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Integration

Functions for integrating population frequency spectra.

five_pops(phi, xx, T, nu1=1, nu2=1, nu3=1, nu4=1, nu5=1, m12=0, m13=0, m14=0, m15=0, m21=0, m23=0, m24=0, m25=0, m31=0, m32=0, m34=0, m35=0, m41=0, m42=0, m43=0, m45=0, m51=0, m52=0, m53=0, m54=0, gamma1=0, gamma2=0, gamma3=0, gamma4=0, gamma5=0, h1=0.5, h2=0.5, h3=0.5, h4=0.5, h5=0.5, theta0=1, initial_t=0, frozen1=False, frozen2=False, frozen3=False, frozen4=False, frozen5=False, deme_ids=None)

Integrate a 5-dimensional phi foward.

Note

  • nu's, gamma's, m's, and theta0 may be functions of time.

  • Generalizing to different grids in different phi directions is straightforward. The tricky part will be later doing the extrapolation correctly.

Parameters:

Name Type Description Default
phi array - like

Initial 5-dimensional phi

 required
xx array - like

1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed that this grid is used in all dimensions.

 required
T float

Time at which to halt integration

 required
nu1 float

Population sizes

 1
nu2 float

Population sizes

 1
nu3 float

Population sizes

 1
nu4 float

Population sizes

 1
nu5 float

Population sizes

 1
m12 float

Migration rates. Note that m12 is the rate into 1 from 2.

 0
m13 float

Migration rates. Note that m13 is the rate into 1 from 3.

 0
m14 float

Migration rates. Note that m14 is the rate into 1 from 4.

 0
m15 float

Migration rates. Note that m15 is the rate into 1 from 5.

 0
m21 float

Migration rates. Note that m21 is the rate into 2 from 1.

 0
m23 float

Migration rates. Note that m23 is the rate into 2 from 3.

 0
m24 float

Migration rates. Note that m24 is the rate into 2 from 4.

 0
m25 float

Migration rates. Note that m25 is the rate into 2 from 5.

 0
m31 float

Migration rates. Note that m31 is the rate into 3 from 1.

 0
m32 float

Migration rates. Note that m32 is the rate into 3 from 2.

 0
m34 float

Migration rates. Note that m34 is the rate into 3 from 4.

 0
m35 float

Migration rates. Note that m35 is the rate into 3 from 5.

 0
m41 float

Migration rates. Note that m41 is the rate into 4 from 1.

 0
m42 float

Migration rates. Note that m42 is the rate into 4 from 2.

 0
m43 float

Migration rates. Note that m43 is the rate into 4 from 3.

 0
m45 float

Migration rates. Note that m45 is the rate into 4 from 5.

 0
m51 float

Migration rates. Note that m51 is the rate into 5 from 1.

 0
m52 float

Migration rates. Note that m52 is the rate into 5 from 2.

 0
m53 float

Migration rates. Note that m53 is the rate into 5 from 3.

 0
m54 float

Migration rates. Note that m54 is the rate into 5 from 4.

 0
gamma1 float

Selection coefficients on all segregating alleles

 0
gamma2 float

Selection coefficients on all segregating alleles

 0
gamma3 float

Selection coefficients on all segregating alleles

 0
gamma4 float

Selection coefficients on all segregating alleles

 0
gamma5 float

Selection coefficients on all segregating alleles

 0
h1 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h2 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h3 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h4 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h5 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
theta0 float

Propotional to ancestral size. Typically constant.

 1
initial_t float

Time at which to start integration. (Note that this only matters if one of the demographic parameters is a function of time.)

 0
frozen1 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen2 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen3 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen4 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen5 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
deme_ids list[str])

sequence of strings representing the names of demes

 None
Source code in dadi/Integration.py 
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def five_pops(phi, xx, T, nu1=1, nu2=1, nu3=1, nu4=1, nu5=1,
              m12=0, m13=0, m14=0, m15=0, m21=0, m23=0, m24=0, m25=0,
              m31=0, m32=0, m34=0, m35=0, m41=0, m42=0, m43=0, m45=0,
              m51=0, m52=0, m53=0, m54=0, 
              gamma1=0, gamma2=0, gamma3=0, gamma4=0, gamma5=0,
              h1=0.5, h2=0.5, h3=0.5, h4=0.5, h5=0.5,
              theta0=1, initial_t=0, frozen1=False, frozen2=False,
              frozen3=False, frozen4=False, frozen5=False, deme_ids=None):
    """
    Integrate a 5-dimensional phi foward.

    Note:
        - nu's, gamma's, m's, and theta0 may be functions of time.

        - Generalizing to different grids in different phi directions is
            straightforward. The tricky part will be later doing the extrapolation
            correctly.

    Args:
        phi (array-like): Initial 5-dimensional phi
        xx (array-like): 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed
            that this grid is used in all dimensions.
        T (float): Time at which to halt integration
        nu1 (float): Population sizes
        nu2 (float): Population sizes
        nu3 (float): Population sizes
        nu4 (float): Population sizes
        nu5 (float): Population sizes
        m12 (float): Migration rates. Note that m12 is the rate 
             *into 1 from 2*.
        m13 (float): Migration rates. Note that m13 is the rate 
             *into 1 from 3*.
        m14 (float): Migration rates. Note that m14 is the rate
             *into 1 from 4*.
        m15 (float): Migration rates. Note that m15 is the rate
             *into 1 from 5*.
        m21 (float): Migration rates. Note that m21 is the rate 
             *into 2 from 1*.
        m23 (float): Migration rates. Note that m23 is the rate 
             *into 2 from 3*.
        m24 (float): Migration rates. Note that m24 is the rate
             *into 2 from 4*.
        m25 (float): Migration rates. Note that m25 is the rate
             *into 2 from 5*.
        m31 (float): Migration rates. Note that m31 is the rate 
             *into 3 from 1*.
        m32 (float): Migration rates. Note that m32 is the rate 
             *into 3 from 2*.
        m34 (float): Migration rates. Note that m34 is the rate
             *into 3 from 4*.
        m35 (float): Migration rates. Note that m35 is the rate
             *into 3 from 5*.
        m41 (float): Migration rates. Note that m41 is the rate
             *into 4 from 1*.
        m42 (float): Migration rates. Note that m42 is the rate
             *into 4 from 2*.
        m43 (float): Migration rates. Note that m43 is the rate
             *into 4 from 3*.
        m45 (float): Migration rates. Note that m45 is the rate
             *into 4 from 5*.
        m51 (float): Migration rates. Note that m51 is the rate
             *into 5 from 1*.
        m52 (float): Migration rates. Note that m52 is the rate
             *into 5 from 2*.
        m53 (float): Migration rates. Note that m53 is the rate
             *into 5 from 3*.
        m54 (float): Migration rates. Note that m54 is the rate
             *into 5 from 4*.
        gamma1 (float): Selection coefficients on *all* segregating alleles
        gamma2 (float): Selection coefficients on *all* segregating alleles
        gamma3 (float): Selection coefficients on *all* segregating alleles
        gamma4 (float): Selection coefficients on *all* segregating alleles
        gamma5 (float): Selection coefficients on *all* segregating alleles
        h1 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h2 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h3 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h4 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h5 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        theta0 (float): Propotional to ancestral size. Typically constant.
        initial_t (float): Time at which to start integration. (Note that this only matters
                if one of the demographic parameters is a function of time.)
        frozen1 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen2 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen3 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen4 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen5 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        deme_ids (list[str])): sequence of strings representing the names of demes
    """
    if T - initial_t == 0:
        return phi
    elif T - initial_t < 0:
        raise ValueError('Final integration time T (%f) is less than '
                         'intial_time (%f). Integration cannot be run '
                         'backwards.' % (T, initial_t))

    if (frozen1 and (m12 != 0 or m21 != 0 or m13 !=0 or m31 != 0 or m41 != 0 or m14 != 0 or m15 != 0 or m51 != 0))\
       or (frozen2 and (m12 != 0 or m21 != 0 or m23 != 0 or m32 != 0 or m24 != 0 or m42 != 0 or m25 != 0 or m52 != 0))\
       or (frozen3 and (m13 != 0 or m31 != 0 or m23 != 0 or m32 != 0 or m34 != 0 or m43 != 0 or m35 != 0 or m53 !=0))\
       or (frozen4 and (m14 != 0 or m41 != 0 or m24 != 0 or m42 != 0 or m34 != 0 or m43 != 0 or m45 != 0 or m54 != 0))\
       or (frozen5 and (m15 != 0 or m51 != 0 or m25 != 0 or m52 != 0 or m35 != 0 or m53 != 0 or m45 != 0 or m54 != 0)):
        raise ValueError('Population cannot be frozen and have non-zero '
                         'migration to or from it.')
    bb = aa = zz = yy = xx

    nu1_f, nu2_f = Misc.ensure_1arg_func(nu1), Misc.ensure_1arg_func(nu2)
    nu3_f, nu4_f = Misc.ensure_1arg_func(nu3), Misc.ensure_1arg_func(nu4)
    nu5_f = Misc.ensure_1arg_func(nu5)
    gamma1_f, gamma2_f = Misc.ensure_1arg_func(gamma1), Misc.ensure_1arg_func(gamma2)
    gamma3_f, gamma4_f = Misc.ensure_1arg_func(gamma3), Misc.ensure_1arg_func(gamma4)
    gamma5_f = Misc.ensure_1arg_func(gamma5)
    h1_f, h2_f = Misc.ensure_1arg_func(h1), Misc.ensure_1arg_func(h2)
    h3_f, h4_f = Misc.ensure_1arg_func(h3), Misc.ensure_1arg_func(h4)
    h5_f = Misc.ensure_1arg_func(h5)
    m12_f, m13_f, m14_f, m15_f = Misc.ensure_1arg_func(m12), Misc.ensure_1arg_func(m13), Misc.ensure_1arg_func(m14), Misc.ensure_1arg_func(m15)
    m21_f, m23_f, m24_f, m25_f = Misc.ensure_1arg_func(m21), Misc.ensure_1arg_func(m23), Misc.ensure_1arg_func(m24), Misc.ensure_1arg_func(m25)
    m31_f, m32_f, m34_f, m35_f = Misc.ensure_1arg_func(m31), Misc.ensure_1arg_func(m32), Misc.ensure_1arg_func(m34), Misc.ensure_1arg_func(m35)
    m41_f, m42_f, m43_f, m45_f = Misc.ensure_1arg_func(m41), Misc.ensure_1arg_func(m42), Misc.ensure_1arg_func(m43), Misc.ensure_1arg_func(m45)
    m51_f, m52_f, m53_f, m54_f = Misc.ensure_1arg_func(m51), Misc.ensure_1arg_func(m52), Misc.ensure_1arg_func(m53), Misc.ensure_1arg_func(m54)
    theta0_f = Misc.ensure_1arg_func(theta0)

    if cuda_enabled:
        import dadi.cuda
        phi = dadi.cuda.Integration._five_pops_temporal_params(phi, xx, T, initial_t, 
            nu1_f, nu2_f, nu3_f, nu4_f, nu5_f,
            m12_f, m13_f, m14_f, m15_f, m21_f, m23_f, m24_f, m25_f, m31_f, m32_f, m34_f, m35_f,
            m41_f, m42_f, m43_f, m45_f, m51_f, m52_f, m53_f, m54_f, 
            gamma1_f, gamma2_f, gamma3_f, gamma4_f, gamma5_f,
            h1_f, h2_f, h3_f, h4_f, h5_f, theta0_f, frozen1, frozen2, frozen3, frozen4, frozen5, deme_ids)
        return phi

    current_t = initial_t
    nu1, nu2, nu3, nu4, nu5 = nu1_f(current_t), nu2_f(current_t), nu3_f(current_t), nu4_f(current_t), nu5_f(current_t)
    gamma1, gamma2, gamma3, gamma4, gamma5 = gamma1_f(current_t), gamma2_f(current_t), gamma3_f(current_t), gamma4_f(current_t), gamma5_f(current_t)
    h1, h2, h3, h4, h5 = h1_f(current_t), h2_f(current_t), h3_f(current_t), h4_f(current_t), h5_f(current_t)
    m12, m13, m14, m15 = m12_f(current_t), m13_f(current_t), m14_f(current_t), m15_f(current_t)
    m21, m23, m24, m25 = m21_f(current_t), m23_f(current_t), m24_f(current_t), m25_f(current_t)
    m31, m32, m34, m35 = m31_f(current_t), m32_f(current_t), m34_f(current_t), m35_f(current_t)
    m41, m42, m43, m45 = m41_f(current_t), m42_f(current_t), m43_f(current_t), m45_f(current_t)
    m51, m52, m53, m54 = m51_f(current_t), m52_f(current_t), m53_f(current_t), m54_f(current_t)

    dx,dy,dz,da,db = numpy.diff(xx),numpy.diff(yy),numpy.diff(zz),numpy.diff(aa),numpy.diff(bb)
    demes_hist = [[0, [nu1,nu2,nu3,nu4,nu5], [m12,m13,m14,m15,m21,m23,m24,m25,m31,m32,m34,m35,m41,m42,m43,m45,m51,m52,m53,m54]]]
    while current_t < T:
        dt = min(_compute_dt(dx,nu1,[m12,m13,m14,m15],gamma1,h1),
                 _compute_dt(dy,nu2,[m21,m23,m24,m25],gamma2,h2),
                 _compute_dt(dz,nu3,[m31,m32,m34,m35],gamma3,h3),
                 _compute_dt(da,nu4,[m41,m42,m43,m45],gamma4,h4),
                 _compute_dt(db,nu5,[m51,m52,m53,m54],gamma5,h5))
        this_dt = min(dt, T - current_t)

        next_t = current_t + this_dt

        nu1, nu2, nu3, nu4, nu5 = nu1_f(next_t), nu2_f(next_t), nu3_f(next_t), nu4_f(next_t), nu5_f(next_t)
        gamma1, gamma2, gamma3, gamma4, gamma5 = gamma1_f(next_t), gamma2_f(next_t), gamma3_f(next_t), gamma4_f(next_t), gamma5_f(next_t)
        h1, h2, h3, h4, h5 = h1_f(next_t), h2_f(next_t), h3_f(next_t), h4_f(next_t), h5_f(next_t)
        m12, m13, m14, m15 = m12_f(next_t), m13_f(next_t), m14_f(next_t), m15_f(next_t)
        m21, m23, m24, m25 = m21_f(next_t), m23_f(next_t), m24_f(next_t), m25_f(next_t)
        m31, m32, m34, m35 = m31_f(next_t), m32_f(next_t), m34_f(next_t), m35_f(next_t)
        m41, m42, m43, m45 = m41_f(next_t), m42_f(next_t), m43_f(next_t), m45_f(next_t)
        m51, m52, m53, m54 = m51_f(next_t), m52_f(next_t), m53_f(next_t), m54_f(next_t)
        theta0 = theta0_f(next_t)

        demes_hist.append([next_t, [nu1,nu2,nu3,nu4,nu5], [m12,m13,m14,m15,m21,m23,m24,m25,m31,m32,m34,m35,m41,m42,m43,m45,m51,m52,m53,m54]])
        if numpy.any(numpy.less([T,nu1,nu2,nu3,nu4,nu5,m12,m13,m14,m15,m21,
                                 m23,m24,m25, m31,m32,m34,m35, m41,m42,m43,m45,
                                 m51,m52,m53,m54, theta0],
                                0)):
            raise ValueError('A time, population size, migration rate, or '
                             'theta0 is < 0. Has the model been mis-specified?')
        if numpy.any(numpy.equal([nu1,nu2,nu3,nu4,nu5], 0)):
            raise ValueError('A population size is 0. Has the model been '
                             'mis-specified?')

        _inject_mutations_5D(phi, this_dt, xx, yy, zz, aa, bb, theta0,
                             frozen1, frozen2, frozen3, frozen4, frozen5)
        if not frozen1:
            phi = int_c.implicit_5Dx(phi, xx, yy, zz, aa, bb, nu1, m12, m13, m14, m15,
                                     gamma1, h1, this_dt, use_delj_trick)
        if not frozen2:
            phi = int_c.implicit_5Dy(phi, xx, yy, zz, aa, bb, nu2, m21, m23, m24, m25,
                                     gamma2, h2, this_dt, use_delj_trick)
        if not frozen3:
            phi = int_c.implicit_5Dz(phi, xx, yy, zz, aa, bb, nu3, m31, m32, m34, m35,
                                     gamma3, h3, this_dt, use_delj_trick)
        if not frozen4:
            phi = int_c.implicit_5Da(phi, xx, yy, zz, aa, bb, nu4, m41, m42, m43, m45,
                                     gamma4, h4, this_dt, use_delj_trick)
        if not frozen5:
            phi = int_c.implicit_5Db(phi, xx, yy, zz, aa, bb, nu5, m51, m52, m53, m54,
                                     gamma5, h5, this_dt, use_delj_trick)

        current_t = next_t
    Demes.cache.append(Demes.IntegrationNonConst(history = demes_hist, deme_ids=deme_ids))
    return phi

four_pops(phi, xx, T, nu1=1, nu2=1, nu3=1, nu4=1, m12=0, m13=0, m14=0, m21=0, m23=0, m24=0, m31=0, m32=0, m34=0, m41=0, m42=0, m43=0, gamma1=0, gamma2=0, gamma3=0, gamma4=0, h1=0.5, h2=0.5, h3=0.5, h4=0.5, theta0=1, initial_t=0, frozen1=False, frozen2=False, frozen3=False, frozen4=False, deme_ids=None)

Integrate a 4-dimensional phi foward.

Note

  • nu's, gamma's, m's, and theta0 may be functions of time.

  • Generalizing to different grids in different phi directions is straightforward. The tricky part will be later doing the extrapolation correctly.

Parameters:

Name Type Description Default
phi array - like

Initial 4-dimensional phi

 required
xx array - like

1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed that this grid is used in all dimensions.

 required
T float

Time at which to halt integration

 required
nu1 float

Population sizes

 1
nu2 float

Population sizes

 1
nu3 float

Population sizes

 1
nu4 float

Population sizes

 1
m12 float

Migration rates. Note that m12 is the rate into 1 from 2.

 0
m13 float

Migration rates. Note that m13 is the rate into 1 from 3.

 0
m14 float

Migration rates. Note that m14 is the rate into 1 from 4.

 0
m21 float

Migration rates. Note that m21 is the rate into 2 from 1.

 0
m23 float

Migration rates. Note that m23 is the rate into 2 from 3.

 0
m24 float

Migration rates. Note that m24 is the rate into 2 from 4.

 0
m31 float

Migration rates. Note that m31 is the rate into 3 from 1.

 0
m32 float

Migration rates. Note that m32 is the rate into 3 from 2.

 0
m34 float

Migration rates. Note that m34 is the rate into 3 from 4.

 0
m41 float

Migration rates. Note that m41 is the rate into 4 from 1.

 0
m42 float

Migration rates. Note that m42 is the rate into 4 from 2.

 0
m43 float

Migration rates. Note that m43 is the rate into 4 from 3.

 0
gamma1 float

Selection coefficients on all segregating alleles

 0
gamma2 float

Selection coefficients on all segregating alleles

 0
gamma3 float

Selection coefficients on all segregating alleles

 0
gamma4 float

Selection coefficients on all segregating alleles

 0
h1 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h2 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h3 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h4 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
theta0 float

Propotional to ancestral size. Typically constant.

 1
initial_t float

Time at which to start integration. (Note that this only matters if one of the demographic parameters is a function of time.)

 0
frozen1 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen2 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen3 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen4 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
deme_ids list[str]

sequence of strings representing the names of demes

 None
Source code in dadi/Integration.py 
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def four_pops(phi, xx, T, nu1=1, nu2=1, nu3=1, nu4=1,
              m12=0, m13=0, m14=0, m21=0, m23=0, m24=0, 
              m31=0, m32=0, m34=0, m41=0, m42=0, m43=0,
              gamma1=0, gamma2=0, gamma3=0, gamma4=0, 
              h1=0.5, h2=0.5, h3=0.5, h4=0.5,
              theta0=1, initial_t=0, frozen1=False, frozen2=False,
              frozen3=False, frozen4=False, deme_ids=None):
    """
    Integrate a 4-dimensional phi foward.

    Note:
        - nu's, gamma's, m's, and theta0 may be functions of time.

        - Generalizing to different grids in different phi directions is
            straightforward. The tricky part will be later doing the extrapolation
            correctly.

    Args:
        phi (array-like): Initial 4-dimensional phi
        xx (array-like): 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed
            that this grid is used in all dimensions.
        T (float): Time at which to halt integration
        nu1 (float): Population sizes
        nu2 (float): Population sizes
        nu3 (float): Population sizes
        nu4 (float): Population sizes
        m12 (float): Migration rates. Note that m12 is the rate 
             *into 1 from 2*.
        m13 (float): Migration rates. Note that m13 is the rate 
             *into 1 from 3*.
        m14 (float): Migration rates. Note that m14 is the rate
             *into 1 from 4*.
        m21 (float): Migration rates. Note that m21 is the rate 
             *into 2 from 1*.
        m23 (float): Migration rates. Note that m23 is the rate 
             *into 2 from 3*.
        m24 (float): Migration rates. Note that m24 is the rate
             *into 2 from 4*.
        m31 (float): Migration rates. Note that m31 is the rate 
             *into 3 from 1*.
        m32 (float): Migration rates. Note that m32 is the rate 
             *into 3 from 2*.
        m34 (float): Migration rates. Note that m34 is the rate
             *into 3 from 4*.
        m41 (float): Migration rates. Note that m41 is the rate
             *into 4 from 1*.
        m42 (float): Migration rates. Note that m42 is the rate
             *into 4 from 2*.
        m43 (float): Migration rates. Note that m43 is the rate
             *into 4 from 3*.
        gamma1 (float): Selection coefficients on *all* segregating alleles
        gamma2 (float): Selection coefficients on *all* segregating alleles
        gamma3 (float): Selection coefficients on *all* segregating alleles
        gamma4 (float): Selection coefficients on *all* segregating alleles
        h1 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h2 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h3 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h4 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        theta0 (float): Propotional to ancestral size. Typically constant.
        initial_t (float): Time at which to start integration. (Note that this only matters
                if one of the demographic parameters is a function of time.)
        frozen1 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen2 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen3 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen4 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        deme_ids (list[str]): sequence of strings representing the names of demes
    """
    if T - initial_t == 0:
        return phi
    elif T - initial_t < 0:
        raise ValueError('Final integration time T (%f) is less than '
                         'intial_time (%f). Integration cannot be run '
                         'backwards.' % (T, initial_t))


    if (frozen1 and (m12 != 0 or m21 != 0 or m13 !=0 or m31 != 0 or m41 != 0 or m14 != 0))\
       or (frozen2 and (m12 != 0 or m21 != 0 or m23 != 0 or m32 != 0 or m24 != 0 or m42 != 0))\
       or (frozen3 and (m13 != 0 or m31 != 0 or m23 !=0 or m32 != 0 or m34 != 0 or m43 != 0))\
       or (frozen4 and (m14 != 0 or m41 != 0 or m24 !=0 or m42 != 0 or m34 != 0 or m43 != 0)):
        raise ValueError('Population cannot be frozen and have non-zero '
                         'migration to or from it.')
    aa = zz = yy = xx

    nu1_f, nu2_f = Misc.ensure_1arg_func(nu1), Misc.ensure_1arg_func(nu2)
    nu3_f, nu4_f = Misc.ensure_1arg_func(nu3), Misc.ensure_1arg_func(nu4)
    gamma1_f, gamma2_f = Misc.ensure_1arg_func(gamma1), Misc.ensure_1arg_func(gamma2)
    gamma3_f, gamma4_f = Misc.ensure_1arg_func(gamma3), Misc.ensure_1arg_func(gamma4)
    h1_f, h2_f = Misc.ensure_1arg_func(h1), Misc.ensure_1arg_func(h2)
    h3_f, h4_f = Misc.ensure_1arg_func(h3), Misc.ensure_1arg_func(h4)
    m12_f, m13_f, m14_f = Misc.ensure_1arg_func(m12), Misc.ensure_1arg_func(m13), Misc.ensure_1arg_func(m14)
    m21_f, m23_f, m24_f = Misc.ensure_1arg_func(m21), Misc.ensure_1arg_func(m23), Misc.ensure_1arg_func(m24)
    m31_f, m32_f, m34_f = Misc.ensure_1arg_func(m31), Misc.ensure_1arg_func(m32), Misc.ensure_1arg_func(m34)
    m41_f, m42_f, m43_f = Misc.ensure_1arg_func(m41), Misc.ensure_1arg_func(m42), Misc.ensure_1arg_func(m43)
    theta0_f = Misc.ensure_1arg_func(theta0)

    if cuda_enabled:
        import dadi.cuda
        phi = dadi.cuda.Integration._four_pops_temporal_params(phi, xx, T, initial_t,
                nu1_f, nu2_f, nu3_f, nu4_f, m12_f, m13_f, m14_f, m21_f, m23_f, m24_f, m31_f, m32_f, m34_f,
                m41_f, m42_f, m43_f, gamma1_f, gamma2_f, gamma3_f, gamma4_f, h1_f, h2_f, h3_f, h4_f,
                theta0_f, frozen1, frozen2, frozen3, frozen4, deme_ids)
        return phi

    current_t = initial_t
    nu1, nu2, nu3, nu4 = nu1_f(current_t), nu2_f(current_t), nu3_f(current_t), nu4_f(current_t)
    gamma1, gamma2, gamma3, gamma4 = gamma1_f(current_t), gamma2_f(current_t), gamma3_f(current_t), gamma4_f(current_t)
    h1, h2, h3, h4 = h1_f(current_t), h2_f(current_t), h3_f(current_t), h4_f(current_t)
    m12, m13, m14 = m12_f(current_t), m13_f(current_t), m14_f(current_t)
    m21, m23, m24 = m21_f(current_t), m23_f(current_t), m24_f(current_t)
    m31, m32, m34 = m31_f(current_t), m32_f(current_t), m34_f(current_t)
    m41, m42, m43 = m41_f(current_t), m42_f(current_t), m43_f(current_t)

    dx,dy,dz,da = numpy.diff(xx),numpy.diff(yy),numpy.diff(zz),numpy.diff(aa)
    demes_hist = [[0, [nu1,nu2,nu3,nu4], [m12,m13,m14,m21,m23,m24,m31,m32,m34,m41,m42,m43]]]
    while current_t < T:
        dt = min(_compute_dt(dx,nu1,[m12,m13,m14],gamma1,h1),
                 _compute_dt(dy,nu2,[m21,m23,m24],gamma2,h2),
                 _compute_dt(dz,nu3,[m31,m32,m34],gamma3,h3),
                 _compute_dt(da,nu4,[m41,m42,m43],gamma4,h4))
        this_dt = min(dt, T - current_t)

        next_t = current_t + this_dt

        nu1, nu2, nu3, nu4 = nu1_f(next_t), nu2_f(next_t), nu3_f(next_t), nu4_f(next_t)
        gamma1, gamma2, gamma3, gamma4 = gamma1_f(next_t), gamma2_f(next_t), gamma3_f(next_t), gamma4_f(next_t)
        h1, h2, h3, h4 = h1_f(next_t), h2_f(next_t), h3_f(next_t), h4_f(next_t)
        m12, m13, m14 = m12_f(next_t), m13_f(next_t), m14_f(next_t)
        m21, m23, m24 = m21_f(next_t), m23_f(next_t), m24_f(next_t)
        m31, m32, m34 = m31_f(next_t), m32_f(next_t), m34_f(next_t)
        m41, m42, m43 = m41_f(next_t), m42_f(next_t), m43_f(next_t)
        theta0 = theta0_f(next_t)

        demes_hist.append([next_t, [nu1,nu2,nu3,nu4], [m12,m13,m14,m21,m23,m24,m31,m32,m34,m41,m42,m43]])
        if numpy.any(numpy.less([T,nu1,nu2,nu3,nu4,m12,m13,m14,m21,
                                 m23, m24, m31, m32, m34, m41, m42, m43, theta0],
                                0)):
            raise ValueError('A time, population size, migration rate, or '
                             'theta0 is < 0. Has the model been mis-specified?')
        if numpy.any(numpy.equal([nu1,nu2,nu3,nu4], 0)):
            raise ValueError('A population size is 0. Has the model been '
                             'mis-specified?')

        _inject_mutations_4D(phi, this_dt, xx, yy, zz, aa, theta0,
                             frozen1, frozen2, frozen3, frozen4)
        if not frozen1:
            phi = int_c.implicit_4Dx(phi, xx, yy, zz, aa, nu1, m12, m13, m14,
                                     gamma1, h1, this_dt, use_delj_trick)
        if not frozen2:
            phi = int_c.implicit_4Dy(phi, xx, yy, zz, aa, nu2, m21, m23, m24,
                                     gamma2, h2, this_dt, use_delj_trick)
        if not frozen3:
            phi = int_c.implicit_4Dz(phi, xx, yy, zz, aa, nu3, m31, m32, m34,
                                     gamma3, h3, this_dt, use_delj_trick)
        if not frozen4:
            phi = int_c.implicit_4Da(phi, xx, yy, zz, aa, nu4, m41, m42, m43,
                                     gamma4, h4, this_dt, use_delj_trick)

        current_t = next_t
    Demes.cache.append(Demes.IntegrationNonConst(history = demes_hist, deme_ids=deme_ids))
    return phi

one_pop(phi, xx, T, nu=1, gamma=0, h=0.5, theta0=1.0, initial_t=0, frozen=False, beta=1, deme_ids=None)

Integrate a 1-dimensional phi foward.

Parameters:

Name Type Description Default
phi array - like

Initial 1-dimensional phi

 required
xx array - like

Grid upon (0,1) overwhich phi is defined. nu, gamma, and theta0 may be functions of time.

 required
T float

Time at which to halt integration

 required
nu float

Population size

 1
gamma float

Selection coefficient on all segregating alleles

 0
h float

Dominance coefficient. h = 0.5 corresponds to genic selection. Heterozygotes have fitness 1+2sh and homozygotes have fitness 1+2s.

 0.5
theta0 float

Propotional to ancestral size. Typically constant.

 1.0
beta float

Breeding ratio, beta=Nf/Nm.

 1
initial_t float

Time at which to start integration. (Note that this only matters if one of the demographic parameters is a function of time.)

 0
frozen bool

If True, population is 'frozen' so that it does not change. In the one_pop case, this is equivalent to not running the integration at all.

 False
deme_ids list[str]

sequence of strings representing the names of demes

 None
Source code in dadi/Integration.py 
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def one_pop(phi, xx, T, nu=1, gamma=0, h=0.5, theta0=1.0, initial_t=0, 
            frozen=False, beta=1, deme_ids=None):
    """
    Integrate a 1-dimensional phi foward.

    Args:
        phi (array-like): Initial 1-dimensional phi
        xx (array-like): Grid upon (0,1) overwhich phi is defined.
            nu, gamma, and theta0 may be functions of time.
        T (float): Time at which to halt integration
        nu (float): Population size
        gamma (float): Selection coefficient on *all* segregating alleles
        h (float): Dominance coefficient. h = 0.5 corresponds to genic selection. 
                Heterozygotes have fitness 1+2sh and homozygotes have fitness 1+2s.
        theta0 (float): Propotional to ancestral size. Typically constant.
        beta (float): Breeding ratio, beta=Nf/Nm.
        initial_t (float): Time at which to start integration. (Note that this only matters
                if one of the demographic parameters is a function of time.)
        frozen (bool): If True, population is 'frozen' so that it does not change.
                In the one_pop case, this is equivalent to not running the
                integration at all.
        deme_ids (list[str]): sequence of strings representing the names of demes
    """
    phi = phi.copy()

    # For a one population integration, freezing means just not integrating.
    if frozen:
        return phi

    if T - initial_t == 0:
        return phi
    elif T - initial_t < 0:
        raise ValueError('Final integration time T (%f) is less than '
                         'intial_time (%f). Integration cannot be run '
                         'backwards.' % (T, initial_t))

    vars_to_check = (nu, gamma, h, theta0, beta)
    if numpy.all([numpy.isscalar(var) for var in vars_to_check]):
        Demes.cache.append(Demes.IntegrationConst(duration = T-initial_t, start_sizes = [nu], deme_ids=deme_ids))
        return _one_pop_const_params(phi, xx, T, nu, gamma, h, theta0, 
                                     initial_t, beta)

    nu_f = Misc.ensure_1arg_func(nu)
    gamma_f = Misc.ensure_1arg_func(gamma)
    h_f = Misc.ensure_1arg_func(h)
    theta0_f = Misc.ensure_1arg_func(theta0)
    beta_f = Misc.ensure_1arg_func(beta)

    current_t = initial_t
    nu, gamma, h = nu_f(current_t), gamma_f(current_t), h_f(current_t)
    beta = beta_f(current_t)
    dx = numpy.diff(xx)
    demes_hist = [[0, [nu], []]]
    while current_t < T:
        dt = _compute_dt(dx,nu,[0],gamma,h)
        this_dt = min(dt, T - current_t)

        # Because this is an implicit method, I need the *next* time's params.
        # So there's a little inconsistency here, in that I'm estimating dt
        # using the last timepoints nu,gamma,h.
        next_t = current_t + this_dt
        nu, gamma, h = nu_f(next_t), gamma_f(next_t), h_f(next_t)
        beta = beta_f(next_t)
        theta0 = theta0_f(next_t)
        demes_hist.append([next_t, [nu], []])

        if numpy.any(numpy.less([T,nu,theta0], 0)):
            raise ValueError('A time, population size, migration rate, or '
                             'theta0 is < 0. Has the model been mis-specified?')
        if numpy.any(numpy.equal([nu], 0)):
            raise ValueError('A population size is 0. Has the model been '
                             'mis-specified?')

        _inject_mutations_1D(phi, this_dt, xx, theta0)
        # Do each step in C, since it will be faster to compute the a,b,c
        # matrices there.
        phi = int_c.implicit_1Dx(phi, xx, nu, gamma, h, beta, this_dt, 
                                 use_delj_trick=use_delj_trick)
        current_t = next_t
    Demes.cache.append(Demes.IntegrationNonConst(history = demes_hist, deme_ids=deme_ids))
    return phi

one_pop_X(phi, xx, T, nu=1, gamma=0, h=0.5, beta=1, alpha=1, theta0=1.0, initial_t=0, frozen=False)

Integrate a 1-dimensional phi foward.

nu, gamma, and theta0 may be functions of time.

Parameters:

Name Type Description Default
phi array - like

Initial 1-dimensional phi

 required
xx array - like

Grid upon (0,1) overwhich phi is defined.

 required
T float

Time at which to halt integration

 required
nu float

Population size

 1
gamma float

Scaled selection coefficient on all segregating alleles

 0
h float

Dominance coefficient. h = 0.5 corresponds to genic selection. Heterozygous females have fitness 1+2sh and homozygous females have fitness 1+2s. Male carriers have fitness 1+2s.

 0.5
theta0 float

Propotional to ancestral size. Typically constant.

 1.0
beta float

Breeding ratio, beta=Nf/Nm.

 1
alpha float

Male to female mutation rate ratio, beta = mu_m / mu_f.

 1
initial_t float

Time at which to start integration. (Note that this only matters if one of the demographic parameters is a function of time.)

 0
frozen bool

If True, population is 'frozen' so that it does not change. In the one_pop case, this is equivalent to not running the integration at all.

 False
Source code in dadi/Integration.py 
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def one_pop_X(phi, xx, T, nu=1, gamma=0, h=0.5, beta=1, alpha=1, theta0=1.0, 
              initial_t=0, frozen=False):
    """
    Integrate a 1-dimensional phi foward.

    nu, gamma, and theta0 may be functions of time.

    Args:
        phi (array-like): Initial 1-dimensional phi
        xx (array-like): Grid upon (0,1) overwhich phi is defined.
        T (float): Time at which to halt integration
        nu (float): Population size
        gamma (float): Scaled selection coefficient on *all* segregating alleles
        h (float): Dominance coefficient. h = 0.5 corresponds to genic selection. 
                   Heterozygous females have fitness 1+2sh and homozygous females have
                   fitness 1+2s. Male carriers have fitness 1+2s.
        theta0 (float): Propotional to ancestral size. Typically constant.
        beta (float): Breeding ratio, beta=Nf/Nm.
        alpha (float): Male to female mutation rate ratio, beta = mu_m / mu_f.
        initial_t (float): Time at which to start integration. (Note that this only matters
                if one of the demographic parameters is a function of time.)
        frozen (bool): If True, population is 'frozen' so that it does not change.
                In the one_pop case, this is equivalent to not running the
                integration at all.
    """
    phi = phi.copy()

    # For a one population integration, freezing means just not integrating.
    if frozen:
        return phi

    if T - initial_t == 0:
        return phi
    elif T - initial_t < 0:
        raise ValueError('Final integration time T (%f) is less than '
                         'intial_time (%f). Integration cannot be run '
                         'backwards.' % (T, initial_t))

    vars_to_check = (nu, gamma, h, theta0, beta, alpha)
    if numpy.all([numpy.isscalar(var) for var in vars_to_check]):
        return _one_pop_const_params_X(phi, xx, T, nu, gamma, h, beta, alpha, 
                                       theta0, initial_t)
    else:
        raise NotImplementedError('X chromosome integration currently only '
                                  'implemented for constant parameters.')

set_timescale_factor(pts, factor=10)

Controls the fineness of timesteps during integration.

The timestep will be proportional to Numerics.default_grid(pts)[1]/factor. Typically, pts should be set to the largest number of grid points used in extrapolation.

An adjustment factor of 10 typically results in acceptable accuracy. It may be desirable to increase this factor, particularly when population sizes are changing continously and rapidly.

Source code in dadi/Integration.py 
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def set_timescale_factor(pts, factor=10):
    """
    Controls the fineness of timesteps during integration.

    The timestep will be proportional to Numerics.default_grid(pts)[1]/factor.
    Typically, pts should be set to the *largest* number of grid points used in
    extrapolation. 

    An adjustment factor of 10 typically results in acceptable accuracy. It may
    be desirable to increase this factor, particularly when population sizes
    are changing continously and rapidly.
    """
    # Implementation note: This cannot be easily be set automatically, because
    # the integration doesn't know whether its results will be used in an
    # extrapolation.
    global timescale_factor
    logger.warning('set_timescale_factor has been deprecated, as it may be too '
                'conservative (and thus slow) in choosing timesteps. If you '
                'wish to take smaller timesteps for accuracy (particularly for '
                'a very quickly growing population), manually set '
                'dadi.Integration.timescale_factor to a smaller value. '
                '(Current value is %g.)' % timescale_factor)
    timescale_factor = Numerics.default_grid(pts)[1]/factor

three_pops(phi, xx, T, nu1=1, nu2=1, nu3=1, m12=0, m13=0, m21=0, m23=0, m31=0, m32=0, gamma1=0, gamma2=0, gamma3=0, h1=0.5, h2=0.5, h3=0.5, theta0=1, initial_t=0, frozen1=False, frozen2=False, frozen3=False, enable_cuda_cached=False, deme_ids=None)

Integrate a 3-dimensional phi foward.

Note

  • nu's, gamma's, m's, and theta0 may be functions of time.

  • Generalizing to different grids in different phi directions is straightforward. The tricky part will be later doing the extrapolation correctly.

Parameters:

Name Type Description Default
phi array - like

Initial 3-dimensional phi

 required
xx array - like

1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed that this grid is used in all dimensions.

 required
T float

Time at which to halt integration

 required
nu1 float

Population sizes

 1
nu2 float

Population sizes

 1
nu3 float

Population sizes

 1
m12 float

Migration rates. Note that m12 is the rate into 1 from 2.

 0
m13 float

Migration rates. Note that m13 is the rate into 1 from 3.

 0
m21 float

Migration rates. Note that m21 is the rate into 2 from 1.

 0
m23 float

Migration rates. Note that m23 is the rate into 2 from 3.

 0
m31 float

Migration rates. Note that m31 is the rate into 3 from 1.

 0
m32 float

Migration rates. Note that m32 is the rate into 3 from 2.

 0
gamma1 float

Selection coefficients on all segregating alleles

 0
gamma2 float

Selection coefficients on all segregating alleles

 0
gamma3 float

Selection coefficients on all segregating alleles

 0
h1 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h2 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h3 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
theta0 float

Propotional to ancestral size. Typically constant.

 1
initial_t float

Time at which to start integration. (Note that this only matters if one of the demographic parameters is a function of time.)

 0
frozen1 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen2 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen3 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
enable_cuda_cached bool

If True, enable CUDA integration with slower constant parameter method. Likely useful only for benchmarking.

 False
deme_ids list[str]

sequence of strings representing the names of demes

 None
Source code in dadi/Integration.py 
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def three_pops(phi, xx, T, nu1=1, nu2=1, nu3=1,
               m12=0, m13=0, m21=0, m23=0, m31=0, m32=0,
               gamma1=0, gamma2=0, gamma3=0, h1=0.5, h2=0.5, h3=0.5,
               theta0=1, initial_t=0, frozen1=False, frozen2=False,
               frozen3=False, enable_cuda_cached=False, deme_ids=None):
    """
    Integrate a 3-dimensional phi foward.

    Note:
        - nu's, gamma's, m's, and theta0 may be functions of time.

        - Generalizing to different grids in different phi directions is
          straightforward. The tricky part will be later doing the extrapolation
          correctly.

    Args:
        phi (array-like): Initial 3-dimensional phi
        xx (array-like): 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed
            that this grid is used in all dimensions.
        T (float): Time at which to halt integration
        nu1 (float): Population sizes
        nu2 (float): Population sizes
        nu3 (float): Population sizes
        m12 (float): Migration rates. Note that m12 is the rate 
             *into 1 from 2*.
        m13 (float): Migration rates. Note that m13 is the rate 
             *into 1 from 3*.
        m21 (float): Migration rates. Note that m21 is the rate 
             *into 2 from 1*.
        m23 (float): Migration rates. Note that m23 is the rate 
             *into 2 from 3*.
        m31 (float): Migration rates. Note that m31 is the rate 
             *into 3 from 1*.
        m32 (float): Migration rates. Note that m32 is the rate 
             *into 3 from 2*.
        gamma1 (float): Selection coefficients on *all* segregating alleles
        gamma2 (float): Selection coefficients on *all* segregating alleles
        gamma3 (float): Selection coefficients on *all* segregating alleles
        h1 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h2 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h3 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        theta0 (float): Propotional to ancestral size. Typically constant.
        initial_t (float): Time at which to start integration. (Note that this only matters
                if one of the demographic parameters is a function of time.)
        frozen1 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen2 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen3 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        enable_cuda_cached (bool): If True, enable CUDA integration with slower constant
                        parameter method. Likely useful only for benchmarking.
        deme_ids (list[str]): sequence of strings representing the names of demes
    """
    phi = phi.copy()

    if T - initial_t == 0:
        return phi
    elif T - initial_t < 0:
        raise ValueError('Final integration time T (%f) is less than '
                         'intial_time (%f). Integration cannot be run '
                         'backwards.' % (T, initial_t))


    if (frozen1 and (m12 != 0 or m21 != 0 or m13 !=0 or m31 != 0))\
       or (frozen2 and (m12 != 0 or m21 != 0 or m23 !=0 or m32 != 0))\
       or (frozen3 and (m13 != 0 or m31 != 0 or m23 !=0 or m32 != 0)):
        raise ValueError('Population cannot be frozen and have non-zero '
                         'migration to or from it.')

    vars_to_check = [nu1,nu2,nu3,m12,m13,m21,m23,m31,m32,gamma1,gamma2,
                     gamma3,h1,h2,h3,theta0]
    if numpy.all([numpy.isscalar(var) for var in vars_to_check]):
        if not cuda_enabled or (cuda_enabled and enable_cuda_cached):
            Demes.cache.append(Demes.IntegrationConst(duration = T-initial_t, 
                               start_sizes = [nu1, nu2, nu3],
                               mig = [m12, m13, m21, m23, m31, m32], deme_ids=deme_ids))
            return _three_pops_const_params(phi, xx, T, nu1, nu2, nu3,
                                            m12, m13, m21, m23, m31, m32,
                                            gamma1, gamma2, gamma3, h1, h2, h3,
                                            theta0, initial_t,
                                            frozen1, frozen2, frozen3)
    zz = yy = xx

    nu1_f = Misc.ensure_1arg_func(nu1)
    nu2_f = Misc.ensure_1arg_func(nu2)
    nu3_f = Misc.ensure_1arg_func(nu3)
    m12_f = Misc.ensure_1arg_func(m12)
    m13_f = Misc.ensure_1arg_func(m13)
    m21_f = Misc.ensure_1arg_func(m21)
    m23_f = Misc.ensure_1arg_func(m23)
    m31_f = Misc.ensure_1arg_func(m31)
    m32_f = Misc.ensure_1arg_func(m32)
    gamma1_f = Misc.ensure_1arg_func(gamma1)
    gamma2_f = Misc.ensure_1arg_func(gamma2)
    gamma3_f = Misc.ensure_1arg_func(gamma3)
    h1_f = Misc.ensure_1arg_func(h1)
    h2_f = Misc.ensure_1arg_func(h2)
    h3_f = Misc.ensure_1arg_func(h3)
    theta0_f = Misc.ensure_1arg_func(theta0)

    if cuda_enabled:
        import dadi.cuda
        phi = dadi.cuda.Integration._three_pops_temporal_params(phi, xx, T, initial_t,
                nu1_f, nu2_f, nu3_f, m12_f, m13_f, m21_f, m23_f, m31_f, m32_f, 
                gamma1_f, gamma2_f, gamma3_f, h1_f, h2_f, h3_f, 
                theta0_f, frozen1, frozen2, frozen3, deme_ids)
        return phi

    current_t = initial_t
    nu1,nu2,nu3 = nu1_f(current_t), nu2_f(current_t), nu3_f(current_t)
    m12,m13 = m12_f(current_t), m13_f(current_t)
    m21,m23 = m21_f(current_t), m23_f(current_t)
    m31,m32 = m31_f(current_t), m32_f(current_t)
    gamma1,gamma2 = gamma1_f(current_t), gamma2_f(current_t)
    gamma3 = gamma3_f(current_t)
    h1,h2,h3 = h1_f(current_t), h2_f(current_t), h3_f(current_t)
    dx,dy,dz = numpy.diff(xx),numpy.diff(yy),numpy.diff(zz)
    demes_hist = [[0, [nu1,nu2,nu3], [m12,m13,m21,m23,m31,m32]]]
    while current_t < T:
        dt = min(_compute_dt(dx,nu1,[m12,m13],gamma1,h1),
                 _compute_dt(dy,nu2,[m21,m23],gamma2,h2),
                 _compute_dt(dz,nu3,[m31,m32],gamma3,h3))
        this_dt = min(dt, T - current_t)

        next_t = current_t + this_dt

        nu1,nu2,nu3 = nu1_f(next_t), nu2_f(next_t), nu3_f(next_t)
        m12,m13 = m12_f(next_t), m13_f(next_t)
        m21,m23 = m21_f(next_t), m23_f(next_t)
        m31,m32 = m31_f(next_t), m32_f(next_t)
        gamma1,gamma2 = gamma1_f(next_t), gamma2_f(next_t)
        gamma3 = gamma3_f(next_t)
        h1,h2,h3 = h1_f(next_t), h2_f(next_t), h3_f(next_t)
        theta0 = theta0_f(next_t)
        demes_hist.append([next_t, [nu1,nu2,nu3], [m12,m13,m21,m23,m31,m32]])

        if numpy.any(numpy.less([T,nu1,nu2,nu3,m12,m13,m21,m23,m31,m32,theta0],
                                0)):
            raise ValueError('A time, population size, migration rate, or '
                             'theta0 is < 0. Has the model been mis-specified?')
        if numpy.any(numpy.equal([nu1,nu2,nu3], 0)):
            raise ValueError('A population size is 0. Has the model been '
                             'mis-specified?')

        _inject_mutations_3D(phi, this_dt, xx, yy, zz, theta0,
                             frozen1, frozen2, frozen3)
        if not frozen1:
            phi = int_c.implicit_3Dx(phi, xx, yy, zz, nu1, m12, m13, 
                                     gamma1, h1, this_dt, use_delj_trick)
        if not frozen2:
            phi = int_c.implicit_3Dy(phi, xx, yy, zz, nu2, m21, m23, 
                                     gamma2, h2, this_dt, use_delj_trick)
        if not frozen3:
            phi = int_c.implicit_3Dz(phi, xx, yy, zz, nu3, m31, m32, 
                                     gamma3, h3, this_dt, use_delj_trick)

        current_t = next_t
    Demes.cache.append(Demes.IntegrationNonConst(history = demes_hist, deme_ids=deme_ids))
    return phi

two_pops(phi, xx, T, nu1=1, nu2=1, m12=0, m21=0, gamma1=0, gamma2=0, h1=0.5, h2=0.5, theta0=1, initial_t=0, frozen1=False, frozen2=False, nomut1=False, nomut2=False, enable_cuda_cached=False, deme_ids=None)

Integrate a 2-dimensional phi foward.

Note

  • nu's, gamma's, m's, and theta0 may be functions of time.

  • Generalizing to different grids in different phi directions is straightforward. The tricky part will be later doing the extrapolation correctly.

Parameters:

Name Type Description Default
phi array - like

Initial 2-dimensional phi

 required
xx array - like

1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed that this grid is used in all dimensions.

 required
T float

Time at which to halt integration

 required
nu1 float

Population sizes

 1
nu2 float

Population sizes

 1
gamma1 float

Selection coefficients on all segregating alleles

 0
gamma2 float

Selection coefficients on all segregating alleles

 0
h1 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
h2 float

Dominance coefficients. h = 0.5 corresponds to genic selection.

 0.5
m12 float

Migration rates. Note that m12 is the rate into 1 from 2.

 0
m21 float

Migration rates. Note that m12 is the rate into 1 from 2.

 0
theta0 float

Propotional to ancestral size. Typically constant.

 1
initial_t float

Time at which to start integration. (Note that this only matters if one of the demographic parameters is a function of time.)

 0
frozen1 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
frozen2 bool

If True, the corresponding population is "frozen" in time (no new mutations and no drift), so the resulting spectrum will correspond to an ancient DNA sample from that population.

 False
nomut1 bool

If True, no new mutations will be introduced into the given population.

 False
nomut2 bool

If True, no new mutations will be introduced into the given population.

 False
enable_cuda_cached bool

If True, enable CUDA integration with slower constant parameter method. Likely useful only for benchmarking.

 False
deme_ids list[str]

sequence of strings representing the names of demes

 None
Source code in dadi/Integration.py 
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def two_pops(phi, xx, T, nu1=1, nu2=1, m12=0, m21=0, gamma1=0, gamma2=0,
             h1=0.5, h2=0.5, theta0=1, initial_t=0, frozen1=False,
             frozen2=False, nomut1=False, nomut2=False, enable_cuda_cached=False, deme_ids=None):
    """
    Integrate a 2-dimensional phi foward.

    Note:
        - nu's, gamma's, m's, and theta0 may be functions of time.

        - Generalizing to different grids in different phi directions is
          straightforward. The tricky part will be later doing the extrapolation
          correctly.

    Args:
        phi (array-like): Initial 2-dimensional phi
        xx (array-like): 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed
            that this grid is used in all dimensions.
        T (float): Time at which to halt integration
        nu1 (float): Population sizes
        nu2 (float): Population sizes
        gamma1 (float): Selection coefficients on *all* segregating alleles
        gamma2 (float): Selection coefficients on *all* segregating alleles
        h1 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        h2 (float): Dominance coefficients. h = 0.5 corresponds to genic selection.
        m12 (float): Migration rates. Note that m12 is the rate *into 1 from 2*.
        m21 (float): Migration rates. Note that m12 is the rate *into 1 from 2*.
        theta0 (float): Propotional to ancestral size. Typically constant.
        initial_t (float): Time at which to start integration. (Note that this only matters
                if one of the demographic parameters is a function of time.)
        frozen1 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        frozen2 (bool): If True, the corresponding population is "frozen" in time
                        (no new mutations and no drift), so the resulting spectrum
                        will correspond to an ancient DNA sample from that
                        population.
        nomut1 (bool): If True, no new mutations will be introduced into the
                    given population.
        nomut2 (bool): If True, no new mutations will be introduced into the
                    given population.
        enable_cuda_cached (bool): If True, enable CUDA integration with slower constant
                        parameter method. Likely useful only for benchmarking.
        deme_ids (list[str]): sequence of strings representing the names of demes
    """
    phi = phi.copy()

    if T - initial_t == 0:
        return phi
    elif T - initial_t < 0:
        raise ValueError('Final integration time T (%f) is less than '
                         'intial_time (%f). Integration cannot be run '
                         'backwards.' % (T, initial_t))

    if (frozen1 or frozen2) and (m12 != 0 or m21 != 0):
        raise ValueError('Population cannot be frozen and have non-zero '
                         'migration to or from it.')

    vars_to_check = [nu1,nu2,m12,m21,gamma1,gamma2,h1,h2,theta0]
    if numpy.all([numpy.isscalar(var) for var in vars_to_check]):
        # Constant integration with CUDA turns out to be slower,
        # so we only use it in specific circumsances.
        Demes.cache.append(Demes.IntegrationConst(duration = T-initial_t, 
                           start_sizes = [nu1, nu2], mig = [m12,m21], deme_ids=deme_ids))
        if not cuda_enabled or (cuda_enabled and enable_cuda_cached):
            return _two_pops_const_params(phi, xx, T, nu1, nu2, m12, m21,
                    gamma1, gamma2, h1, h2, theta0, initial_t,
                    frozen1, frozen2, nomut1, nomut2)
    yy = xx

    nu1_f = Misc.ensure_1arg_func(nu1)
    nu2_f = Misc.ensure_1arg_func(nu2)
    m12_f = Misc.ensure_1arg_func(m12)
    m21_f = Misc.ensure_1arg_func(m21)
    gamma1_f = Misc.ensure_1arg_func(gamma1)
    gamma2_f = Misc.ensure_1arg_func(gamma2)
    h1_f = Misc.ensure_1arg_func(h1)
    h2_f = Misc.ensure_1arg_func(h2)
    theta0_f = Misc.ensure_1arg_func(theta0)

    if cuda_enabled:
        import dadi.cuda
        phi = dadi.cuda.Integration._two_pops_temporal_params(phi, xx, T, initial_t,
                nu1_f, nu2_f, m12_f, m21_f, gamma1_f, gamma2_f, h1_f, h2_f, theta0_f, 
                frozen1, frozen2, nomut1, nomut2, deme_ids)
        return phi

    current_t = initial_t
    nu1,nu2 = nu1_f(current_t), nu2_f(current_t)
    m12,m21 = m12_f(current_t), m21_f(current_t)
    gamma1,gamma2 = gamma1_f(current_t), gamma2_f(current_t)
    h1,h2 = h1_f(current_t), h2_f(current_t)
    dx,dy = numpy.diff(xx),numpy.diff(yy)

    demes_hist = [[0, [nu1,nu2], [m12,m21]]]
    while current_t < T:
        dt = min(_compute_dt(dx,nu1,[m12],gamma1,h1),
                 _compute_dt(dy,nu2,[m21],gamma2,h2))
        this_dt = min(dt, T - current_t)

        next_t = current_t + this_dt

        nu1,nu2 = nu1_f(next_t), nu2_f(next_t)
        m12,m21 = m12_f(next_t), m21_f(next_t)
        gamma1,gamma2 = gamma1_f(next_t), gamma2_f(next_t)
        h1,h2 = h1_f(next_t), h2_f(next_t)
        theta0 = theta0_f(next_t)
        demes_hist.append([next_t, [nu1,nu2], [m12,m21]])

        if numpy.any(numpy.less([T,nu1,nu2,m12,m21,theta0], 0)):
            raise ValueError('A time, population size, migration rate, or '
                             'theta0 is < 0. Has the model been mis-specified?')
        if numpy.any(numpy.equal([nu1,nu2], 0)):
            raise ValueError('A population size is 0. Has the model been '
                             'mis-specified?')

        _inject_mutations_2D(phi, this_dt, xx, yy, theta0, frozen1, frozen2,
                             nomut1, nomut2)
        if not frozen1:
            phi = int_c.implicit_2Dx(phi, xx, yy, nu1, m12, gamma1, h1,
                                     this_dt, use_delj_trick)
        if not frozen2:
            phi = int_c.implicit_2Dy(phi, xx, yy, nu2, m21, gamma2, h2,
                                     this_dt, use_delj_trick)

        current_t = next_t
    Demes.cache.append(Demes.IntegrationNonConst(history = demes_hist, deme_ids=deme_ids))
    return phi