# Source code for moments.Demographics2D

```
"""
Two-population demographic models.
"""
import numpy
import moments
[docs]def snm(ns, pop_ids=None):
"""
ns = [n1, n2]
Standard neutral model with a split but no divergence.
:param ns: List of population sizes in first and second populations.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
sts = moments.LinearSystem_1D.steady_state_1D(ns[0] + ns[1])
fs = moments.Spectrum(sts)
fs = moments.Manips.split_1D_to_2D(fs, ns[0], ns[1])
fs.pop_ids = pop_ids
return fs
[docs]def bottlegrowth(params, ns, pop_ids=None):
"""
params = (nuB, nuF, T)
ns = [n1, n2]
Instantanous size change followed by exponential growth with no population
split.
- nuB: Ratio of population size after instantanous change to ancient
population size
- nuF: Ratio of contempoary to ancient population size
- T: Time in the past at which instantaneous change happened and growth began
(in units of 2*Na generations)
- n1, n2: Sample sizes of resulting Spectrum.
:param params: List of parameters, (nuB, nuF, T).
:param ns: List of population sizes in first and second populations.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
nuB, nuF, T = params
return bottlegrowth_split_mig((nuB, nuF, 0, T, 0), ns, pop_ids=pop_ids)
[docs]def bottlegrowth_split(params, ns, pop_ids=None):
"""
params = (nuB, nuF, T, Ts)
ns = [n1, n2]
Instantanous size change followed by exponential growth then split.
- nuB: Ratio of population size after instantanous change to ancient
population size
- nuF: Ratio of contempoary to ancient population size
- T: Time in the past at which instantaneous change happened and growth began
(in units of 2*Na generations)
- Ts: Time in the past at which the two populations split.
- n1, n2: Sample sizes of resulting Spectrum.
:param ns: List of population sizes in first and second populations.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
nuB, nuF, T, Ts = params
return bottlegrowth_split_mig((nuB, nuF, 0.0, T, Ts), ns, pop_ids=pop_ids)
[docs]def bottlegrowth_split_mig(params, ns, pop_ids=None):
"""
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.
:param ns: List of population sizes in first and second populations.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
nuB, nuF, m, T, Ts = params
nu_func = lambda t: [nuB * numpy.exp(numpy.log(nuF / nuB) * t / T)]
sts = moments.LinearSystem_1D.steady_state_1D(ns[0] + ns[1])
fs = moments.Spectrum(sts)
fs.integrate(nu_func, T - Ts, dt_fac=0.01)
# we split the population
fs = moments.Manips.split_1D_to_2D(fs, ns[0], ns[1])
nu0 = nu_func(T - Ts)[0]
nu_func = lambda t: 2 * [nu0 * numpy.exp(numpy.log(nuF / nu0) * t / Ts)]
fs.integrate(nu_func, Ts, m=numpy.array([[0, m], [m, 0]]))
fs.pop_ids = pop_ids
return fs
[docs]def split_mig(params, ns, pop_ids=None):
"""
Split into two populations of specifed size, with migration.
params = (nu1, nu2, T, m)
ns = [n1, n2]
:param params: Tuple of length 4.
- 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)
:param ns: List of length two specifying sample sizes n1 and n2.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
nu1, nu2, T, m = params
sts = moments.LinearSystem_1D.steady_state_1D(ns[0] + ns[1])
fs = moments.Spectrum(sts)
fs = moments.Manips.split_1D_to_2D(fs, ns[0], ns[1])
fs.integrate([nu1, nu2], T, m=numpy.array([[0, m], [m, 0]]))
fs.pop_ids = pop_ids
return fs
[docs]def IM(params, ns, pop_ids=None):
"""
Isolation-with-migration model with exponential pop growth.
params = (s, nu1, nu2, T, m12, m21)
ns = [n1, n2]
:param params: Tuple of length 6.
- 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
:param ns: List of population sizes in first and second populations.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
s, nu1, nu2, T, m12, m21 = params
sts = moments.LinearSystem_1D.steady_state_1D(ns[0] + ns[1])
fs = moments.Spectrum(sts)
fs = moments.Manips.split_1D_to_2D(fs, ns[0], ns[1])
nu1_func = lambda t: s * (nu1 / s) ** (t / T)
nu2_func = lambda t: (1 - s) * (nu2 / (1 - s)) ** (t / T)
nu_func = lambda t: [nu1_func(t), nu2_func(t)]
fs.integrate(nu_func, T, dt_fac=0.01, m=numpy.array([[0, m12], [m21, 0]]))
fs.pop_ids = pop_ids
return fs
[docs]def IM_pre(params, ns, pop_ids=None):
"""
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.
:param ns: List of population sizes in first and second populations.
:param pop_ids: List of population IDs.
"""
if pop_ids is not None and len(pop_ids) != 2:
raise ValueError("pop_ids must be a list of two population IDs")
nuPre, TPre, s, nu1, nu2, T, m12, m21 = params
sts = moments.LinearSystem_1D.steady_state_1D(ns[0] + ns[1])
fs = moments.Spectrum(sts)
fs.integrate([nuPre], TPre, dt_fac=0.01)
fs = moments.Manips.split_1D_to_2D(fs, ns[0], ns[1])
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)
nu_func = lambda t: [nu1_func(t), nu2_func(t)]
fs.integrate(nu_func, T, dt_fac=0.01, m=numpy.array([[0, m12], [m21, 0]]))
fs.pop_ids = pop_ids
return fs
```