def No_mig(params, ns, pts):
"""
params = (nuPre,TPre,s,nu1,nu2,T)
ns = (n1,n2)
Isolation-with-migration model with exponential pop growth and a size change
prior to split.
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)
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
nuPre, TPre, s, nu1, nu2, T = 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=0, m21=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def CMG(params, ns, pts):
nu1, nu2, b1, b2, m, T = params
"""
Model with migration during the divergence.
nu1: Size of population 1 after split.
nu2: Size of population 2 after split.
b: Population growth coefficient
m: Migration rate between populations (2*Na*m)
T: The scaled time between the split (in units of 2*Na generations).
"""
# Define the grid we'll use
xx = Numerics.default_grid(pts)
# phi for the equilibrium ancestral population
phi = PhiManip.phi_1D(xx)
# Now do the divergence event
phi = PhiManip.phi_1D_to_2D(xx, phi)
# We start the population size change after the split and set the migration rates to m12 and m21
bnu1_func = lambda t: nu1 * b1**(t / T)
bnu2_func = lambda t: nu2 * b2**(t / T)
phi = Integration.two_pops(phi, xx, T, bnu1_func, bnu2_func, m12=m, m21=m)
###
## Finally, calculate the spectrum.
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def ancmig_adj_2(params, ns, pts):
"""
Model with split between pop 1 and (2,3), with gene flow. Split
between pops 2 and 3, and all gene flow ceases.
shorter isolation
"""
#7 parameters
nu1, nuA, nu2, nu3, mA, 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=nu1, nu2=nuA, m12=mA, m21=mA)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=0,
m21=0,
m23=0,
m32=0,
m13=0,
m31=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def split_symmig_all(params, ns, pts):
"""
Model with split between pop 1 and (2,3), then split between 2 and 3.
Migration is symmetrical between all population pairs (ie 1<->2, 2<->3, and 1<->3).
"""
#10 parameters
nu1, nuA, nu2, nu3, mA, m1, m2, m3, 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=nu1, nu2=nuA, m12=mA, m21=mA)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=m1,
m21=m1,
m23=m2,
m32=m2,
m13=m3,
m31=m3)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def refugia_adj_3(params, ns, pts):
"""
Model with split between pop 1 and (2,3), gene flow does not occur, but then
secondary contact occurs. Split between pops 2 and 3 occurs with gene flow, and gene flow
happens between 1 and 2 as well.
shortest isolation
"""
#10 parameters
nu1, nuA, nu2, nu3, mA, m1, m2, T1a, T1b, 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, T1a, nu1=nu1, nu2=nuA, m12=0, m21=0)
phi = Integration.two_pops(phi, xx, T1b, nu1=nu1, nu2=nuA, m12=mA, m21=mA)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=m1,
m21=m1,
m23=m2,
m32=m2,
m13=0,
m31=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def ancmig_adj_3(params, ns, pts):
"""
Model with split between pop 1 and (2,3), with gene flow, which then stops. Split
between pops 2 and 3, gene flow does not occur at all.
longest isolation
"""
#8 parameters
nu1, nuA, nu2, nu3, mA, T1a, T1b, 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, T1a, nu1=nu1, nu2=nuA, m12=mA, m21=mA)
phi = Integration.two_pops(phi, xx, T1b, nu1=nu1, nu2=nuA, m12=0, m21=0)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=0,
m21=0,
m23=0,
m32=0,
m13=0,
m31=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def refugia_adj_2(params, ns, pts):
"""
Model with split between pop 1 and (2,3), gene flow does not occur. Split between pops
2 and 3, with gene flow. After appearance of 2 and 3, gene flow also occurs between 1
and 2.
shorter isolation
"""
#8 parameters
nu1, nuA, nu2, nu3, 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=nu1, nu2=nuA, m12=0, m21=0)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=m1,
m21=m1,
m23=m2,
m32=m2,
m13=0,
m31=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def split_nomig(params, ns, pts):
"""
Model with split between pop 1 and (2,3), then split between 2 and 3.
Migration does not occur between any population pair.
"""
#6 parameters
nu1, nuA, nu2, nu3, 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=nu1, nu2=nuA, m12=0, m21=0)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=0,
m21=0,
m23=0,
m32=0,
m13=0,
m31=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def split_ancient_symmig_size(params, ns, pts):
"""
Model with split and no gene flow, followed by period of size change and symmetrical gene flow.
nu1b: Size of population 1 after split.
nu2b: Size of population 2 after split.
T1: Time in the past of split (in units of 2*Na generations)
nu1r: Size of population 1 after time interval.
nu2r: Size of population 2 after time interval.
T2: The scale time between the ancient migration and present.
m: Migration between pop 2 and pop 1.
ns: Size of fs to generate.
pts: Number of points to use in grid for evaluation.
"""
nu1b, nu2b, nu1r, nu2r, T1, T2, 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, T1, nu1b, nu2b, m12=m, m21=m)
phi = Integration.two_pops(phi, xx, T2, nu1r, nu2r, m12=0, m21=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def split_secondary_contact_sym_size(params, ns, pts):
"""
Model with split, complete isolation, followed by secondary contact with asymmetrical gene flow
nu1b: Size of population 1 after split.
nu2b: Size of population 2 after split.
T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).
nu1r: Size of population 1 after time interval.
nu2r: Size of population 2 after time interval.
T2: The scale time between the secondary contact and present.
m: Migration between pop 2 and pop 1.
ns: Size of fs to generate.
pts: Number of points to use in grid for evaluation.
"""
nu1b, nu2b, nu1r, nu2r, T1, T2, 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, T1, nu1b, nu2b, m12=0, m21=0)
phi = Integration.two_pops(phi, xx, T2, nu1r, nu2r, m12=m, m21=m)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def split_no_mig_size(params, ns, pts):
"""
params = (nu1b,nu2b,nu1r,nu2r,T1,T2)
ns = (n1,n2)
Split into two populations of specifed size, with no migration, period of size change and no migration.
nu1b: Size of population 1 after split.
nu2b: Size of population 2 after split.
T1: Time in the past of split (in units of 2*Na generations)
nu1r: Size of population 1 after time interval.
nu2r: Size of population 2 after time interval.
T2: Time of population size change.
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
nu1b, nu2b, nu1r, nu2r, 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, nu1b, nu2b, m12=0, m21=0)
phi = Integration.two_pops(phi, xx, T2, nu1r, nu2r, m12=0, m21=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def split_secondary_contact_sym(params, ns, pts):
"""
Model with split and no gene flow, followed by period of no size change and symmetrical gene flow
nu1: Size of population 1 after split.
nu2: Size of population 2 after split.
m: Migration between pop 2 and pop 1.
T: The scaled time between the split and the secondary contact (in units of 2*Na generations).
Tsc: The scale time between the secondary contact and present.
ns: Size of fs to generate.
pts: Number of points to use in grid for evaluation.
"""
nu1, nu2, m, T, Tsc = 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)
phi = Integration.two_pops(phi, xx, Tsc, nu1, nu2, m12=m, m21=m)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def split_mig(params, ns, pts):
"""
params = (nu1,nu2,T,m)
ns = (n1,n2)
Split into two populations of specifed size, with migration.
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)
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
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
def split_symmig_adjacent(params, ns, pts):
"""
Model with split between pop 1 and (2,3), then split between 2 and 3. Assume 2 occurs
in between populations 1 and 3, which do not come in to contact with one another.
Migration is symmetrical between 'adjacent' population pairs (ie 1<->2, 2<->3, but not 1<->3).
"""
#9 parameters
nu1, nuA, nu2, nu3, mA, 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=nu1, nu2=nuA, m12=mA, m21=mA)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
phi = Integration.three_pops(phi,
xx,
T2,
nu1=nu1,
nu2=nu2,
nu3=nu3,
m12=m1,
m21=m1,
m23=m2,
m32=m2,
m13=0,
m31=0)
fs = Spectrum.from_phi(phi, ns, (xx, xx, xx))
return fs
def priorsize_asym_mig(params, ns, pts):
"""
Size change followed by split with asymmetric migration
nua: First Size of population before split.
T1: Duration of first time before split
nu1b: Size of population 1 after split.
nu2b: Size of population 2 after split.
T2: Time in the past of split (units of 2*Na generations)
m12: Migration from pop 2 to pop 1 (2*Na*m12)
m21: Migration from pop 1 to pop 2
"""
nua, T1,nu1b, nu2b, T2, m12, m21 = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = Integration.one_pop(phi, xx, T1, nua)
phi = PhiManip.phi_1D_to_2D(xx, phi)
phi = Integration.two_pops(phi, xx, T2, nu1b, nu2b, m12=m12, m21=m21)
fs = Spectrum.from_phi(phi, ns, (xx,xx))
return fs
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.
nu1a: Size of population 1 after split.
nu2a: Size of population 2 after split.
T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).
nu1b: Size of population 1 after time interval.
nu2b: Size of population 2 after time interval.
T2: The scale time between the secondary contact and isolation.
T3: The scaled time between the isolation and present.
m12: Migration from pop 2 to pop 1 (2*Na*m12).
m21: Migration from pop 1 to pop 2.
"""
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
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 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.
m12: Migration from pop 2 to pop 1 (2*Na*m12).
m21: Migration from pop 1 to pop 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.
"""
nuA, nu1, nu2, m12, m21, T1, T2, s = 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 = Integration.two_pops(phi, xx, T2, nu1, nu2, m12=m12, m21=m21)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def isolation_asym_mig_base(nu1a, nu2a, T1,nu1b, nu2b, T2, m12, m21, ns, pts):
"""
Split followed by two size changes with continuous asymmetric migration
nu1a: Size of population 1 after split in first time interval.
nu2a: Size of population 2 after split.
T1: First time interval after split (units of 2*Na generations)
nu1b: Size of population 1 after split in second time interval.
nu2b: Size of population 2 after split.
T2: Second time interval after split (units of 2*Na generations)
m12: Migration from pop 2 to pop 1 (2*Na*m12)
m21: Migration from pop 1 to pop 2
"""
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
def simple_iso(params, ns, pts):
"""
params = (nuPre,TPre,nu1,nu2,T)
ns = (n1,n2)
Simple migration model, the population size is constant
nuPre: Size after first size change
TPre: Time before split of first size change.
nu1: size of pop 1.
nu2: size of pop 2.
T1: Time from divergence to migration end (in units of 2*Na generations)
T2: Time from migration end to present
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
nuPre,TPre,nu1,nu2,T = 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, T, nu1, nu2, m12=0, m21=0)
fs = Spectrum.from_phi(phi, ns, (xx,xx))
return fs
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 IM(params, ns, pts):
"""
ns = (n1,n2)
params = (s,nu1,nu2,T,m12,m21)
Isolation-with-migration model with exponential pop growth.
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
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
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
def sec_contact_sym_mig_size(params, ns, pts):
"""
Split with no gene flow, followed by size change with symmetrical gene flow.
nu1a: Size of population 1 after split.
nu2a: Size of population 2 after split.
T1: The scaled time between the split and the secondary contact (in units of 2*Na generations).
nu1b: Size of population 1 after time interval.
nu2b: Size of population 2 after time interval.
T2: The scale time between the secondary contact and present.
m: Migration between pop 2 and pop 1.
"""
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
def sec_contact_sym_mig_three_epoch(params, ns, pts):
"""
Split with no gene flow, followed by period of symmetrical gene flow, then isolation.
nu1: Size of population 1 after split.
nu2: Size of population 2 after split.
m: Migration between pop 2 and pop 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.
"""
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
def asym_mig_size(params, ns, pts):
"""
Split with different migration rates, then size change with different migration rates.
nu1a: Size of population 1 after split.
nu2a: Size of population 2 after split.
T1: Time in the past of split (in units of 2*Na generations)
nu1b: Size of population 1 after time interval.
nu2b: Size of population 2 after time interval.
T2: Time of population size change.
m12: Migration from pop 2 to pop 1 (2*Na*m12)
m21: Migration from pop 1 to pop 2
"""
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
def anc_asym_mig_size(params, ns, pts):
"""
Split with asymmetrical gene flow, followed by size change with no gene flow.
nu1a: Size of population 1 after split.
nu2a: Size of population 2 after split.
T1: Time in the past of split (in units of 2*Na generations)
nu1b: Size of population 1 after time interval.
nu2b: Size of population 2 after time interval.
T2: The scale time between the ancient migration and present.
m12: Migration from pop 2 to pop 1 (2*Na*m12).
m21: Migration from pop 1 to pop 2.
"""
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
def founder_asym(params, ns, pts):
"""
Split into two populations, with two migration rates. 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.
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
"""
nuA, nu1, nu2, m12, m21, T, s = 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 / T)
#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, T, nu1, nu2_func, m12=m12, m21=m21)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def sym_mig_size(params, ns, pts):
"""
Split with symmetric migration, then size change with symmetric migration.
nu1a: Size of population 1 after split.
nu2a: Size of population 2 after split.
T1: Time in the past of split (in units of 2*Na generations)
nu1b: Size of population 1 after time interval.
nu2b: Size of population 2 after time interval.
T2: Time of population size change.
m: Migration rate between populations (2*Na*m)
"""
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
def IM(params, ns, pts):
"""
ns = (n1,n2)
params = (s,nu1,nu2,T,m12,m21)
Isolation-with-migration model with exponential pop growth.
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
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
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
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 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 split_mig(params, ns, pts):
"""
params = (nu1,nu2,T,m)
ns = (n1,n2)
Split into two populations of specifed size, with migration.
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)
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
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
def bottlegrowth_split_mig(params, ns, pts):
"""
params = (nuB,nuF,m,T,Ts)
ns = (n1,n2)
Instantanous size change followed by exponential growth then split with
migration.
nuB: Ratio of population size after instantanous change to ancient
population size
nuF: Ratio of contempoary 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.
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
nuB, nuF, m, T, Ts = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
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)
fs = Spectrum.from_phi(phi, ns, (xx, xx))
return fs
def bottlegrowth_split_mig(params, ns, pts):
"""
params = (nuB,nuF,m,T,Ts)
ns = (n1,n2)
Instantanous size change followed by exponential growth then split with
migration.
nuB: Ratio of population size after instantanous change to ancient
population size
nuF: Ratio of contempoary 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.
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
nuB,nuF,m,T,Ts = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
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)
fs = Spectrum.from_phi(phi, ns, (xx,xx))
return fs
def snm2(notused, ns, pts):
"""
ns = (n1,n2)
Standard neutral model, populations never diverge.
"""
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
def bottlegrowth(params, ns, pts):
"""
Instantanous size change followed by exponential growth.
params = (nuB,nuF,T)
ns = (n1,)
nuB: Ratio of population size after instantanous 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)
n1: Number of samples in resulting Spectrum
pts: Number of grid points to use in integration.
"""
nuB,nuF,T = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
nu_func = lambda t: nuB*numpy.exp(numpy.log(nuF/nuB) * t/T)
phi = Integration.one_pop(phi, xx, T, nu_func)
fs = Spectrum.from_phi(phi, ns, (xx,))
return fs
def bottleneck_1d(params, n1, pts):
nuC, T = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = Integration.one_pop(phi, xx, T, nuC)
model_sfs = Spectrum.from_phi(phi, n1, (xx,))
return model_sfs
def snm(notused, ns, pts):
"""
Standard neutral model.
ns = (n1,)
n1: Number of samples in resulting Spectrum
pts: Number of grid points to use in integration.
"""
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
fs = Spectrum.from_phi(phi, ns, (xx,))
return fs
def IM_pre(params, ns, pts):
"""
params = (nuPre,TPre,s,nu1,nu2,T,m12,m21)
ns = (n1,n2)
Isolation-with-migration model with exponential pop growth and a size change
prior to split.
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
n1,n2: Sample sizes of resulting Spectrum
pts: Number of grid points to use in integration.
"""
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
def two_epoch(params, ns, pts):
"""
Instantaneous size change some time ago.
params = (nu,T)
ns = (n1,)
nu: Ratio of contemporary to ancient population size
T: Time in the past at which size change happened (in units of 2*Na
generations)
n1: Number of samples in resulting Spectrum
pts: Number of grid points to use in integration.
"""
nu,T = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = Integration.one_pop(phi, xx, T, nu)
fs = Spectrum.from_phi(phi, ns, (xx,))
return fs
def growth(params, ns, pts):
"""
Exponential growth beginning some time ago.
params = (nu,T)
ns = (n1,)
nu: Ratio of contemporary to ancient population size
T: Time in the past at which growth began (in units of 2*Na
generations)
n1: Number of samples in resulting Spectrum
pts: Number of grid points to use in integration.
"""
nu,T = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
nu_func = lambda t: numpy.exp(numpy.log(nu) * t/T)
phi = Integration.one_pop(phi, xx, T, nu_func)
fs = Spectrum.from_phi(phi, ns, (xx,))
return fs
def three_epoch(params, ns, pts):
"""
params = (nuB,nuF,TB,TF)
ns = (n1,)
nuB: Ratio of bottleneck population size to ancient pop size
nuF: Ratio of contemporary to ancient pop size
TB: Length of bottleneck (in units of 2*Na generations)
TF: Time since bottleneck recovery (in units of 2*Na generations)
n1: Number of samples in resulting Spectrum
pts: Number of grid points to use in integration.
"""
nuB,nuF,TB,TF = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = Integration.one_pop(phi, xx, TB, nuB)
phi = Integration.one_pop(phi, xx, TF, nuF)
fs = Spectrum.from_phi(phi, ns, (xx,))
return fs
"""
Dadi demographic models for WY and CO populations of E. gillettii.
"""
import numpy
from dadi import Numerics, PhiManip, Integration
from dadi.Spectrum_mod import Spectrum
#one ancestral population splits at time T ago with no migration
def bottleneck_split(params, (n1,n2), pts):
nuW, nuC, 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, nuW, nuC)
model_sfs = Spectrum.from_phi(phi, (n1,n2), (xx,xx))
return model_sfs
#one dimensional demographic inference of bottlneck size and timing
def bottleneck_1d(params, n1, pts):
nuC, T = params
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = Integration.one_pop(phi, xx, T, nuC)
model_sfs = Spectrum.from_phi(phi, n1, (xx,))
return model_sfs
import numpy
from dadi import Numerics, PhiManip, Integration, Spectrum
def OutOfAfrica((nuAf, nuB, nuEu0, nuEu, nuAs0, nuAs,
mAfB, mAfEu, mAfAs, mEuAs, TAf, TB, TEuAs), (n1,n2,n3), pts):
xx = Numerics.default_grid(pts)
phi = PhiManip.phi_1D(xx)
phi = Integration.one_pop(phi, xx, TAf, nu=nuAf)
phi = PhiManip.phi_1D_to_2D(xx, phi)
phi = Integration.two_pops(phi, xx, TB, nu1=nuAf, nu2=nuB,
m12=mAfB, m21=mAfB)
phi = PhiManip.phi_2D_to_3D_split_2(xx, phi)
nuEu_func = lambda t: nuEu0*(nuEu/nuEu0)**(t/TEuAs)
nuAs_func = lambda t: nuAs0*(nuAs/nuAs0)**(t/TEuAs)
phi = Integration.three_pops(phi, xx, TEuAs, nu1=nuAf,
nu2=nuEu_func, nu3=nuAs_func,
m12=mAfEu, m13=mAfAs, m21=mAfEu, m23=mEuAs,
m31=mAfAs, m32=mEuAs)
fs = Spectrum.from_phi(phi, (n1,n2,n3), (xx,xx,xx))
return fs
def OutOfAfrica_mscore((nuAf, nuB, nuEu0, nuEu, nuAs0, nuAs,
mAfB, mAfEu, mAfAs, mEuAs, TAf, TB, TEuAs)):
alphaEu = numpy.log(nuEu/nuEu0)/TEuAs
alphaAs = numpy.log(nuAs/nuAs0)/TEuAs