Outline of the talk

1. What do we need simulations for?
2. The tree sequence
3. Applications

slides: github.com/petrelharp/osu-may-2021

Some questions

1. What forces contribute to the variation in genetic diversity along the genome? (explaining variation in diversity)

2. Which locations along the genome have been the recent targets of positive natural selection? (identifying sweeps)

3. Where did this individual come from? (inferring location)

4. How do organisms disperse across the landscape? (dispersal maps)

Inverse problems

Inverse problems

Inverse problems

Inverse problems

Simulation-based inference

• bespoke confirmatory simulations
• optimization of one or two parameters
• machine learning predictors (e.g., random forests)
• Approximate Bayesian Computation (ABC)
• deep learning

Wish list:

Enter SLiM

by Ben Haller and Philipp Messer

• a forwards simulator
• arbitary life cycles
• continuous geography and local interactions
• quantitative traits
• anything is possible

Ben Haller

messerlab.org/SLiM

• Whole genomes,*

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.

The succinct tree sequence

jerome kelleher

Example: three samples; two trees; two variant sites

Nodes and edges

Edges

Who inherits from who.

Records: interval (left, right); parent node; child node.

Nodes

The ancestors those happen in.

Records: time ago (of birth); ID (implicit).

Sites and mutations

Mutations

When state changes along the tree.

Records: site it occured at; node it occurred in; derived state.

Sites

Where mutations fall on the genome.

Records: genomic position; ancestral (root) state; ID (implicit).

The result: an encoding of the genomes and all the genealogical trees.

File sizes

For \(N\) samples genotyped at \(M\) sites

Fast genotype statistics, too!

The main idea

If we record the tree sequence that relates everyone to everyone else,

after the simulation is over we can put neutral mutations down on the trees.

This means recording the entire genetic history of everyone in the population, ever.

A 100x speedup!

What else can you do with tree sequences?

• recorded pedigree and migration history
• true ancestry assignment
• recapitation: fast, post-hoc initialization with coalescent simulation
• fast, convenient computation

For example:

• genome as human chr7 (\(1.54 \times 10^8\)bp)
• \(\approx\) 10,000 diploids
• 500,000 overlapping generations
• continuous, square habitat
• selected mutations at rate \(10^{-10}\)
• neutral mutations added afterwards

Runtime: 8 hours

Diversity correlates with recombination rate

Hudson 1994; Cutter & Payseur 2013; Corbett-Detig et al 2015

The Mimulus aurantiacus species complex

Simulations

Conclusions:

• neutral
• background selection
• selection against introgressed alleles
• positive selection
• local adaptation

locator (Battey et al 2020)

• genetic versus geographic distance between pairs of 272 desert tortoises (McCartney-Melstad, Shaffer)
• clouds are comparisons within/between the two colors

Software development goals

• open
• welcoming and supportive
• reproducible and well-tested
• backwards compatible
• well-documented
• capacity building

tskit.dev

Thanks!