Abstract
Measuring the overlap between the var gene repertoires of two Plasmodium falciparum parasites is, in principle, easy. Each parasite genome contains a repertoire of approximately 60 var genes, so upon fully sequencing both parasites' genomes, the number of shared var sequences can be directly counted. In practice, however, only a fraction of each parasite's var repertoire is likely to be sampled due to the difficulties of whole-genome sequencing for var genes and the stochastic sample provided by PCR techniques. Although a method exists for quantifying repertoire overlap under these subsampled conditions, its bias is well documented and the uncertainty of its estimates cannot be quantified. Here we derive and validate a method to rigorously estimate the repertoire overlap between two parasites from the overlap of their subsampled repertoires. By solving a Bayesian inference problem, this method takes into account the rates of subsampling and produces unbiased and Bayes-optimal estimates of overlap. In addition, it provides a natural framework for computing the uncertainty of its estimates, and can be used in laboratory planning by quantifying the tradeoff between sequencing effort and uncertainty.
