# Source code for moments.Demographics1D

```
"""
Single-population demographic models.
"""
import numpy
import moments
[docs]def snm(ns, pop_ids=None):
"""
Standard neutral model with theta=1.
:param ns: Number of samples in resulting Spectrum. Must be a list
of length one.
:param pop_ids: Optional list of length one specifying the population ID.
"""
if pop_ids is not None and len(pop_ids) != 1:
raise ValueError("pop_ids must have length 1")
sts = moments.LinearSystem_1D.steady_state_1D(ns[0])
fs = moments.Spectrum(sts, pop_ids=pop_ids)
return fs
[docs]def two_epoch(params, ns, pop_ids=None):
"""
Instantaneous size change some time ago.
params = (nu, T)
:param params: Tuple of length two, specifying (nu, T).
- nu: the ratio of contemporary to ancient population size.
- T: the time in the past at which size change happened
(in units of 2*Ne generations).
:param ns: Number of samples in resulting Spectrum. Must be a list of
length one.
:param pop_ids: Optional list of length one specifying the population ID.
"""
if pop_ids is not None and len(pop_ids) != 1:
raise ValueError("pop_ids must have length 1")
nu, T = params
sts = moments.LinearSystem_1D.steady_state_1D(ns[0])
fs = moments.Spectrum(sts, pop_ids=pop_ids)
fs.integrate([nu], T)
return fs
[docs]def growth(params, ns, pop_ids=None):
"""
Exponential growth beginning some time ago.
params = (nu, T)
:param params: Tupe of length two, specifying (nu, t).
- nu: the final population size.
- T: the time in the past at which growth began
(in units of 2*Ne generations).
:param ns: Number of samples in resulting Spectrum. Must be a list of
length one.
:param pop_ids: Optional list of length one specifying the population ID.
"""
if pop_ids is not None and len(pop_ids) != 1:
raise ValueError("pop_ids must have length 1")
nu, T = params
nu_func = lambda t: [numpy.exp(numpy.log(nu) * t / T)]
sts = moments.LinearSystem_1D.steady_state_1D(ns[0])
fs = moments.Spectrum(sts, pop_ids=pop_ids)
fs.integrate(nu_func, T, 0.01)
return fs
[docs]def bottlegrowth(params, ns, pop_ids=None):
"""
Instantanous size change followed by exponential growth.
params = (nuB, nuF, T)
:param params: Tuple of length three specifying (nuB, nuF, T).
- 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).
:param ns: Number of samples in resulting Spectrum.
:param pop_ids: Optional list of length one specifying the population ID.
"""
if pop_ids is not None and len(pop_ids) != 1:
raise ValueError("pop_ids must have length 1")
nuB, nuF, T = params
nu_func = lambda t: [nuB * numpy.exp(numpy.log(nuF / nuB) * t / T)]
sts = moments.LinearSystem_1D.steady_state_1D(ns[0])
fs = moments.Spectrum(sts, pop_ids=pop_ids)
fs.integrate(nu_func, T, 0.01)
return fs
[docs]def three_epoch(params, ns, pop_ids=None):
"""
Three epoch model of constant sizes.
params = (nuB, nuF, TB, TF)
:param params: Tuple of length four specifying (nuB, nuF, TB, TF).
- 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).
:param ns: Number of samples in resulting Spectrum.
:param pop_ids: Optional list of length one specifying the population ID.
"""
if pop_ids is not None and len(pop_ids) != 1:
raise ValueError("pop_ids must have length 1")
nuB, nuF, TB, TF = params
sts = moments.LinearSystem_1D.steady_state_1D(ns[0])
fs = moments.Spectrum(sts, pop_ids=pop_ids)
fs.integrate([nuB], TB, 0.01)
fs.integrate([nuF], TF, 0.01)
return fs
```