The bounded coalescent model: conditioning a genealogy on a minimum root date

Abstract

The coalescent model represents how individuals sampled from a population may have originated from a last common ancestor. The bounded coalescent model is obtained by conditioning the coalescent model such that the last common ancestor must have existed after a certain date. This conditioned model arises in a variety of applications, such as speciation, horizontal gene transfer or transmission analysis, and yet the bounded coalescent model has not been previously analysed in detail. Here we describe a new algorithm to simulate from this model directly, without resorting to rejection sampling. We show that this direct simulation algorithm is more computationally efficient than the rejection sampling approach. We also show how to calculate the probability of the last common ancestor occurring after a given date, which is required to compute the probability of realisations under the bounded coalescent model. Our results are applicable in both the isochronous (when all samples have the same date) and heterochronous (where samples can have different dates) settings. We explore the effect of setting a bound on the date of the last common ancestor, and show that it affects a number of properties of the resulting phylogenies. All our methods are implemented in a new R package called BoundedCoalescent which is freely available online.

Distinguishing imported cases from locally acquired cases within a geographically limited genomic sample of an infectious disease

“…However, here we consider an alternative equivalent formulation of the coalescent model, in which the phylogeny is formed by iterating over the leaves one by one in increasing order of date, and considering how each leaf coalesces with the phylogeny made by the previous leaves (Didelot et al 2014; Carson et al 2022). To do so, we consider that the dates s 1: n of the leaves are in increasing order, and that the dates c 1:( n− 1) of the internal nodes are ordered so that c k corresponds to the internal node created when adding the leaf s k +1 to the tree made of the first k leaves.…”

Distinguishing imported cases from locally acquired cases within a geographically limited genomic sample of an infectious disease

“…However, here we consider an alternative equivalent formulation of the coalescent model, in which the phylogeny is formed by iterating over the leaves one by one in increasing order of date, and considering how each leaf coalesces with the phylogeny made by the previous leaves (Didelot et al, 2014;Carson et al, 2022). To do so, we consider that the dates s 1:n of the leaves are in increasing order, and that the dates c 1:(n−1) of the internal nodes are ordered so that c k−1 corresponds to the date of the internal node created when adding the leaf indexed k to the tree made of the first k − 1 leaves.…”