Gaussian stabilizing selection on a single trait (with a sudden optimum shift)

This simulation script shows how to simulate stabilizing selection on a single trait. The fitness model is Gaussian stabilizing selection. The example is quite detailed, with a command-line interface implemented using argparse.

The simulation can track individuals as nodes in tree sequences after the time of the optimum shift. For example, to preserve 50 randomly-chosen individuals every 10 generations (starting from the time of the shift):

python3 -N 5000 --mu 5e-3 --sigma 0.1 --preserve 10 --num_ind 50 --filename pop.lzma

The output file, pop.lzma, is a compressed file containing the pickled population and its corresponding tree sequence.

Evolution of a single genomic region under Gaussian Stabilizing Selection
with a moving optimum, or "GSSmo".

The simulation allows the recording of quantitative-genetics statistics
over time as well as the preservation of samples into the tree sequence
after the optimum shift.

The demographic model is constant-size Wright-Fisher for 10N generations
around an optimal trait value of zero.  Then, the optimum changes and
the population continues to evolve for a length of time specified
by the user.

The mutation model is uniform across the genome with effect sizes
given by a Gaussian distribution with mean zero and a user-specified
standard deviation.

The genetic model is additive effects with fitness determined by
Gaussian stabilizing selection based on the squared distance from
the optimum.

import argparse
import lzma
import math
import os
import pickle
import sqlite3
import sys
from collections import namedtuple

import numpy as np
import pandas as pd

import fwdpy11

# Simulations with tree sequence recording need
# to know the max position in a genome.  Here,
# we use a length of 1.0. Thus, all mutation
# and recombination events will be uniform
# random variables on the continuous interval

# When recording quant-genetic statistics during a simulation,
# we will use this type. Named tuples are extremely efficient,
# and they are easily converted into Pandas DataFrame objects,
# which is very convenient for analysis and output.
DATA = namedtuple("Data", ["generation", "zbar", "vg", "wbar"])

def make_parser():
    Create a command-line interface to the script.
    parser = argparse.ArgumentParser(

    required = parser.add_argument_group("Required arguments")
    required.add_argument("--popsize", "-N", type=int, help="Diploid population size")
        "--mu", "-m", type=float, help="Mutation rate (per gamete, per generation)"
        help="Standard deviation of Gaussian" "distribution of mutational effects",
        help="Output file name.  The population will be"
        "pickled to this file, and the file will be"
        "compressed using the lzma algorithm",

    optional = parser.add_argument_group("Optional arguments")
        "--rho", type=float, default=1000.0, help="Scaled recombination rate, rho=4Nr"
        help="Inverse strength of stabilizing selection",
        "--opt", type=float, default=1.0, help="Value of new phenotypic optimum"
        help="Amount of time to simulate past" "optimum shift, in units of N",
        help="Record statistics such as VG from population " "each generation",
        help="File name to record statistics." "The format is an sqlite3 database.",
        help="Record ancient samples every X generations"
        "after optimum shift. A value of -1 means not"
        "to record.",
        help="Number of diploids to record as" "ancient samples",
    optional.add_argument("--seed", type=int, default=42, help="Random number seed.")

    return parser

def validate_arguments(args):
    Validate input arguments.
    Note: this is likely incomplete.
    if args.popsize < 0:
        raise ValueError("Population size must be non-negative")
    if < 0 or math.isfinite( is False:
        raise ValueError("Mutation rate must be non-negative and finite")
    if args.sigma < 0 or math.isfinite(args.sigma) is False:
        raise ValueError(
            "Std. dev. of distribution of effect sizes"
            "must be non-negative and finite"
    if args.filename is None:
        raise ValueError("ouptut filename cannot be None")

    if args.record > 0 and args.statfile is None:
        raise ValueError(
            "Must profile a stats file name when recording"
            "statistics during simulation"

    if args.statfile is not None and os.path.exists(args.statfile):
        raise RuntimeError("statfile already exists!")

    if args.preserve > 0:
        if args.num_ind > args.popsize:
            raise ValueError(
                "Number of ancient samples is" "greater than population size"

class Recorder(object):
    fwdpy11 allows you to define objects that record data
    from populations during simulation.  Such objects must
    be callable, and the easiest way to do things is to
    create a class with a __call__ function.

    def __init__(self, record_stats, interval, nsam): = []
        self.record = record_stats
        self.interval = interval
        self.nsam = nsam

    def __call__(self, pop, recorder):
        if self.record is True:
            # Record mean trait value each generation.
            t = np.array(pop.diploid_metadata, copy=False)
                DATA(pop.generation, t["g"].mean(), t["g"].var(), t["w"].mean())

        if self.interval > 0 and pop.generation >= 10 * pop.N:
            if pop.generation % self.interval == 0.0:
                if self.nsam < pop.N:
                    s = np.random.choice(pop.N, self.nsam, replace=False)
                    s = np.arange(pop.N, dtype=np.int32)


def runsim(args):
    Run the simulation and deliver output to files.
    pop = fwdpy11.DiploidPopulation(args.popsize, GENOME_LENGTH)

    rng = fwdpy11.GSLrng(args.seed)

    GSSmo = fwdpy11.GSSmo(
            fwdpy11.Optimum(when=0, optimum=0.0, VS=args.VS),
            fwdpy11.Optimum(when=10 * args.popsize, optimum=args.opt, VS=args.VS),

    p = {
        "nregions": [],  # No neutral mutations -- add them later!
        "gvalue": fwdpy11.Additive(2.0, GSSmo),
        "sregions": [fwdpy11.GaussianS(0, GENOME_LENGTH, 1, args.sigma)],
        "recregions": [fwdpy11.Region(0, GENOME_LENGTH, 1)],
        "rates": (0.0,, args.rho / float(4 * args.popsize)),
        # Keep mutations at frequency 1 in the pop if they affect fitness.
        "prune_selected": False,
        "demography": fwdpy11.DiscreteDemography(),
        "simlen": 10 * args.popsize + int(args.time + float(args.popsize)),
    params = fwdpy11.ModelParams(**p)

    r = Recorder(args.record, args.preserve, args.num_ind)
    fwdpy11.evolvets(rng, pop, params, 100, r, suppress_table_indexing=True)

    with, "wb") as f:
        pickle.dump(pop, f)

    if args.statfile is not None:
        stats = pd.DataFrame(, columns=DATA._fields)
        # Write the statistics to an sqlite3 database,
        # which can be processed in R via dplyr.
        conn = sqlite3.connect(args.statfile)
        stats.to_sql("data", conn)

if __name__ == "__main__":
    parser = make_parser()
    args = parser.parse_args(sys.argv[1:])

Processing the samples stored in tree sequences

This script plots the mean trait value at every time point as a function of time:

Plots the mean genetic value for all time periods
present in the tree sequence.

Usage: python3 filename

filename should contain a pickled population output by
import lzma
import pickle
import sys

import numpy as np
import seaborn as sns

with[1], "rb") as f:
    pop = pickle.load(f)

nodes = np.array(pop.tables.nodes, copy=False)

times = []
mean_trait_values = []
for t, n, m in pop.sample_timepoints():

# plot the time vs trait value
xyplot = sns.lineplot(times, mean_trait_values)
xyplot.set_xlabel("Time (generations")
xyplot.set_ylabel("Mean trait value")
xyplot.get_figure().savefig("mean_trait_value_from_tree_sequences.png", dpi=300)

This script goes over every time point, iterates over the variants, and re-calculates the genetic values. The output is a plot of the genetic value stored in the metadata versus the recalculated value. The reason we can do this is that the simulation assumes strict additivity.

import lzma
import pickle
import sys

import numpy as np
import seaborn as sns

import fwdpy11

with[1], "rb") as f:
    pop = pickle.load(f)

genetic_trait_values_from_sim = []
genetic_values_from_ts = []
idx = 0
for n, s, m in pop.sample_timepoints():
    vi = fwdpy11.VariantIterator(pop.tables, s)
    sum_esizes = np.zeros(len(s))
    for variant in vi:
        g = variant.genotypes
        r = variant.records[0]
        mutant = np.where(g == 1)[0]
        sum_esizes[mutant] += pop.mutations[r.key].s
    ind = int(len(s) / 2)
    temp_gvalues = np.zeros(ind)
    temp_gvalues += sum_esizes[0::2]
    temp_gvalues += sum_esizes[1::2]

# plot the time vs trait value
xyplot = sns.scatterplot(genetic_trait_values_from_sim, genetic_values_from_ts)
xyplot.set_xlabel("From simulation")
xyplot.set_ylabel("From tree sequences")
xyplot.get_figure().savefig("compare_genetic_values.png", dpi=300)