Phylogenetic double placement of mixed samples

Motivation
Consider a simple computational problem. The inputs are (i) the set of mixed reads generated from a sample that combines two organisms and (ii) separate sets of reads for several reference genomes of known origins. The goal is to find the two organisms that constitute the mixed sample. When constituents are absent from the reference set, we seek to phylogenetically position them with respect to the underlying tree of the reference species. This simple yet fundamental problem (which we call phylogenetic double-placement) has enjoyed surprisingly little attention in the literature. As genome skimming (low-pass sequencing of genomes at low coverage, precluding assembly) becomes more prevalent, this problem finds wide-ranging applications in areas as varied as biodiversity research, food production and provenance, and evolutionary reconstruction.
Results
We introduce a model that relates distances between a mixed sample and reference species to the distances between constituent...