def vic_two_epoch_admix(params, ns, pts):
"""
Split with no gene flow, followed by no migration but a discrete admixture
event from pop 1 into pop 2 occurs. Populations are fractions of ancient population, where population 2 is
represented by nuA*(s), and population 1 is represented by nuA*(1-s).
nuA: Ancient population size
s: Fraction of nuA that goes to pop2. (Pop 1 has size nuA*(1-s).)
nu1: Size of population 1 after split.
nu2: Size of population 2 after split.
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.
f: Fraction of updated population 2 to be derived from population 1.
"""
nuA, nu1, nu2, T1, T2, s, f = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = PhiManip.phi_1D_to_2D(xx, phi)
nu1 = nuA * (1 - s)
nu2 = nuA * s
phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=0, m21=0)
phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)
phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=0, m21=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def founder_nomig_admix_two_epoch(params, ns, pts):
"""
Split into two populations, with no migration. Populations are fractions of ancient
population, where population 2 is represented by nuA*(s), and population 1 is represented by nuA*(1-s).
Population two undergoes an exponential growth event, while population one is constant.
nuA: Ancient population size
s: Fraction of nuA that goes to pop2. (Pop 1 has size nuA*(1-s).)
nu1: Final size of pop 1.
nu2: Final size of pop 2.
T1: Time in the past of split (in units of 2*Na generations)
T2: The scaled time between the admixture event and present.
f: Fraction of updated population 2 to be derived from population 1.
"""
nuA, nu1, nu2, T1, T2, s, f = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx, nu=nuA)
phi = PhiManip.phi_1D_to_2D(xx, phi)
nu1 = nuA * (1 - s)
nu2_0 = nuA * s
nu2_func = lambda t: nu2_0 * (nu2 / nu2_0)**(t / T1)
#note, the nu2_0 can be eliminated and the function can appear as:
#nu2_func = lambda t: (nuA*(1-s)) * (nu2/(nuA*(1-s)))**(t/T)
phi = Integration.two_pops(phi, xx, T1, nu1, 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, nu2, m12=0, m21=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def vic_no_mig_admix_late(params, ns, pts):
"""
Split into two populations, no migration but a discrete admixture event from pop 1 into
pop 2 occurs. Populations are fractions of ancient population, where population 2 is
represented by nuA*(s), and population 1 is represented by nuA*(1-s).
nuA: Ancient population size
s: Fraction of nuA that goes to pop2. (Pop 1 has size nuA*(1-s).)
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)
f: Fraction of updated population 2 to be derived from population 1.
"""
nuA, nu1, nu2, T, s, f = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = PhiManip.phi_1D_to_2D(xx, phi)
nu1 = nuA * (1 - s)
nu2 = nuA * s
phi = Integration.two_pops(phi, xx, T, nu1, nu2, 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
def vic_two_epoch_admix(params, ns, pts):
"""
Split into two populations, no migration but a discrete admixture event from pop 1 into
pop 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.
params = 4
s: Fraction of Nref that goes to pop2. Pop2 size = s. Pop 1 size = 1-s.
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.
f: Fraction of updated population 2 to be derived from population 1.
"""
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
def vic_no_mig_admix_late(params, ns, pts):
"""
Split into two populations, no migration but a discrete admixture event from pop 1 into
pop 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.
params = 3
s: Fraction of Nref that goes to pop2. Pop2 size = s. Pop 1 size = 1-s.
T: Time in the past of split (in units of 2*Na generations)
f: Fraction of updated population 2 to be derived from population 1.
"""
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
def custom_model(params, ns, pts):
nuPre, TPre, nu1, nu2, T1, T2, m12, m21, f = 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)
phi = Integration.two_pops(phi, xx, T1, nu1, nu2, m12=m12, m21=m21)
phi = PhiManip.phi_2D_admix_1_into_2(phi, f, xx, xx)
phi = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m12, m21=m21)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def founder_nomig_admix_two_epoch(params, ns, pts):
"""
Split into two populations, no migration but a discrete admixture event from pop 1 into
pop 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 two undergoes an exponential growth event to obtain size nu2, while
population one is constant. Admixture occurs after size nu2 is achieved. Nref implicitly has size = 1.
params = 5
s: Fraction of Nref that goes to pop2. Pop2 size = s. Pop 1 size = 1-s.
nu2: Final size of pop 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.
f: Fraction of updated population 2 to be derived from population 1.
"""
nu2, T1, T2, s, f = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = PhiManip.phi_1D_to_2D(xx, phi)
nu2_func = lambda t: 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
