Timepieces

Every great watch begins as a pile of parts on the bench.

Each Timepiece is a complete algorithm from population genetics, disassembled and rebuilt from scratch. Like a watchmaker laying out parts on the bench, we examine every gear before assembling the whole mechanism. Nothing is taken on faith. Nothing is hidden behind “see supplementary materials.”

Verification Status

Disclaimer

The code examples in each Timepiece are verified by automated unit tests that re-implement the documented functions and check their mathematical properties. No Timepiece has been independently verified by a domain expert. If you find an error – mathematical, pedagogical, or computational – please open an issue. The table below shows the current verification status.

The Timepieces are grouped by what they do, with verification status for each.

Simulators – tools that generate ground truth

#	Timepiece	Tests	Verified	What it does
IV	msprime	190	–	Neutral coalescent with recombination. The clockwork that generates ground truth.
XVI	SLiM	67	–	Forward-time simulation with natural selection. The forge that builds what the coalescent cannot.
XVIII	discoal	132	–	Coalescent simulation with selective sweeps via trajectory + structured coalescent.

Demographic inference – estimating population size history

#	Timepiece	Tests	Verified	What it does
I	PSMC	186	–	Population size history from a single diploid genome. The simplest inference Timepiece.
II	SMC++	112	–	Extends PSMC to multiple unphased genomes with a distinguished lineage approach.
XIII	Gamma-SMC	107	–	Ultrafast pairwise TMRCA inference with gamma-distributed posteriors.
XIV	PHLASH	130	–	GPU-accelerated Bayesian inference of population size history via SVGD.

SFS-based demographic inference – using the site frequency spectrum

#	Timepiece	Tests	Verified	What it does
X	moments	162	–	Demographic inference from the SFS using moment equations.
XI	dadi	84	–	Demographic inference from the SFS by solving the Wright-Fisher diffusion PDE.
XII	momi2	140	–	Demographic inference from the SFS via coalescent tensor algebra.

Genealogy and ARG inference – reconstructing ancestral histories

#	Timepiece	Tests	Verified	What it does
III	Li & Stephens HMM	158	–	The copying model: a haplotype as a mosaic of references. A gear inside many Timepieces.
V	ARGweaver	120	–	Bayesian ARG sampling with discretized time. SINGER’s predecessor.
VI	tsinfer	142	–	Deterministic tree sequence inference at biobank scale.
VII	SINGER	172	–	Bayesian ARG sampling with continuous time and two-HMM architecture.
VIII	Threads	56	–	Deterministic ARG inference at biobank scale with PBWT pre-filtering.
XVII	Relate	66	–	Genome-wide genealogy estimation via asymmetric painting + MCMC branch lengths.

Dating and selection – calibrating genealogies and detecting selection

#	Timepiece	Tests	Verified	What it does
IX	tsdate	139	–	Dates tree sequence nodes using the molecular clock.
XV	CLUES	93	–	Full-likelihood estimation of selection coefficients from gene trees and ancient DNA.