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Demographics2D

Two-population demographic models.

IM(params, ns, pts)

Isolation-with-migration model with exponential population growth.

Parameters:

Name Type Description Default
params tuple

(s, nu1, nu2, T, m12, m21)

  • s: Size of pop 1 after split. (Pop 2 has size 1-s.)

  • nu1: Final size of pop 1.

  • nu2: Final size of pop 2.

  • T: Time in the past of split (in units of 2*Na generations).

  • m12: Migration from pop 2 to pop 1 (2Nam12).

  • m21: Migration from pop 1 to pop 2.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def IM(params, ns, pts):
    """
    Isolation-with-migration model with exponential population growth.

    Parameters:
        params (tuple): (s, nu1, nu2, T, m12, m21)

            - s: Size of pop 1 after split. (Pop 2 has size 1-s.)

            - nu1: Final size of pop 1.

            - nu2: Final size of pop 2.

            - T: Time in the past of split (in units of 2*Na generations).

            - m12: Migration from pop 2 to pop 1 (2*Na*m12).

            - m21: Migration from pop 1 to pop 2.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    s,nu1,nu2,T,m12,m21 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    nu1_func = lambda t: s * (nu1/s)**(t/T)
    nu2_func = lambda t: (1-s) * (nu2/(1-s))**(t/T)
    phi = Integration.two_pops(phi, xx, T, nu1_func, nu2_func,
                               m12=m12, m21=m21)

    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

IM_mscore(params)

ms core command for IM.

Parameters:

Name Type Description Default
params tuple

(s, nu1, nu2, T, m12, m21)

 required

Returns:

Name Type Description
output str

ms core command string.
Source code in dadi/Demographics2D.py 
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def IM_mscore(params):
    """
    ms core command for IM.

    Parameters:
        params (tuple): (s, nu1, nu2, T, m12, m21)

    Returns:
        output (str): ms core command string.
    """
    s,nu1,nu2,T,m12,m21 = params

    alpha1 = numpy.log(nu1/s)/T
    alpha2 = numpy.log(nu2/(1-s))/T
    command = "-n 1 %(nu1)f -n 2 %(nu2)f "\
            "-eg 0 1 %(alpha1)f -eg 0 2 %(alpha2)f "\
            "-ma x %(m12)f %(m21)f x "\
            "-ej %(T)f 2 1 -en %(T)f 1 1"

    sub_dict = {'nu1':nu1, 'nu2':nu2, 'alpha1':2*alpha1, 'alpha2':2*alpha2,
                'm12':2*m12, 'm21':2*m21, 'T': T/2}

    return command % sub_dict

IM_pre(params, ns, pts)

Isolation-with-migration model with exponential population growth and a size change prior to split.

Parameters:

Name Type Description Default
params tuple

(nuPre, TPre, s, nu1, nu2, T, m12, m21)

  • nuPre: Size after first size change.

  • TPre: Time before split of first size change.

  • s: Fraction of nuPre that goes to pop1. (Pop 2 has size nuPre*(1-s).)

  • nu1: Final size of pop 1.

  • nu2: Final size of pop 2.

  • T: Time in the past of split (in units of 2*Na generations).

  • m12: Migration from pop 2 to pop 1 (2Nam12).

  • m21: Migration from pop 1 to pop 2.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def IM_pre(params, ns, pts):
    """
    Isolation-with-migration model with exponential population growth and a size change prior to split.

    Parameters:
        params (tuple): (nuPre, TPre, s, nu1, nu2, T, m12, m21)

            - nuPre: Size after first size change.

            - TPre: Time before split of first size change.

            - s: Fraction of nuPre that goes to pop1. (Pop 2 has size nuPre*(1-s).)

            - nu1: Final size of pop 1.

            - nu2: Final size of pop 2.

            - T: Time in the past of split (in units of 2*Na generations).

            - m12: Migration from pop 2 to pop 1 (2*Na*m12).

            - m21: Migration from pop 1 to pop 2.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nuPre,TPre,s,nu1,nu2,T,m12,m21 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = Integration.one_pop(phi, xx, TPre, nu=nuPre)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    nu1_0 = nuPre*s
    nu2_0 = nuPre*(1-s)
    nu1_func = lambda t: nu1_0 * (nu1/nu1_0)**(t/T)
    nu2_func = lambda t: nu2_0 * (nu2/nu2_0)**(t/T)
    phi = Integration.two_pops(phi, xx, T, nu1_func, nu2_func,
                               m12=m12, m21=m21)

    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

IM_pre_mscore(params)

ms core command for IM_pre.

Parameters:

Name Type Description Default
params tuple

(nuPre, TPre, s, nu1, nu2, T, m12, m21)

 required

Returns:

Name Type Description
output str

ms core command string.
Source code in dadi/Demographics2D.py 
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def IM_pre_mscore(params):
    """
    ms core command for IM_pre.

    Parameters:
        params (tuple): (nuPre, TPre, s, nu1, nu2, T, m12, m21)

    Returns:
        output (str): ms core command string.
    """
    nuPre,TPre,s,nu1,nu2,T,m12,m21 = params

    nu1_0 = nuPre*s
    nu2_0 = nuPre*(1-s)
    alpha1 = numpy.log(nu1/nu1_0)/T
    alpha2 = numpy.log(nu2/nu2_0)/T
    command = "-n 1 %(nu1)f -n 2 %(nu2)f "\
            "-eg 0 1 %(alpha1)f -eg 0 2 %(alpha2)f "\
            "-ma x %(m12)f %(m21)f x "\
            "-ej %(T)f 2 1 -en %(T)f 1 %(nuP)f "\
            "-en %(TP)f 1 1"

    sub_dict = {'nu1':nu1, 'nu2':nu2, 'alpha1':2*alpha1, 'alpha2':2*alpha2,
                'm12':2*m12, 'm21':2*m21, 'T': T/2, 'nuP':nuPre, 'TP':(T+TPre)/2}

    return command % sub_dict

anc_asym_mig(params, ns, pts)

Split with asymmetric migration followed by isolation.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m12, m21, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

  • T2: The scaled time between the ancient migration and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def anc_asym_mig(params, ns, pts):
    """
    Split with asymmetric migration followed by isolation.

    Parameters:
        params (tuple): (nu1, nu2, m12, m21, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

            - T2: The scaled time between the ancient migration and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m12, m21, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=m12, m21=m21)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))

    return fs

anc_asym_mig_size(params, ns, pts)

Split with asymmetrical gene flow, followed by size change with no gene flow.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: The scale time between the ancient migration and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def anc_asym_mig_size(params, ns, pts):
    """
    Split with asymmetrical gene flow, followed by size change with no gene flow.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: The scale time between the ancient migration and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=m12, m21=m21)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

anc_sym_mig(params, ns, pts)

Split with symmetric migration followed by isolation.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m: Migration between population 2 and population 1.

  • T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

  • T2: The scaled time between the ancient migration and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def anc_sym_mig(params, ns, pts):
    """
    Split with symmetric migration followed by isolation.

    Parameters:
        params (tuple): (nu1, nu2, m, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m: Migration between population 2 and population 1.

            - T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

            - T2: The scaled time between the ancient migration and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=m, m21=m)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

anc_sym_mig_size(params, ns, pts)

Split with symmetrical gene flow, followed by size change with no gene flow.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m: Migration between population 2 and population 1.

  • T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

  • T2: The scale time between the ancient migration and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def anc_sym_mig_size(params, ns, pts):
    """
    Split with symmetrical gene flow, followed by size change with no gene flow.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m: Migration between population 2 and population 1.

            - T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

            - T2: The scale time between the ancient migration and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=m, m21=m)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

asym_mig(params, ns, pts)

Split into two populations with different migration rates.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m12, m21, T)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T: Time in the past of split (in units of 2*Na generations).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def asym_mig(params, ns, pts):
    """
    Split into two populations with different migration rates.

    Parameters:
        params (tuple): (nu1, nu2, m12, m21, T)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T: Time in the past of split (in units of 2*Na generations).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m12, m21, T = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T, nu1, nu2, m12=m12, m21=m21)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

asym_mig_size(params, ns, pts)

Split with different migration rates, then size change with different migration rates.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: Time of population size change.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def asym_mig_size(params, ns, pts):
    """
    Split with different migration rates, then size change with different migration rates.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: Time of population size change.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=m12, m21=m21)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m12, m21=m21)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

asym_mig_twoepoch(params, ns, pts)

Split into two populations with different migration rates. A second period of asymmetric migration occurs, but can be at different rates. Population size is the same.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m12a, m21a, m12b, m21b, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m12a: Migration from population 2 to population 1 during first epoch (2Nam12).

  • m21a: Migration from population 1 to population 2 during first epoch.

  • m12b: Migration from population 2 to population 1 during second epoch (2Nam12).

  • m21b: Migration from population 1 to population 2 during second epoch.

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: Time in the past of second epoch (in units of 2*Na generations).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def asym_mig_twoepoch(params, ns, pts):
    """
    Split into two populations with different migration rates. A second period of asymmetric
    migration occurs, but can be at different rates. Population size is the same.

    Parameters:
        params (tuple): (nu1, nu2, m12a, m21a, m12b, m21b, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m12a: Migration from population 2 to population 1 during first epoch (2*Na*m12).

            - m21a: Migration from population 1 to population 2 during first epoch.

            - m12b: Migration from population 2 to population 1 during second epoch (2*Na*m12).

            - m21b: Migration from population 1 to population 2 during second epoch.

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: Time in the past of second epoch (in units of 2*Na generations).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m12a, m21a, m12b, m21b, T1, T2 = params
    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=m12a, m21=m21a)

    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m12b, m21=m21b)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))

    return fs

bottlegrowth_2d(params, ns, pts)

Instantaneous size change followed by exponential growth with no population split.

Parameters:

Name Type Description Default
params tuple

(nuB, nuF, T)

  • nuB: Ratio of population size after instantaneous change to ancient population size.

  • nuF: Ratio of contemporary to ancient population size.

  • T: Time in the past at which instantaneous change happened and growth began (in units of 2*Na generations).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def bottlegrowth_2d(params, ns, pts):
    """
    Instantaneous size change followed by exponential growth with no population split.

    Parameters:
        params (tuple): (nuB, nuF, T)

            - nuB: Ratio of population size after instantaneous change to ancient population size.

            - nuF: Ratio of contemporary to ancient population size.

            - T: Time in the past at which instantaneous change happened and growth began 
               (in units of 2*Na generations).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nuB,nuF,T = params
    return bottlegrowth_split_mig((nuB,nuF,0,T,0), ns, pts)

bottlegrowth_split(params, ns, pts)

Instantaneous size change followed by exponential growth then split.

Parameters:

Name Type Description Default
params tuple

(nuB, nuF, T, Ts)

  • nuB: Ratio of population size after instantaneous change to ancient population size.

  • nuF: Ratio of contemporary to ancient population size.

  • T: Time in the past at which instantaneous change happened and growth began (in units of 2*Na generations).

  • Ts: Time in the past at which the two populations split.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def bottlegrowth_split(params, ns, pts):
    """
    Instantaneous size change followed by exponential growth then split.

    Parameters:
        params (tuple): (nuB, nuF, T, Ts)

            - nuB: Ratio of population size after instantaneous change to ancient population size.

            - nuF: Ratio of contemporary to ancient population size.

            - T: Time in the past at which instantaneous change happened and growth began 
               (in units of 2*Na generations).

            - Ts: Time in the past at which the two populations split.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nuB,nuF,T,Ts = params
    return bottlegrowth_split_mig((nuB,nuF,0,T,Ts), ns, pts)

bottlegrowth_split_mig(params, ns, pts)

Instantaneous size change followed by exponential growth then split with migration.

Parameters:

Name Type Description Default
params tuple

(nuB, nuF, m, T, Ts)

  • nuB: Ratio of population size after instantaneous change to ancient population size.

  • nuF: Ratio of contemporary to ancient population size.

  • m: Migration rate between the two populations (2Nam).

  • T: Time in the past at which instantaneous change happened and growth began (in units of 2*Na generations).

  • Ts: Time in the past at which the two populations split.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def bottlegrowth_split_mig(params, ns, pts):
    """
    Instantaneous size change followed by exponential growth then split with migration.

    Parameters:
        params (tuple): (nuB, nuF, m, T, Ts)

            - nuB: Ratio of population size after instantaneous change to ancient population size.

            - nuF: Ratio of contemporary to ancient population size.

            - m: Migration rate between the two populations (2*Na*m).

            - T: Time in the past at which instantaneous change happened and growth began 
               (in units of 2*Na generations).

            - Ts: Time in the past at which the two populations split.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nuB,nuF,m,T,Ts = params

    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)

    if T >= Ts:
        nu_func = lambda t: nuB*numpy.exp(numpy.log(nuF/nuB) * t/T)
        phi = Integration.one_pop(phi, xx, T-Ts, nu_func)

        phi = PhiManip.phi_1D_to_2D(xx, phi)
        nu0 = nu_func(T-Ts)
        nu_func = lambda t: nu0*numpy.exp(numpy.log(nuF/nu0) * t/Ts)
        phi = Integration.two_pops(phi, xx, Ts, nu_func, nu_func, m12=m, m21=m)
    else:
        phi = PhiManip.phi_1D_to_2D(xx, phi)
        phi = Integration.two_pops(phi, xx, Ts-T, 1, 1, m12=m, m21=m)
        nu_func = lambda t: nuB*numpy.exp(numpy.log(nuF/nuB) * t/T)
        phi = Integration.two_pops(phi, xx, T, nu_func, nu_func, m12=m, m21=m)

    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

founder_asym(params, ns, pts)

Split into two populations with two migration rates.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Population 2 undergoes an exponential growth event to obtain size nu2, while population 1 is constant. Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(nu2, m12, m21, T, s)

  • nu2: Final size of population 2, after exponential growth.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def founder_asym(params, ns, pts):
    """
    Split into two populations with two migration rates.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Population 2 undergoes an exponential growth event to obtain size nu2,
    while population 1 is constant. Nref implicitly has size = 1.

    Parameters:
        params (tuple): (nu2, m12, m21, T, s)

            - nu2: Final size of population 2, after exponential growth.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu2, m12, m21, T, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    def nu2_func(t):
        return s * (nu2/s)**(t/T)

    phi = Integration.two_pops(
        phi, xx, T, nu1=1-s, nu2=nu2_func, m12=m12, m21=m21)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

founder_nomig(params, ns, pts)

Split into two populations with no migration.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Population 2 undergoes an exponential growth event to obtain size nu2, while population 1 is constant. Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(nu2, T, s)

  • nu2: Final size of population 2, after exponential growth.

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def founder_nomig(params, ns, pts):
    """
    Split into two populations with no migration.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Population 2 undergoes an exponential growth event to obtain size nu2,
    while population 1 is constant. Nref implicitly has size = 1.

    Parameters:
        params (tuple): (nu2, T, s)

            - nu2: Final size of population 2, after exponential growth.

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu2, T, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    def nu2_func(t):
        return s * (nu2/s)**(t/T)

    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=nu2_func, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

founder_nomig_admix_early(params, ns, pts)

Split into two populations with no migration but a discrete admixture event from population 1 into population 2 occurs (before drift).

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Population 2 undergoes an exponential growth event to obtain size nu2, while population 1 is constant. Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(nu2, T, s, f)

  • nu2: Final size of population 2, after exponential growth.

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

  • f: Fraction of updated population 2 to be derived from population 1.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def founder_nomig_admix_early(params, ns, pts):
    """
    Split into two populations with no migration but a discrete admixture event
    from population 1 into population 2 occurs (before drift).

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Population 2 undergoes an exponential growth event to obtain size
    nu2, while population 1 is constant. Nref implicitly has size = 1.

    Parameters:
        params (tuple): (nu2, T, s, f)

            - nu2: Final size of population 2, after exponential growth.

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

            - f: Fraction of updated population 2 to be derived from population 1.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu2, T, s, f = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)

    def nu2_func(t):
        return s * (nu2/s)**(t/T)

    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=nu2_func, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

founder_nomig_admix_late(params, ns, pts)

Split into two populations with no migration but a discrete admixture event from population 1 into population 2 occurs (after drift).

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Population 2 undergoes an exponential growth event to obtain size nu2, while population 1 is constant. Admixture occurs when size nu2 is achieved. Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(nu2, T, s, f)

  • nu2: Final size of population 2, after exponential growth.

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

  • f: Fraction of updated population 2 to be derived from population 1.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def founder_nomig_admix_late(params, ns, pts):
    """
    Split into two populations with no migration but a discrete admixture event
    from population 1 into population 2 occurs (after drift).

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Population 2 undergoes an exponential growth event to obtain size nu2,
    while population 1 is constant. Admixture occurs when size nu2 is achieved. Nref implicitly has size = 1.

    Parameters:
        params (tuple): (nu2, T, s, f)

            - nu2: Final size of population 2, after exponential growth.

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

            - f: Fraction of updated population 2 to be derived from population 1.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu2, T, s, f = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    def nu2_func(t):
        return s * (nu2/s)**(t/T)

    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=nu2_func, m12=0, m21=0)

    phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

founder_nomig_admix_two_epoch(params, ns, pts)

Split into two populations with no migration but a discrete admixture event from population 1 into population 2 occurs (between two drift events).

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Population 2 undergoes an exponential growth event to obtain size nu2, while population 1 is constant. Admixture occurs after size nu2 is achieved. Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(nu2, T1, T2, s, f)

  • nu2: Final size of population 2, after exponential growth.

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: The scaled time between the admixture event and present.

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

  • f: Fraction of updated population 2 to be derived from population 1.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def founder_nomig_admix_two_epoch(params, ns, pts):
    """
    Split into two populations with no migration but a discrete admixture event
    from population 1 into population 2 occurs (between two drift events).

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Population 2 undergoes an exponential growth event to obtain size nu2,
    while population 1 is constant. Admixture occurs after size nu2 is achieved. Nref implicitly has size = 1.

    Parameters:
        params (tuple): (nu2, T1, T2, s, f)

            - nu2: Final size of population 2, after exponential growth.

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: The scaled time between the admixture event and present.

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

            - f: Fraction of updated population 2 to be derived from population 1.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu2, T1, T2, s, f = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    def nu2_func(t):
        return s * (nu2/s)**(t/T1)

    phi = Integration.two_pops(
        phi, xx, T1, nu1=1-s, nu2=nu2_func, m12=0, m21=0)

    phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)

    phi = Integration.two_pops(phi, xx, T2, nu1=1-s, nu2=nu2, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

founder_sym(params, ns, pts)

Split into two populations with one migration rate.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Population 2 undergoes an exponential growth event to obtain size nu2, while population 1 is constant. Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(nu2, m, T, s)

  • nu2: Final size of population 2, after exponential growth.

  • T: Time in the past of split (in units of 2*Na generations).

  • m: Migration (2Nam12).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def founder_sym(params, ns, pts):
    """
    Split into two populations with one migration rate.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Population 2 undergoes an exponential growth event to obtain size nu2,
    while population 1 is constant. Nref implicitly has size = 1.

    Parameters:
        params (tuple): (nu2, m, T, s)

            - nu2: Final size of population 2, after exponential growth.

            - T: Time in the past of split (in units of 2*Na generations).

            - m: Migration (2*Na*m12).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu2, m, T, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    def nu2_func(t):
        return s * (nu2/s)**(t/T)

    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=nu2_func, m12=m, m21=m)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

no_mig(params, ns, pts)

Split into two populations with no migration.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, T)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • T: Time in the past of split (in units of 2*Na generations).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def no_mig(params, ns, pts):
    """
    Split into two populations with no migration.

    Parameters:
        params (tuple): (nu1, nu2, T)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - T: Time in the past of split (in units of 2*Na generations).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, T = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T, nu1, nu2, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

no_mig_size(params, ns, pts)

Split with no migration, then size change with no migration.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: Time of population size change.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def no_mig_size(params, ns, pts):
    """
    Split with no migration, then size change with no migration.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: Time of population size change.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_asym_mig(params, ns, pts)

Split with no gene flow, followed by period of asymmetrical gene flow.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m12, m21, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scaled time between the secondary contact and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_asym_mig(params, ns, pts):
    """
    Split with no gene flow, followed by period of asymmetrical gene flow.

    Parameters:
        params (tuple): (nu1, nu2, m12, m21, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

            - T2: The scaled time between the secondary contact and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m12, m21, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m12, m21=m21)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_asym_mig_size(params, ns, pts)

Split with no gene flow, followed by size change with asymmetrical gene flow.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scale time between the secondary contact and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_asym_mig_size(params, ns, pts):
    """
    Split with no gene flow, followed by size change with asymmetrical gene flow.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

            - T2: The scale time between the secondary contact and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m12, m21=m21)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_asym_mig_size_three_epoch(params, ns, pts)

Split with no gene flow, followed by size change with asymmetrical gene flow, then isolation.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2, T3)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scale time between the secondary contact and isolation.

  • T3: The scaled time between the isolation and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_asym_mig_size_three_epoch(params, ns, pts):
    """
    Split with no gene flow, followed by size change with asymmetrical gene flow, then isolation.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2, T3)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the secondary contact
            (in units of 2*Na generations).

            - T2: The scale time between the secondary contact and isolation.

            - T3: The scaled time between the isolation and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m12, m21, T1, T2, T3 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m12, m21=m21)
    phi = Integration.two_pops(phi, xx, T3, nu1b, nu2b, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_asym_mig_three_epoch(params, ns, pts)

Split with no gene flow, followed by period of asymmetrical gene flow, then isolation.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m12, m21, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scaled time between the secondary contact and third epoch.

  • T3 (not used): The scaled time between the isolation and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_asym_mig_three_epoch(params, ns, pts):
    """
    Split with no gene flow, followed by period of asymmetrical gene flow,
    then isolation.

    Parameters:
        params (tuple): (nu1, nu2, m12, m21, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the secondary contact
            (in units of 2*Na generations).

            - T2: The scaled time between the secondary contact and third epoch.

            - T3 (not used): The scaled time between the isolation and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m12, m21, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m12, m21=m21)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_sym_mig(params, ns, pts)

Split with no gene flow, followed by period of symmetrical gene flow.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m: Migration between population 2 and population 1.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scaled time between the secondary contact and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_sym_mig(params, ns, pts):
    """
    Split with no gene flow, followed by period of symmetrical gene flow.

    Parameters:
        params (tuple): (nu1, nu2, m, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m: Migration between population 2 and population 1.

            - T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

            - T2: The scaled time between the secondary contact and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m, m21=m)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_sym_mig_size(params, ns, pts)

Split with no gene flow, followed by size change with symmetrical gene flow.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m: Migration between population 2 and population 1.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scale time between the secondary contact and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_sym_mig_size(params, ns, pts):
    """
    Split with no gene flow, followed by size change with symmetrical gene flow.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m: Migration between population 2 and population 1.

            - T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

            - T2: The scale time between the secondary contact and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m, m21=m)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_sym_mig_size_three_epoch(params, ns, pts)

Split with no gene flow, followed by size change with symmetrical gene flow, then isolation.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m, T1, T2, T3)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m: Migration between population 2 and population 1.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scale time between the secondary contact and isolation.

  • T3: The scaled time between the isolation and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_sym_mig_size_three_epoch(params, ns, pts):
    """
    Split with no gene flow, followed by size change with
    symmetrical gene flow, then isolation.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m, T1, T2, T3)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m: Migration between population 2 and population 1.

            - T1: The scaled time between the split and the secondary contact
            (in units of 2*Na generations).

            - T2: The scale time between the secondary contact and isolation.

            - T3: The scaled time between the isolation and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m, T1, T2, T3 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m, m21=m)
    phi = Integration.two_pops(phi, xx, T3, nu1b, nu2b, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sec_contact_sym_mig_three_epoch(params, ns, pts)

Split with no gene flow, followed by period of symmetrical gene flow, then isolation.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m, T1, T2, T3)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m: Migration between population 2 and population 1.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scaled time between the secondary contact and third epoch.

  • T3: The scaled time between the isolation and present.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sec_contact_sym_mig_three_epoch(params, ns, pts):
    """
    Split with no gene flow, followed by period of symmetrical gene flow, then isolation.

    Parameters:
        params (tuple): (nu1, nu2, m, T1, T2, T3)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m: Migration between population 2 and population 1.

            - T1: The scaled time between the split and the secondary contact
            (in units of 2*Na generations).

            - T2: The scaled time between the secondary contact and third epoch.

            - T3: The scaled time between the isolation and present.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m, T1, T2, T3 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m, m21=m)
    phi = Integration.two_pops(phi, xx, T3, nu1, nu2, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

snm_2d(notused, ns, pts)

Standard neutral model where populations never diverge.

Parameters:

Name Type Description Default
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.
Source code in dadi/Demographics2D.py 
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def snm_2d(notused, ns, pts):
    """
    Standard neutral model where populations never diverge.

    Parameters:
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.
    """
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

split_asym_mig(params, ns, pts)

Split into two populations of specified size, with asymmetric migration.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, T, m12, m21)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • T: Time in the past of split (in units of 2*Na generations).

  • m12: Migration from pop 2 to pop 1 (2Nam12).

  • m21: Migration from pop 1 to pop 2 (2Nam21).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def split_asym_mig(params, ns, pts):
    """
    Split into two populations of specified size, with asymmetric migration.

    Parameters:
        params (tuple): (nu1, nu2, T, m12, m21)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - T: Time in the past of split (in units of 2*Na generations).

            - m12: Migration from pop 2 to pop 1 (2*Na*m12).

            - m21: Migration from pop 1 to pop 2 (2*Na*m21).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1,nu2,T,m12,m21 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T, nu1, nu2, m12=m12, m21=m21)

    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

split_delay_mig(params, ns, pts)

Split into two populations of specified size, with migration after some time has passed post split.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, Tpre, Tmig, m12, m21)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • Tpre: Time in the past after split but before migration (in units of 2*Na generations).

  • Tmig: Time in the past after migration starts (in units of 2*Na generations).

  • m12: Migration from pop 2 to pop 1 (2Nam12).

  • m21: Migration from pop 1 to pop 2 (2Nam21).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def split_delay_mig(params, ns, pts):
    """
    Split into two populations of specified size, with migration after some time has passed post split.

    Parameters:
        params (tuple): (nu1, nu2, Tpre, Tmig, m12, m21)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - Tpre: Time in the past after split but before migration (in units of 2*Na generations).

            - Tmig: Time in the past after migration starts (in units of 2*Na generations).

            - m12: Migration from pop 2 to pop 1 (2*Na*m12).

            - m21: Migration from pop 1 to pop 2 (2*Na*m21).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1,nu2,Tpre,Tmig,m12,m21 = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, Tpre, nu1, nu2, m12=0, m21=0)
    phi = Integration.two_pops(phi, xx, Tmig, nu1, nu2, m12=m12, m21=m21)

    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

split_mig(params, ns, pts)

Split into two populations of specified size, with migration.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, T, m)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • T: Time in the past of split (in units of 2*Na generations).

  • m: Migration rate between populations (2Nam).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/Demographics2D.py 
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def split_mig(params, ns, pts):
    """
    Split into two populations of specified size, with migration.

    Parameters:
        params (tuple): (nu1, nu2, T, m)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - T: Time in the past of split (in units of 2*Na generations).

            - m: Migration rate between populations (2*Na*m).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1,nu2,T,m = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T, nu1, nu2, m12=m, m21=m)

    fs = Spectrum.from_phi(phi, ns, (xx,xx))
    return fs

split_mig_mscore(params)

ms core command for split_mig.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, T, m)

 required

Returns:

Name Type Description
output str

ms core command string.
Source code in dadi/Demographics2D.py 
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def split_mig_mscore(params):
    """
    ms core command for split_mig.

    Parameters:
        params (tuple): (nu1, nu2, T, m)

    Returns:
        output (str): ms core command string.
    """
    nu1,nu2,T,m = params

    command = "-n 1 %(nu1)f -n 2 %(nu2)f "\
            "-ma x %(m12)f %(m21)f x "\
            "-ej %(T)f 2 1 -en %(T)f 1 1"

    sub_dict = {'nu1':nu1, 'nu2':nu2, 'm12':2*m, 'm21':2*m, 'T': T/2}

    return command % sub_dict

sym_mig(params, ns, pts)

Split into two populations with symmetric migration.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m, T)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m: Migration rate between populations (2Nam).

  • T: Time in the past of split (in units of 2*Na generations).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sym_mig(params, ns, pts):
    """
    Split into two populations with symmetric migration.

    Parameters:
        params (tuple): (nu1, nu2, m, T)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m: Migration rate between populations (2*Na*m).

            - T: Time in the past of split (in units of 2*Na generations).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m, T = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T, nu1, nu2, m12=m, m21=m)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sym_mig_size(params, ns, pts)

Split with symmetric migration, then size change with symmetric migration.

Parameters:

Name Type Description Default
params tuple

(nu1a, nu2a, nu1b, nu2b, m, T1, T2)

  • nu1a: Size of population 1 after split.

  • nu2a: Size of population 2 after split.

  • nu1b: Size of population 1 after time interval.

  • nu2b: Size of population 2 after time interval.

  • m: Migration rate between populations (2Nam).

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: Time of population size change.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sym_mig_size(params, ns, pts):
    """
    Split with symmetric migration, then size change with symmetric migration.

    Parameters:
        params (tuple): (nu1a, nu2a, nu1b, nu2b, m, T1, T2)

            - nu1a: Size of population 1 after split.

            - nu2a: Size of population 2 after split.

            - nu1b: Size of population 1 after time interval.

            - nu2b: Size of population 2 after time interval.

            - m: Migration rate between populations (2*Na*m).

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: Time of population size change.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1a, nu2a, nu1b, nu2b, m, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1a, nu2a, m12=m, m21=m)
    phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m, m21=m)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

sym_mig_twoepoch(params, ns, pts)

Split into two populations with symmetric migration. A second period of symmetric migration occurs, but can be a different rate. Population size is the same.

Parameters:

Name Type Description Default
params tuple

(nu1, nu2, m1, m2, T1, T2)

  • nu1: Size of population 1 after split.

  • nu2: Size of population 2 after split.

  • m1: Migration rate between populations during first epoch (2Nam).

  • m2: Migration rate between populations during second epoch (2Nam).

  • T1: Time in the past of split (in units of 2*Na generations).

  • T2: Time in the past of second epoch (in units of 2*Na generations).

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def sym_mig_twoepoch(params, ns, pts):
    """
    Split into two populations with symmetric migration. A second period of symmetric
    migration occurs, but can be a different rate. Population size is the same.

    Parameters:
        params (tuple): (nu1, nu2, m1, m2, T1, T2)

            - nu1: Size of population 1 after split.

            - nu2: Size of population 2 after split.

            - m1: Migration rate between populations during first epoch (2*Na*m).

            - m2: Migration rate between populations during second epoch (2*Na*m).

            - T1: Time in the past of split (in units of 2*Na generations).

            - T2: Time in the past of second epoch (in units of 2*Na generations).
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    nu1, nu2, m1, m2, T1, T2 = params
    xx = Numerics.default_grid(pts)
    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=m1, m21=m1)
    phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m2, m21=m2)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_anc_asym_mig(params, ns, pts)

Split with asymmetric migration followed by isolation.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(m12, m21, T1, T2, s)

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

  • T2: The scaled time between the ancient migration and present.

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_anc_asym_mig(params, ns, pts):
    """
    Split with asymmetric migration followed by isolation.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (m12, m21, T1, T2, s)

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

            - T2: The scaled time between the ancient migration and present.

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    m12, m21, T1, T2, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1=1-s, nu2=s, m12=m12, m21=m21)
    phi = Integration.two_pops(phi, xx, T2, nu1=1-s, nu2=s, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_anc_sym_mig(params, ns, pts)

Split with symmetric migration followed by isolation.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(m, T1, T2, s)

  • m: Migration between population 2 and population 1 (2Nam).

  • T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

  • T2: The scaled time between the ancient migration and present.

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_anc_sym_mig(params, ns, pts):
    """
    Split with symmetric migration followed by isolation.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (m, T1, T2, s)

            - m: Migration between population 2 and population 1 (2*Na*m).

            - T1: The scaled time between the split and the ancient migration (in units of 2*Na generations).

            - T2: The scaled time between the ancient migration and present.

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    m, T1, T2, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T1, nu1=1-s, nu2=s, m12=m, m21=m)
    phi = Integration.two_pops(phi, xx, T2, nu1=1-s, nu2=s, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_no_mig(params, ns, pts)

Split into two populations with no migration.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(T, s)

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_no_mig(params, ns, pts):
    """
    Split into two populations with no migration.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (T, s)

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    T, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)
    phi = PhiManip.phi_1D_to_2D(xx, phi)
    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=s, m12=0, m21=0)
    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_no_mig_admix_early(params, ns, pts)

Split into two populations with no migration but a discrete admixture event from population 1 into population 2 occurs (before drift).

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(T, s, f)

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

  • f: Fraction of updated population 2 to be derived from population 1.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_no_mig_admix_early(params, ns, pts):
    """
    Split into two populations with no migration but a discrete admixture event
    from population 1 into population 2 occurs (before drift).

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (T, s, f)

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

            - f: Fraction of updated population 2 to be derived from population 1.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    T, s, f = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)

    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=s, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_no_mig_admix_late(params, ns, pts)

Split into two populations with no migration but a discrete admixture event from population 1 into population 2 occurs (after drift).

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(T, s, f)

  • T: Time in the past of split (in units of 2*Na generations).

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

  • f: Fraction of updated population 2 to be derived from population 1.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_no_mig_admix_late(params, ns, pts):
    """
    Split into two populations with no migration but a discrete admixture event
    from population 1 into population 2 occurs (after drift).

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (T, s, f)

            - T: Time in the past of split (in units of 2*Na generations).

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

            - f: Fraction of updated population 2 to be derived from population 1.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    T, s, f = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T, nu1=1-s, nu2=s, m12=0, m21=0)

    phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_sec_contact_asym_mig(params, ns, pts)

Split with no gene flow, followed by period of asymmetrical gene flow.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(m12, m21, T1, T2, s)

  • m12: Migration from population 2 to population 1 (2Nam12).

  • m21: Migration from population 1 to population 2.

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scaled time between the secondary contact and present.

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_sec_contact_asym_mig(params, ns, pts):
    """
    Split with no gene flow, followed by period of asymmetrical gene flow.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (m12, m21, T1, T2, s)

            - m12: Migration from population 2 to population 1 (2*Na*m12).

            - m21: Migration from population 1 to population 2.

            - T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

            - T2: The scaled time between the secondary contact and present.

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    m12, m21, T1, T2, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T1, nu1=1-s, nu2=s, m12=0, m21=0)

    phi = Integration.two_pops(phi, xx, T2, nu1=1-s, nu2=s, m12=m12, m21=m21)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_sec_contact_sym_mig(params, ns, pts)

Split with no gene flow, followed by period of symmetrical gene flow.

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(m, T1, T2, s)

  • m: Migration between population 2 and population 1 (2Nam).

  • T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

  • T2: The scaled time between the secondary contact and present.

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_sec_contact_sym_mig(params, ns, pts):
    """
    Split with no gene flow, followed by period of symmetrical gene flow.

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (m, T1, T2, s)

            - m: Migration between population 2 and population 1 (2*Na*m).

            - T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).

            - T2: The scaled time between the secondary contact and present.

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    m, T1, T2, s = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T1, nu1=1-s, nu2=s, m12=0, m21=0)

    phi = Integration.two_pops(phi, xx, T2, nu1=1-s, nu2=s, m12=m, m21=m)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs

vic_two_epoch_admix(params, ns, pts)

Split into two populations with no migration but a discrete admixture event from population 1 into population 2 occurs (between two drift events).

Populations are fractions of the reference population, where population 2 is represented by Nref(s), and population 1 is represented by Nref(1-s). Nref implicitly has size = 1.

Parameters:

Name Type Description Default
params tuple

(T1, T2, s, f)

  • T1: The scaled time between the split and admixture event (in units of 2*Na generations).

  • T2: The scaled time between the admixture event and present.

  • s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

  • f: Fraction of updated population 2 to be derived from population 1.

 required
ns tuple

Sample sizes (n1, n2).

 required
pts int

Number of grid points to use in integration.

 required

Returns:

Name Type Description
fs Spectrum

The resulting frequency spectrum.

Raises:

Type Description
ValueError

If params does not contain the expected number of elements.
Source code in dadi/PortikModels/portik_models_2d.py 
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def vic_two_epoch_admix(params, ns, pts):
    """
    Split into two populations with no migration but a discrete admixture event
    from population 1 into population 2 occurs (between two drift events).

    Populations are fractions of the reference population, where population 2 is represented by Nref*(s),
    and population 1 is represented by Nref*(1-s). Nref implicitly has size = 1.

    Parameters:
        params (tuple): (T1, T2, s, f)

            - T1: The scaled time between the split and admixture event (in units of 2*Na generations).

            - T2: The scaled time between the admixture event and present.

            - s: Fraction of Nref that goes to population 2. Population 2 size = s. Population 1 size = 1-s.

            - f: Fraction of updated population 2 to be derived from population 1.
        ns (tuple): Sample sizes (n1, n2).
        pts (int): Number of grid points to use in integration.

    Returns:
        fs (Spectrum): The resulting frequency spectrum.

    Raises:
        ValueError: If `params` does not contain the expected number of elements.
    """
    T1, T2, s, f = params

    xx = Numerics.default_grid(pts)

    phi = PhiManip.phi_1D(xx)

    phi = PhiManip.phi_1D_to_2D(xx, phi)

    phi = Integration.two_pops(phi, xx, T1, nu1=1-s, nu2=s, m12=0, m21=0)

    phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)

    phi = Integration.two_pops(phi, xx, T2, nu1=1-s, nu2=s, m12=0, m21=0)

    fs = Spectrum.from_phi(phi, ns, (xx, xx))
    return fs