  Background: Intra-tumour heterogeneity (ITH) is the result of ongoing
evolutionary change within each cancer. The expansion of genetically distinct
sub-clonal populations may explain the emergence of drug resistance and if so
would have prognostic and predictive utility. However, methods for objectively
quantifying ITH have been missing and are particularly difficult to establish
in cancers where predominant copy number variation prevents accurate
phylogenetic reconstruction owing to horizontal dependencies caused by long and
cascading genomic rearrangements.
  Results: To address these challenges we present MEDICC, a method for
phylogenetic reconstruction and ITH quantification based on a Minimum Event
Distance for Intra-tumour Copynumber Comparisons. Using a transducer-based
pairwise comparison function we determine optimal phasing of major and minor
alleles, as well as evolutionary distances between samples, and are able to
reconstruct ancestral genomes. Rigorous simulations and an extensive clinical
study show the power of our method, which outperforms state-of-the-art
competitors in reconstruction accuracy and additionally allows unbiased
numerical quantification of ITH.
  Conclusions: Accurate quantification and evolutionary inference are essential
to understand the functional consequences of ITH. The MEDICC algorithms are
independent of the experimental techniques used and are applicable to both
next-generation sequencing and array CGH data.
