The multifurcating skyline plot

Abstract

A variety of methods based on coalescent theory have been developed to infer demographic history from gene sequences sampled from natural populations. The "skyline plot" and related approaches are commonly employed as flexible prior distributions for phylogenetic trees in the Bayesian analysis of pathogen gene sequences. In this work we extend the classic and generalised skyline plot methods to phylogenies that contain one or more multifurcations (i.e. hard polytomies). We use the theory of Λ-coalescents (specifically, Beta(2α, α)-coalescents) to develop the "multifurcating skyline plot", which estimates a piecewise constant function of effective population size through time, conditional on a time-scaled multifurcating phylogeny. We implement a smoothing procedure and extend the method to serially-sampled (heterochronous) data, but we do not address here the problem of estimating trees with multifurcations from gene sequence alignments. We validate our estimator on simulated data using maximum likelihood and find that parameters of the Beta(2α, α)-coalescent process can be estimated accurately. Lastly we apply the multifurcating skyline plot to a molecular clock phylogeny of 1,610 Ebola virus sequences from the 2014-2016 West African outbreak. We artificially collapse short branches in this empirical phylogeny in order to mimic different levels of multifurcation and show that variance in the reproductive success of the pathogen through time can be estimated by combining the skyline plot with epidemiological case count data.

Multiple merger genealogies in outbreaks ofMycobacterium tuberculosis

“…To overcome the limitation of assuming synchronous sampling, we encourage future studies to develop MMC models that explicitly consider the time of sampling. Such a model is proposed in Hoscheit and Pybus (2019), but without an explicit mechanism to convert real time units in coalescent time units.…”

“…The Beta coalescent explicitly models populations with skewed offspring distributions (Schweinsberg 2003). Additionally, it was also proposed to capture the genealogies of populations undergoing recurrent bottlenecks and of epidemics characterized by super-spreaders (Tellier andLemaire 2014, Hoscheit andPybus 2019).…”

“…Following Hoscheit and Pybus (2019), we add serial sampling to the MMC and to Kingman's coalescent with exponential growth simply by stopping the coalescent at times (on the coalescent time scale) where further individuals are sampled. Then, we start a new (independent) coalescent tree that has rates and waiting times as the non-serial coalescent (multiple merger or with growth) started in the last state of the stopped coalescent plus adding one block with a single individual for each individual sampled at this time.…”

Cannings models, population size changes and multiple-merger coalescents

“…For a specific case, the Dirac n-coalescent for an exponentially growing population, such a construction has been given in Matuszewski et al (2017), based on the fixed-N Cannings model (modified Moran model) from Eldon and Wakeley (2006). However, also other Λ-n-coalescents (or Cannings models which should converge to these) with changed time scale have been recently discussed and applied as models of genealogies, see Spence et al (2016), Kato et al (2017), Alter and Louzoun (2016) and Hoscheit and Pybus (2018). This leads to the goal of this article, which is to extend the approach in Matuszewski et al (2017) to explicitly give a construction of time-changed Λ-coalescents as limits of Cannings models with fluctuating population sizes.…”