Fig. 1: Method overview.
From: Robust and accurate Bayesian inference of genome-wide genealogies for hundreds of genomes
a–d, The gray lines represent haplotypes, and the circles indicate the allelic states of nodes in coalescent trees. Hollow circles correspond to ancestral alleles, and solid circles are derived alleles. In a, b and c, a partial ARG for the first three haplotypes has already been constructed, and a fourth haplotype is about to be threaded onto this partial ARG. a, The initial step in threading the fourth haplotype involves sampling the joining branch (highlighted in blue) in each marginal coalescent tree of the partial ARG, a process we call ‘branch sampling’. b, Following the determination of the joining branches, the next step is to sample the joining time for each of these joining branches. This step is referred to as ‘time sampling’. c,d, To propose an update to an ARG in MCMC, we first introduce cuts (illustrated by red scissors) to a sequence of marginal coalescent trees to prune subtrees. Then we re-graft them by solving the threading problem for the sub-ARG above the cuts. The branch length in the first two marginal trees and the topology of the third tree are altered after ‘sub-graph pruning and re-grafting’.
