Mapping the drivers of within-host pathogen evolution using massive data sets

Palmer, Duncan S.; Turner, Isaac; Fidler, Sarah; Frater, John; Goedhals, Dominique; Goulder, Philip; Huang, Kuan-Hsiang Gary; Oxenius, Annette; Phillips, Rodney; Shapiro, Roger; Vuuren, Cloete van; McLean, Angela R.; McVean, Gil

The Li and Stephens approximation allows us to evaluate the probability that a member of D arises as an imperfect mosaic of sequences in D B using a hidden Markov model (HMM). To model this process, we must specify a recombination model, and model of sequence evolution. We assume that recombination is site dependent, and occurs with probability r i between site i − 1 and i to any other member of D B uniformly at random. We model sequence change using the NY98 codon model [2] (which distinguishes transitions from transversions via the transition/transversion ratio; κ, and nonsynonymous changes from synonymous changes via the dN dS ratio; ω), with some modifications. To incorporate HLA-associated selection for escape, we define a consensus non-escaped strain C for the region to be analysed. A scaling, h∈H γ h,i , dependent on the host's HLA profile, H, then modifies any non-synonymous codon change from this consensus strain. We model reversion in a similar manner: a boost in codon substitution rate towards the consensus codon C at each site, ζ i . Note that reversion only acts on non-synonymous changes toward the consensus codon C , and as such the parameterisation is identifiable. To switch from rates to probabilities we integrate over the length of a lineage connecting a member of D to D B assuming a standard coalescent. For example for a non-synonymous transition from C i to some codon C,