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.

Evolution on distributive lattices

“…The event poset E in Figure 1 has five linear extensions π: π f (π) (1, 2, 3, 4) (1 + f 1000 )(1 + f 1100 )(1 + f 1110 ) (1,2,4,3) (1 + f 1000 )(1 + f 1100 )f 1101 (2,1,3,4) f 0100 (1 + f 1100 )(1 + f 1110 ) (2,1,4,3) f 0100 (1 + f 1100 )f 1101 (2, 4, 1, 3) (1 + f 0100 )f 0101 (1 + f 1101 )…”

“…We will assume throughout that all φ g ≡ φ are equal. If we assume, in addition, that the resistance landscape is constant on G\{0,1}, with r g ≡ r, then the substitution (11) turns the risk polynomial into a rational function in φ, D, and r. For example, for ritonavir, this rational function is (15φ 2 r 2 + 10φDr + 10φr 2 + D 2 + 2Dr + r 2 )(φr + D + r) 4 (D + r) 6 .…”

“…These statistical models can be used to infer the genotype space from given data. For conjunctive Bayesian networks we recover the distributive lattice of order ideals in E. Of particular interest is the case where E is a directed forest: here the Bayesian network is a mutagenetic tree model [3,4]. The application of our methods to the development of PI resistance in HIV is presented in Section 5.…”

Hyperdiploidy defines a distinct cytogenetic entity of meningiomas

“…The weight of the star-like tree thus indicates the proportion of tumors whose progression is not described by the other estimated components. Oncogenetic trees mixture models can be estimated from data consisting of genetic patterns with an Expectation-Maximization algorithm introduced by Beerenwinkel et al [23,24].…”

Discovering human immunodeficiency virus mutational pathways using temporal Bayesian networks

“…Finally, in [14], the order of appearance of resistance mutations in reverse transcriptase was assessed. In order to overcome the scarce amount of longitudinal data available for patients under the same antiretroviral regimen, the authors used large sets of cross-sectional data.…”