Tracking mutations over time

Tracking mutations over time#

Note

This section makes use of keyword-only arguments to fwdpy11.evolvets. Many of those arguments are somewhat experimental in nature.

This recipe covers tracking the frequencies of all mutations over time during a simulation using a time series recorder. Such tracking requires care, as it is not a common use case. Internally, fwdpy11 doesn’t really care about how often each mutation is present in the population. Usually, the simulation only needs to know if a mutation was removed by simplification, or remains somewhere in the ancestry of the population. Therefore, to track frequencies, we need to work a little harder.

The following listing shows how we will track frequencies. The key elements are:

We initialize instances of the recorder with a “burn-in” time. We do not do anything until the population’s generation is greater than that value. This check allows us to more quickly simulate to equilibrium, which we’ll explain in more detail below.
We record trajectories in a Python dictionary. The key will be tuples of (origin time, position, effect size). The value will be the count of the mutation each generation.
We take special care to not record the count of a fixation over and over again.

import typing
import attr
import fwdpy11


@attr.s(auto_attribs=True)
class PyFreqTracker(object):
    burnin_time: int
    trajectories: typing.Dict = attr.ib(default=attr.Factory(dict))

    def __call__(
        self, pop: fwdpy11.DiploidPopulation, sampler: fwdpy11.SampleRecorder
    ) -> None:
        if pop.generation > self.burnin_time:
            for c, m in zip(pop.mcounts, pop.mutations):
                if c > 0 and c <= 2 * pop.N:
                    k = (m.g, m.pos, m.s)
                    if k in self.trajectories:
                        # Make sure that we only record a fixation once.
                        if self.trajectories[k][-1] < 2 * pop.N:
                            self.trajectories[k].append(c)
                    else:
                        self.trajectories[k] = [c]

Now, let’s simulate a model of a high rate of recurrent hitch-hiking:

pdict = {
    "nregions": [],
    "sregions": [fwdpy11.ExpS(beg=0, end=1, weight=1, mean=0.2)],
    "recregions": [fwdpy11.PoissonInterval(0, 1, 1e-2)],
    "gvalue": [fwdpy11.Multiplicative(2.0)],
    "demography": fwdpy11.ForwardDemesGraph.tubes([100], burnin=100, burnin_is_exact=True),
    "rates": (0.0, 1e-3, None),
    "simlen": 100,
}
params = fwdpy11.ModelParams(**pdict)
pop = fwdpy11.DiploidPopulation(100, 1.0)
rng = fwdpy11.GSLrng(42)
recorder = PyFreqTracker(0)
fwdpy11.evolvets(
    rng,
    pop,
    params,
    10,
    recorder,
    track_mutation_counts=True,
    suppress_table_indexing=False,
)

The arguments to fwdpy11.evolvets need some explanation. We simplify every 10 generations. Setting track_mutation_counts=True tells the function to obtain mutation counts from diploid genomes every generation. Setting suppress_table_indexing=False tells fwdpy11 to index the tables after every simplification event. In generations when simplification occurs, mutation counts are obtained from trees and not from genomes.

Note

The current default behavior of fwdpy11.evolvets is to set suppress_table_indexing=False. However, future releases will likely set that to True. This recipe is written in anticipation of that change.

Converting trajectories to data frames#

We can easily do a lot of analysis from recorder.trajectories. However, there are good reasons to convert things into common formats for analysis, such as the pandas data frame:

import typing

import numpy as np
import pandas as pd


def traj2df(trajectories: typing.Dict, N: int) -> pd.DataFrame:
    dfs = []
    for key, value in trajectories.items():
        df = pd.DataFrame(
            {
                "generation": np.arange(len(value), dtype=np.uint32) + key[0],
                "frequency": np.array(value) / (2 * N),
                "origin_time": [key[0]] * len(value),
                "position": [key[1]] * len(value),
                "effect_size": [key[2]] * len(value),
            }
        )
        dfs.append(df)
    return pd.concat(dfs)

Plotting the trajectories#

Here is a function to plot all trajectories, eliminating those with sojourn times \(< minlen\) generations.

import matplotlib.pyplot as plt

def plot_traj_df(
    df: pd.DataFrame, *, minlen: int, selected_alpha=1.0, neutral_alpha=1.0
) -> typing.Tuple:
    if minlen < 0:
        raise ValueError(f"minlen must be non-negative, got {minlen}")
    f, ax = plt.subplots()
    for n, g in df.groupby(["origin_time", "position", "effect_size"]):
        if len(g.index) >= minlen:
            if g.effect_size[0] == 0.0:
                ax.plot(g.generation, g.frequency, linestyle="--", alpha=neutral_alpha)
            else:
                ax.plot(g.generation, g.frequency, alpha=selected_alpha)
    ax.set_xlabel("Time (generation)")
    ax.set_ylabel("Frequency")

    return f, ax

../_images/a8a3d727fcbcd3113abc9921c76d2b94f3bf10ac7e41e7b7b91cdb548095b4a6.png — Fig. 1 Some sweeps from new mutations.#

Tracking the frequencies of neutral mutations#

One generally doesn’t simulate neutral mutations. However, certain questions regarding linked selection may force you to do so. Neutral mutations do not get added to diploid genomes (in order to save memory), and thus will their counts are not obtained via track_mutation_counts=True. The solution is:

Simplify every generation, so that counts can be obtained from the trees.

pdict = {
    # Add a region for neutral mutations:
    "nregions": [fwdpy11.Region(0, 1, 1)],
    "sregions": [fwdpy11.ExpS(beg=0, end=1, weight=1, mean=0.2)],
    "recregions": [fwdpy11.PoissonInterval(0, 1, 1e-2)],
    "gvalue": [fwdpy11.Multiplicative(2.0)],
    "demography": fwdpy11.ForwardDemesGraph.tubes([100], burnin=100, burnin_is_exact=True),
    # Add a mutation rate for neutral mutations:
    "rates": (5e-3, 1e-3, None),
    "simlen": 100,
}
params = fwdpy11.ModelParams(**pdict)
pop = fwdpy11.DiploidPopulation(100, 1.0)
rng = fwdpy11.GSLrng(54321)
recorder = PyFreqTracker(0)
fwdpy11.evolvets(
    rng,
    pop,
    params,
    1,  # Simplify every generation
    recorder,
    suppress_table_indexing=False,
)

Here, we do not need track_mutation_counts=True because simplifying each generation ends up accomplishing the same thing (for neutral and for selected variants).

Let’s take a look at the plot. We will reduce the opacity of selected variants to make the neutral ones pop a bit more:

../_images/21690eefd9a15866420234f6cb043fed179421f67bd7d56aca3cc846e381c0a1.png — Fig. 2 The hitch-hiking effect. Dotted lines show the trajectories of neutral mutations. The selected variant trajectories have reduced opacity.#

Other considerations#

This recipe needs adjustment for the following cases:

Tracking mutation frequencies with respect to deme.
Tracking mutation frequencies in demes that change size.

While this tracker is quite simple to write, performance may be an issue for very large simulations and one may prefer another approach.