The multifurcating skyline plot

: 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 generalized skyline plot methods to phylogenies that contain one or more multifurcations (i.e. hard polytomies). We use the theory of Λ-coalescents (specifically, Beta(2-α,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(2-α,α) -coalescent process can be estimated accurately. Furthermore, we apply the multifurcating skyline plot to simulated trees generated by tracking transmissions in an individual-based model of epidemic superspreading. We find that high levels of superspreading are consistent with the high-variance assumptions underlying Λ-coalescents and that the estimated parameters of the Λ-coalescent model contain information about the degree of superspreading.