Sweeps in time: leveraging the joint distribution of branch lengths

Abstract

Current methods of identifying positively selected regions of the genome are limited by their underlying model in two key ways: the model cannot account for the timing of the adaptive event and the analytic predictions are limited to single nucleotide polymorphisms. Here we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of the adaptive event. In addition, our framework allows us to go beyond simple polymorphism data. We are able to leverage information contained in patterns of linked variants, and even with very small sample sizes, our analytic framework has high power to identify historically adaptive regions of the genome and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between current theoretical models to recent advances in simulation procedures that have allowed researchers both to examine the evolution of genealogical histories at the level of full chromosomes and build methods that attempt to reconstruct full ancestries from genome sequence data.

Demographically explicit scans for barriers to gene flow using gIMble

“…While a feasible approximate solution to the problem of bi-directional gene flow has been described [69], we currently do not know of a closed-form analytic solution to accounts for the multiple discrete demographic events in the IIM model as required by agemo [38] (see Methods). This limitation applies equally to other useful extensions of model space involving multiple discrete events, such as inference under models of instantaneous admixture or the inclusion of explicit selective events [70].…”

Graph-based algorithms for Laplace transformed coalescence time distributions

“…Including short-range linkage information comes at a computational cost, limiting the applicability to smaller sample sizes. However, previous work has demonstrated that this approach maximizes the information contained in small samples compared to relying on the SFS (Bunnefeld et al, 2015; Bisschop et al, 2021). More importantly however, both frameworks have (independently) combined the same two basic ingredients to efficiently describe coalescent models: a recursive state-space construction and a graph representation for fast evaluation of the represented distributions.…”

“…The GF parameterised by the discrete time T of the event can be recovered by taking the inverse transform of the GF divided by its associated dummy variable ( δ ). This procedure has been used to incorporate population divergence, admixture events, and bottlenecks (Lohse et al, 2011; Bunnefeld et al, 2015), as well as selective sweeps (Bisschop et al, 2021).…”

“…Dividing both sides by δ we recognize . This procedure has been used to incorporate population divergence, ad-mixture events, and bottlenecks (Lohse et al, 2011; Bunnefeld et al, 2015), as well as selective sweeps (Bisschop et al, 2021).…”

“…The Laplace transformed description of the distribution of coalescence times has been used to tackle two major problems in population genetics: fitting explicit models of population history (Lohse et al, 2011; Frantz et al, 2014; Bunnefeld et al, 2015; Lohse et al, 2016) as well as estimating sweep parameters (Bisschop et al, 2021). Note that because the Laplace transform can be interpreted as the generating function (GF) of a continuous random variable, this method is often referred to as the GF approach.…”