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 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 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 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 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 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 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 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
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 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
#Create python dictionary from snps file
dd = Misc.make_data_dict(snps)
#**************
#pop_ids is a list which should match the populations headers of your SNPs file columns
pop_ids = ["North", "South"]
#**************
#projection sizes, in ALLELES not individuals
proj = [16, 32]
#Convert this dictionary into folded AFS object
#[polarized = False] creates folded spectrum object
fs = Spectrum.from_data_dict(dd,
pop_ids=pop_ids,
projections=proj,
polarized=False)
#print some useful information about the afs or jsfs
print(
"\n\n============================================================================"
)
print("\nData for site frequency spectrum:\n")
print("Projection: {}".format(proj))
print("Sample sizes: {}".format(fs.sample_sizes))
print("Sum of SFS: {}".format(numpy.around(fs.S(), 2)))
print(
"\n============================================================================\n"
)
#================================================================================
def get_godambe(func_ex,
grid_pts,
all_boot,
p0,
data,
eps,
log=False,
just_hess=False,
boot_theta_adjusts=[]):
"""
Godambe information and Hessian matrices
func_ex: Model function
grid_pts: Number of grid points to evaluate the model function
all_boot: List of bootstrap frequency spectra
p0: Best-fit parameters for func_ex.
data: Original data frequency spectrum
eps: Fractional stepsize to use when taking finite-difference derivatives
Note that if eps*param is < 1e-6, then the step size for that parameter
will simply be eps, to avoid numerical issues with small parameter
perturbations.
log: If True, calculate derivatives in terms of log-parameters
just_hess: If True, only evaluate and return the Hessian matrix
boot_theta_adjusts: Factors by which to adjust theta for each bootstrap
sample, relative to full data theta.
"""
ns = data.sample_sizes
if not boot_theta_adjusts:
boot_theta_adjusts = numpy.ones(len(all_boot))
# Cache evaluations of the frequency spectrum inside our hessian/J
# evaluation function
cache = {}
def func(params, data, theta_adjust=1):
key = (tuple(params), tuple(ns), tuple(grid_pts))
if key not in cache:
cache[key] = func_ex(params, ns, grid_pts)
# theta_adjust deals with bootstraps that need different thetas
fs = theta_adjust * cache[key]
return Inference.ll(fs, data)
def log_func(logparams, data, theta_adjust=1):
return func(numpy.exp(logparams), data, theta_adjust)
# First calculate the observed hessian.
# theta_adjust defaults to 1.
if not log:
hess = -get_hess(func, p0, eps, args=[data])
else:
hess = -get_hess(log_func, numpy.log(p0), eps, args=[data])
if just_hess:
return hess
# Now the expectation of J over the bootstrap data
J = numpy.zeros((len(p0), len(p0)))
# cU is a column vector
cU = numpy.zeros((len(p0), 1))
for ii, (boot, theta_adjust) in enumerate(zip(all_boot,
boot_theta_adjusts)):
boot = Spectrum(boot)
if not log:
grad_temp = get_grad(func, p0, eps, args=[boot, theta_adjust])
else:
grad_temp = get_grad(log_func,
numpy.log(p0),
eps,
args=[boot, theta_adjust])
J_temp = numpy.outer(grad_temp, grad_temp)
J = J + J_temp
cU = cU + grad_temp
J = J / len(all_boot)
cU = cU / len(all_boot)
# G = H*J^-1*H
J_inv = numpy.linalg.inv(J)
godambe = numpy.dot(numpy.dot(hess, J_inv), hess)
return godambe, hess, J, cU
def get_godambe(func_ex,
grid_pts,
all_boot,
p0,
data,
eps,
log=False,
just_hess=False):
"""
Godambe information and Hessian matrices
NOTE: Assumes that last parameter in p0 is theta.
func_ex: Model function
grid_pts: Number of grid points to evaluate the model function
all_boot: List of bootstrap frequency spectra
p0: Best-fit parameters for func_ex.
data: Original data frequency spectrum
eps: Fractional stepsize to use when taking finite-difference derivatives
log: If True, calculate derivatives in terms of log-parameters
just_hess: If True, only evaluate and return the Hessian matrix
"""
ns = data.sample_sizes
# Cache evaluations of the frequency spectrum inside our hessian/J
# evaluation function
cache = {}
def func(params, data):
key = (tuple(params), tuple(ns), tuple(grid_pts))
if key not in cache:
cache[key] = func_ex(params, ns, grid_pts)
fs = cache[key]
return Inference.ll(fs, data)
def log_func(logparams, data):
return func(numpy.exp(logparams), data)
# First calculate the observed hessian
if not log:
hess = -get_hess(func, p0, eps, args=[data])
else:
hess = -get_hess(log_func, numpy.log(p0), eps, args=[data])
if just_hess:
return hess
# Now the expectation of J over the bootstrap data
J = numpy.zeros((len(p0), len(p0)))
# cU is a column vector
cU = numpy.zeros((len(p0), 1))
for ii, boot in enumerate(all_boot):
boot = Spectrum(boot)
if not log:
grad_temp = get_grad(func, p0, eps, args=[boot])
else:
grad_temp = get_grad(log_func, numpy.log(p0), eps, args=[boot])
J_temp = numpy.outer(grad_temp, grad_temp)
J = J + J_temp
cU = cU + grad_temp
J = J / len(all_boot)
cU = cU / len(all_boot)
# G = H*J^-1*H
J_inv = numpy.linalg.inv(J)
godambe = numpy.dot(numpy.dot(hess, J_inv), hess)
return godambe, hess, J, cU
"""
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
