From IBD tracts to runs of homozygosity: a unified coalescent framework including selection

Identity by descent (IBD) tracts and runs of homozygosity (ROH) represent the theoretical and observable sides of chromosomal autozygosity.

However, the formal relationship between their length distributions has yet to be established.

A coalescent framework is developed here that unifies both concepts within a single analytical formalism, with applications to inferring effective population size (Ne) and detecting selection signatures.

Closed-form probability density functions are derived for IBD tract lengths and extended to the observable ROH length distribution by explicitly modelling the displacement of autozygosity boundaries from true recombination breakpoints to the nearest heterozygous flanking marker sites.

Mutation, gene conversion, finite marker density, and marker heterozygosity are incorporated as parameters linking IBD tracts to ROH.

Background selection introduces a systematic upward bias in apparent tract lengths that requires a generation-dependent Ne that cannot be captured by a single constant value.

Selective sweeps produce an asymmetric distortion of the length distribution around a neutral focal site.

The sign of this asymmetry indicates the side of the focal site on which the selected locus resides.

This directional signal is transient, dissipating quickly after the sweep.

In contrast, the signature given by the local Ne reduction persists considerably longer, making the two signatures complementary to determine the age of the sweep.

Computational tools are provided to predict tract length distributions under background selection and complete or partial selective sweeps.

The application of the theory is illustrated by detecting and localising the selective sweep associated with lactase persistence in European human populations.