\[ \newcommand{\E}{\mathbb{E}} \renewcommand{\P}{\mathbb{P}} \DeclareMathOperator{\var}{var} \]

Simulation in population genetics

Peter Ralph, University of Oregon

EvoLunch // October 2020

Goals

Simulation can help to:

  • make things concrete
  • look for unexpected things
  • guide and test ideas
  • assess sensitivity to assumptions

and to

  • validate and benchmark methods
  • fit models

Goals of scientific software development

  • lower barriers to good research
  • be usable and accessible
  • produce reproducible and reliable results

and so software development should

  • give a voice to stakeholders
  • emphasize usability and documentation
  • produce tested, reproducible, and interoperable results
  • be visualizable and debuggable

In science we stand on each others’ shoulders

and so we should be mindful about
how and where we stand.

What can we simulate, today?

Wish list:

Whole genomes, thousands of samples,
from millions of individuals.

Demography:

  • life history
  • separate sexes
  • selfing
  • polyploidy
  • species interactions

Geography:

  • discrete populations
  • continuous landscapes
  • barriers

History:

  • ancient samples
  • range shifts

Natural selection:

  • selective sweeps
  • introgressing alleles
  • background selection
  • quantitative traits
  • incompatibilities
  • local adaptation

Genomes:

  • recombination rate variation
  • gene conversion
  • infinite-sites mutation
  • nucleotide models
  • context-dependence
  • mobile elements
  • inversions
  • copy number variation

msprime

  • a coalescent simulator, so
  • discrete populations
  • neutral* evolution
  • fast

coming soon:

  • selective sweeps (as in discoal)
  • non-constant finite-sites mutation and recombination
  • gene conversion
  • multiple merger coalescents
  • discrete time Wright-Fisher
ts = msprime.simulate(500, Ne=1e4, length=2e3, recombination_rate=1e-8, random_seed=1913378874)

see github.com/tskit-dev/msprime and Kelleher, Etheridge, and McVean

SLiM

by Ben Haller and Philipp Messer

  • a forwards simulator
  • arbitary life cycles
  • continuous geography and local interactions
  • distributions of fitness coefficients
  • quantitative traits take more work
  • anything is possible
SLiM GUI

msprime + SLiM are interoperable!

You can:

  • use msprime to add mutations to the genealogies of a SLiM simulation

  • use msprime to recapitate uncoalesced lineages in a SLiM simulation

  • use SLiM to simulate selection on neutral diversity generated by msprime

recapitation

from pyslim.readthedocs.io/en/latest/tutorial.html

SLiM + msprime

use msprime to add mutations to the genealogies of a SLiM simulation

from https://onlinelibrary.wiley.com/doi/full/10.1111/1755-0998.12968

from Tree‐sequence recording in SLiM opens new horizons for forward‐time simulation of whole genomes

Tree sequences

History is a sequence of trees

For a set of sampled chromosomes, at each position along the genome there is a genealogical tree that says how they are related.

Trees along a chromosome

The succinct tree sequence

is a way to succinctly describe this, er, sequence of trees

and the resulting genome sequences.

example tree sequence

introduced by Jerome Kelleher, in Kelleher, Etheridge, and McVean

File sizes

file sizes

100Mb chromosomes; from Kelleher et al 2018, Inferring whole-genome histories in large population datasets, Nature Genetics

Fast genotype statistics

efficiency of treestat computation

from R., Thornton and Kelleher 2019, Efficiently summarizing relationships in large samples, Genetics

Figure 7 from “Efficiently summarizing relationships in large samples”

from R., Thornton and Kelleher 2019, Efficiently summarizing relationships in large samples, Genetics

from Bradburd & R., “Spatial population genetics: it’s about time”

from Bradburd & R., “Spatial population genetics: it’s about time”

If you could record everything, ever

about your study organism,

what would you want to measure?

  • Whole genomes,*
  • thousands of samples,
  • from millions of individuals.*

Demography:

  • life history
  • separate sexes*
  • selfing
  • polyploidy*
  • species interactions*

Geography:

  • discrete populations
  • continuous landscapes
  • barriers*

History:

  • ancient samples
  • range shifts

Natural selection:

  • selective sweeps
  • introgressing alleles
  • background selection
  • quantitative traits*
  • incompatibilities*
  • local adaptation*

Genomes:

  • recombination rate variation
  • gene conversion
  • infinite-sites mutation
  • nucleotide models
  • context-dependence*
  • mobile elements*
  • inversions*
  • copy number variation

ok that’s a lot

Do you have to be an expert in all these things?!?

Recombination maps, demographic models, gene conversion, mutation rates… and tree sequences?!?

I’ve spent a year developing my inference method, I can’t spend another year testing it against all possible problems!

I just want some realistic genomes to run my power analysis with!

enter the PopSim Consortium

stdpopsim: A community-maintained library of standard population genetic simulation models.

The idea:

species + demographic model + contig + recombination map 
   [ + selection ... ]

https://stdpopsim.readthedocs.io/en/latest/catalog.html#sec_catalog_DroMel_genome

https://stdpopsim.readthedocs.io/en/latest/catalog.html#sec_catalog_HomSap_models

Simulate 100 samples from two populations of A. thaliana:

import stdpopsim
species = stdpopsim.get_species("AraTha")
contig = species.get_contig("chr4", genetic_map="SalomeAveraged_TAIR7")
model = stdpopsim.IsolationWithMigration(NA=5000, N1=4000, N2=1000, T=1000, M12=0, M21=0)
samples = model.get_samples(50, 50)
engine = stdpopsim.get_engine("msprime")
ts = engine.simulate(model, contig, samples, seed=13)

Compute and plot the joint SFS:

pop_samples = [ts.samples(0), ts.samples(1)]
sfs = ts.allele_frequency_spectrum(sample_sets=[pop_samples],
                                    polarised=True, span_normalise=False)
import allel
allel.plot_joint_sfs(sfs);

Who is doing all this work? and how?

It takes a community

SLiM:
Ben Haller, Philipp Messer, and SLiM Acknowledgements

ben haller jerome kelleher ben jeffery

msprime/tskit:

Jaime Ashander, Franz Baumdicker, Gertjan Bisschop, Bjarki Eldon, E. Castedo Ellerman, Jared Galloway, Ariella Gladstein, Daniel Goldstein, Graham Gower, Simon Gravel, Bing Guo, Ben Jeffery, Jerome Kelleher, Andrew Kern, Jere Koskela, Warren W. Kretzschmar, Ivan Krukov, Konrad Lohse, Michael Matschiner, Dominic Nelson, Nathaniel Pope, Aaron Ragsdale, Peter Ralph, Murillo Rodrigues, Kumar Saunack, Thibaut Sellinger, Kevin Thornton, Georgia Tsambos, Hugo Van Kemenade, Yan Wong, Sha Zhu

stdpopsim:

Jeffrey R Adrion, Christopher B Cole, Noah Dukler, Jared G Galloway, Ariella L Gladstein, Graham Gower, Christopher C Kyriazis, Aaron P Ragsdale, Georgia Tsambos, Franz Baumdicker, Jedidiah Carlson, Reed A Cartwright, Arun Durvasula, Ilan Gronau, Bernard Y Kim, Patrick McKenzie, Philipp W Messer, Ekaterina Noskova, Diego Ortega-Del Vecchyo, Fernando Racimo, Travis J Struck, Simon Gravel, Ryan N Gutenkunst, Kirk E Lohmueller, Peter L Ralph, Daniel R Schrider, Adam Siepel, Jerome Kelleher, Andrew D Kern

Goals

  • respectful and inclusive

  • reproducible and reliable

  • well-documented and accessible

  • relevant and impactful

What we do is almost as important as how we do it.

Communication: lots of github

https://github.com/tskit-dev/msprime/issues

General protocol:

  1. Propose a feature or point out a bug.
  2. Discuss solutions and the interface.
  3. Write a draft solution.
  4. Test it.
  5. Finalize and merge.
https://github.com/tskit-dev/msprime/issues/880

Reproducible and reliable

Testing

  • ensures reliability
  • makes development easier

General strategy:

compute the same thing in two different ways, and compare.

============================= test session starts ==============================
collecting ... collected 2587 items

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https://github.com/tskit-dev/msprime/issues/1000

Usable and accessible

Documentation:

  • quickstart

  • tutorials

  • detailed interface reference

  • user support

  • workshops

SLiM manual, 619 pages

stdpopsim documentation

Workshops

Ariella Gladstein giving a workshop

We welcome contributors!

  • learn git/python

  • become an expert simulator

  • make tools that do what you need

Thanks!

Solid simulation tools, with visualization, output, and documentation.

msprime: https://github.com/tskit-dev/msprime

SLiM: https://messerlab.org/slim/

tskit: https://github.com/tskit-dev/tskit

stdpopsim: https://github.com/popsim-consortium/stdpopsim

want to contribute?

Thanks especially to

Jerome Kelleher
Ben Haller
Andy Kern
Ariella Gladstein
Georgia Tsambos
Murillo Rodrigues
Graham Gower
Jeff Adrion
Yan Wong
Jared Galloway
Boyana Norris
Philipp Messer
Ben Jeffery
Kirk Lohmueller

tskit popsim SLiM

NSF NIH BDI UO

pop0 = msprime.PopulationConfiguration(sample_size=3, initial_size = 500)
pop1 = msprime.PopulationConfiguration(sample_size=3, initial_size = 500)
M = np.array([[0, 0.05],
              [0.02, 0]])
admixture_event  = msprime.MassMigration(time = 50, source = 0, dest = 1, proportion = 0.3)
divergence_event = msprime.MassMigration(
        time = 200, source = 1, dest = 0, proportion = 1)
rate_change = msprime.MigrationRateChange(
    time = 200, rate = 0, matrix_index=None)
ddb = msprime.DemographyDebugger(
    population_configurations=[pop0, pop1], migration_matrix = M,
    demographic_events=[admixture_event, divergence_event, rate_change])
ddb.print_history()

============================
Epoch: 0 -- 50.0 generations
============================
     start     end      growth_rate |     0        1    
   -------- --------       -------- | -------- -------- 
0 |   500      500                0 |     0      0.05   
1 |   500      500                0 |   0.02       0    

Events @ generation 50.0
   - Mass migration: Lineages moved with probability 0.3 backwards in time with source 0 & dest 1
                     (equivalent to migration from 1 to 0 forwards in time)
================================
Epoch: 50.0 -- 200.0 generations
================================
     start     end      growth_rate |     0        1    
   -------- --------       -------- | -------- -------- 
0 |   500      500                0 |     0      0.05   
1 |   500      500                0 |   0.02       0    

Events @ generation 200.0
   - Mass migration: Lineages moved with probability 1 backwards in time with source 1 & dest 0
                     (equivalent to migration from 0 to 1 forwards in time)
   - Migration rate change to 0 everywhere
===============================
Epoch: 200.0 -- inf generations
===============================
     start     end      growth_rate |     0        1    
   -------- --------       -------- | -------- -------- 
0 |   500      500                0 |     0        0    
1 |   500      500                0 |     0        0
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