated population 4 to be derived from population 3. 
        f5 (float): Fraction of updated population 4 to be derived from population 5. 
            A fraction (1-f1-f2-f3-f5) will be derived from the original pop 4.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.
        bb (array): Mapping of points in phi to frequencies in population 5.

    Returns:
        phi (array): The updated phi array.
    """
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _five_pop_admixture_intermediates(phi, f1, f2, f3, 1-f1-f2-f3-f5, xx,yy,zz,aa,bb, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_l = numpy.arange(phi.shape[3])
    for ii in range(phi.shape[0]):
        for jj in range(phi.shape[1]):
            for kk in range(phi.shape[2]):
                for mm in range(phi.shape[4]):
                    phi_int = numpy.zeros((phi.shape[3], phi.shape[3]))
                    phi_int[idx_l, lower_w_index[ii,jj,kk,:,mm]] = lower_cont[ii,jj,kk,:,mm]
                    phi_int[idx_l, upper_w_index[ii,jj,kk,:,mm]] = upper_cont[ii,jj,kk,:,mm]
                    phi[ii,jj,kk,:,mm] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

phi_5D_admix_into_5(phi, f1, f2, f3, f4, xx, yy, zz, aa, bb)

Admix populations 1, 2, 3, and 4 into population 5.

Alters phi in place and returns the new version.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original 5 populations.

 required
f1 float

Fraction of updated population 5 to be derived from population 1.

required
f2 float

Fraction of updated population 5 to be derived from population 2.

required
f3 float

Fraction of updated population 5 to be derived from population 3.

required
f4 float

Fraction of updated population 5 to be derived from population 3. A fraction (1-f1-f2-f3-f4) will be derived from the original pop 5.

 required
xx array

Mapping of points in phi to frequencies in population 1.

 required
yy array

Mapping of points in phi to frequencies in population 2.

 required
zz array

Mapping of points in phi to frequencies in population 3.

 required
aa array

Mapping of points in phi to frequencies in population 4.

 required
bb array

Mapping of points in phi to frequencies in population 5.

 required

Returns:

Name Type Description
phi array

The updated phi array.
Source code in dadi/PhiManip.py 
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def phi_5D_admix_into_5(phi, f1,f2,f3,f4, xx,yy,zz,aa,bb):
    """
    Admix populations 1, 2, 3, and 4 into population 5.

    Alters phi in place and returns the new version.

    Args:
        phi (array): Phi corresponding to original 5 populations.
        f1 (float): Fraction of updated population 5 to be derived from population 1. 
        f2 (float): Fraction of updated population 5 to be derived from population 2. 
        f3 (float): Fraction of updated population 5 to be derived from population 3. 
        f4 (float): Fraction of updated population 5 to be derived from population 3. 
            A fraction (1-f1-f2-f3-f4) will be derived from the original pop 5.
        xx (array): Mapping of points in phi to frequencies in population 1.
        yy (array): Mapping of points in phi to frequencies in population 2.
        zz (array): Mapping of points in phi to frequencies in population 3.
        aa (array): Mapping of points in phi to frequencies in population 4.
        bb (array): Mapping of points in phi to frequencies in population 5.

    Returns:
        phi (array): The updated phi array.
    """
    lower_w_index, upper_w_index, frac_lower, frac_upper, norm \
            = _five_pop_admixture_intermediates(phi, f1, f2, f3, f4, xx,yy,zz,aa,bb, xx)

    lower_cont = frac_lower * norm
    upper_cont = frac_upper * norm

    idx_m = numpy.arange(phi.shape[4])
    for ii in range(phi.shape[0]):
        for jj in range(phi.shape[1]):
            for kk in range(phi.shape[2]):
                for ll in range(phi.shape[3]):
                    phi_int = numpy.zeros((phi.shape[4], phi.shape[4]))
                    phi_int[idx_m, lower_w_index[ii,jj,kk,ll,:]] = lower_cont[ii,jj,kk,ll,:]
                    phi_int[idx_m, upper_w_index[ii,jj,kk,ll,:]] = upper_cont[ii,jj,kk,ll,:]
                    phi[ii,jj,kk,ll,:] = Numerics.trapz(phi_int, xx, axis=0)

    return phi

remove_pop(phi, xx, popnum)

Remove a population from phi.

Returns new phi with one fewer population.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original populations.

 required
xx array

Mapping of points in phi to frequencies in population to be removed.

 required
popnum int

Population number to remove, numbering from 1.

 required

Returns:

Name Type Description
phi array

The updated phi array with one fewer population.
Source code in dadi/PhiManip.py 
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def remove_pop(phi, xx, popnum):
    """
    Remove a population from phi.

    Returns new phi with one fewer population.

    Args:
        phi (array): Phi corresponding to original populations.
        xx (array): Mapping of points in phi to frequencies in population to be removed.
        popnum (int): Population number to remove, numbering from 1.

    Returns:
        phi (array): The updated phi array with one fewer population.
    """
    Demes.cache.append(Demes.Remove(removed=popnum))
    return Numerics.trapz(phi, xx, axis=popnum-1)

reorder_pops(phi, neworder)

Get phi with populations in new order.

Returns new phi with same number of populations, but in a different order.

Parameters:

Name Type Description Default
phi array

Phi corresponding to original populations.

 required
neworder list

Integer list defining new order of populations, indexing the original populations from 1. Must contain all integers from 1 to number of pops.

 required

Returns:

Name Type Description
phi array

The updated phi array with populations in the new order.
Source code in dadi/PhiManip.py 
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def reorder_pops(phi, neworder):
    """
    Get phi with populations in new order.

    Returns new phi with same number of populations, but in a different order.

    Args:
        phi (array): Phi corresponding to original populations.
        neworder (list): Integer list defining new order of populations, indexing the original
            populations from 1. Must contain all integers from 1 to number of pops.

    Returns:
        phi (array): The updated phi array with populations in the new order.
    """
    Demes.cache.append(Demes.Reorder(neworder=neworder))
    if sorted(neworder) != [_+1 for _ in range(phi.ndim)]:
        raise(ValueError("neworder argument misspecified"))
    newaxes = [_-1 for _ in neworder]
    phi = phi.transpose(newaxes)

    return phi