Graph-based algorithms for Laplace transformed coalescence time distributions

Abstract

Extracting information on the selective and demographic past of populations that is contained in samples of genome sequences requires a description of the distribution of the underlying genealogies. Using the Laplace transform, this distribution can be generated with a simple recursive procedure, regardless of model complexity. Assuming an infinite-sites mutation model, the probability of observing specific configurations of linked variants within small haplotype blocks can be recovered from the Laplace transform of the joint distribution of branch lengths. However, the repeated differentiation required to compute these probabilities has proven to be a serious computational bottleneck in earlier implementations. Here, I show that the state space diagram can be turned into a computational graph, allowing efficient evaluation of the Laplace transform by means of a graph traversal algorithm. This general algorithm can, for example, be applied to tabulate the likelihoods of mutational configurations in non-recombining blocks. This work provides a crucial speed up for existing composite likelihood approaches that rely on the joint distribution of branch lengths to fit isolation with migration models and estimate the parameters of selective sweeps. The associated software is available as an open-source Python library, agemo.

Genomic regions of current low hybridisation mark long-term barriers to gene flow in scarce swallowtail butterflies

“…In reality, net gene flow between these species may be bidirectional but asymmetric, a phenomenon which has been demonstrated in other systems (Yan et al 2016, Ngeve et al 2017, Banker et al 2022). Whilst fitting more realistic models of gene flow is not currently feasible using this inference framework, future extensions lie on the horizon (Bisschop 2022).…”