title: Learning multiple evolutionary pathways from cross-sectional data.
abstract: We introduce a mixture model of trees to describe evolutionary processes that are characterized by the ordered accumulation of permanent genetic changes. The basic building block of the model is a directed weighted tree that generates a probability distribution on the set of all patterns of genetic events. We present an EM-like algorithm for learning a mixture model of K trees and show how to determine K with a maximum likelihood approach. As a case study, we consider the accumulation of mutations in the HIV-1 reverse transcriptase that are associated with drug resistance. The fitted model is statistically validated as a density estimator, and the stability of the model topology is analyzed. We obtain a generative probabilistic model for the development of drug resistance in HIV that agrees with biological knowledge. Further applications and extensions of the model are discussed.
authors.affiliation: Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, D-66123 Saarbrücken, Germany.
authors.forename: Niko
authors.initials: N
authors.lastname: Beerenwinkel
authors.forename: Jörg
authors.initials: J
authors.lastname: Rahnenführer
authors.forename: Martin
authors.initials: M
authors.lastname: Däumer
authors.forename: Daniel
authors.initials: D
authors.lastname: Hoffmann
authors.forename: Rolf
authors.initials: R
authors.lastname: Kaiser
authors.forename: Joachim
authors.initials: J
authors.lastname: Selbig
authors.forename: Thomas
authors.initials: T
authors.lastname: Lengauer
mesh_terms: D000465:Algorithms; D019380:Anti-HIV Agents / Q000494:pharmacology*; D005075:Biological Evolution; D003198:Computer Simulation; D003430:Cross-Sectional Studies; D024882:Drug Resistance, Viral / Q000235:genetics*; D014644:Genetic Variation / Q000235:genetics; D054303:HIV Reverse Transcriptase / Q000037:antagonists & inhibitors; D015497:HIV-1 / Q000187:drug effects / Q000235:genetics*; D006801:Humans; D007858:Learning; D016013:Likelihood Functions; D008957:Models, Genetic; D016296:Mutagenesis / Q000235:genetics; D009154:Mutation; D010363:Pattern Recognition, Automated; D012815:Signal Processing, Computer-Assisted
chemical_list: D019380:Anti-HIV Agents; D054303:HIV Reverse Transcriptase