Moduli Spaces of Phylogenetic Trees Describing Tumor Evolutionary   Patterns
  Cancers follow a clonal Darwinian evolution, with fitter subclones replacing more quiescent cells, ultimately giving rise to macroscopic disease. High-throughput genomics provides the opportunity to investigate these processes and determine specific genetic alterations driving disease progression. Genomic sampling of a patient's cancer provides a molecular history, represented by a phylogenetic tree. Cohorts of patients represent a forest of related phylogenetic structures. To extract clinically relevant information, one must represent and statistically compare these collections of trees. We propose a framework based on an application of the work by Billera, Holmes and Vogtmann on phylogenetic tree spaces to the case of unrooted trees of intra-individual cancer tissue samples. We observe that these tree spaces are globally nonpositively curved, allowing for statistical inference on populations of patient histories. A projective tree space is introduced, permitting visualizations of aggregate evolutionary behavior. Published data from three types of human malignancies are explored within our framework. 
Sakellarios Zairis, Hossein Khiabanian, Andrew J. Blumberg, Raul   Rabadan
q-bio.QM q-bio.GN