Moduli Spaces of Phylogenetic Trees Describing Tumor Evolutionary Patterns
Abstract
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.
Cite
@article{arxiv.1410.0980,
title = {Moduli Spaces of Phylogenetic Trees Describing Tumor Evolutionary Patterns},
author = {Sakellarios Zairis and Hossein Khiabanian and Andrew J. Blumberg and Raul Rabadan},
journal= {arXiv preprint arXiv:1410.0980},
year = {2014}
}