The gene evolution model and computing its associated probabilities

Abstract

Phylogeny is both a fundamental tool in biology and a rich source of fascinating modeling and algorithmic problems. Today's wealth of sequenced genomes makes it increasingly important to understand evolutionary events such as duplications, losses, transpositions, inversions, lateral transfers, and domain shuffling. We focus on the gene duplication event, that constitutes a major force in the creation of genes with new function [Ohno 1970;Lynch and Force 2000] and, thereby also, of biodiversity.We introduce the probabilistic gene evolution model, which describes how a gene tree evolves within a given species tree with respect to speciation, gene duplication, and gene loss. The actual relation between gene tree and species tree is captured by a reconciliation, a concept which we generalize for more expressiveness. The model is a canonical generalization of the classical linear birth-death process, obtained by replacing the interval where the process takes place by a tree.For the gene evolution model, we derive efficient algorithms for some associated probability distributions: the probability of a reconciled tree, the probability of a gene tree, the maximum probability reconciliation, the posterior probability of a reconciliation, and sampling reconciliations with respect to the posterior probability. These algorithms provides the basis for several applications, including species tree construction, reconciliation analysis, orthology analysis, biogeography, and host-parasite co-evolution. Arvestad, L. and Lagergren, J., and Sennblad, B. 2009. The gene evolution model and computing its associated probabilities. ACM Reference Format:

Reconciliation With Nonbinary Gene Trees Revisited

“…If D gives a duplication history such that redundant gene copies have the minimum gene loss cost, compared to all other duplication histories with the same mutation cost, then for each i, the speciation history I(g)| D i satisfies: (1). The subtree T (u) below any degree-2 node u cannot be a defect tree.…”

Evolution of Genes Neighborhood within Reconciled Phylogenies: An Ensemble Approach

“…While this Boltzmann ensemble approach has been used for a long time in RNA structure analysis, to the best of our knowledge it is not the case in comparative genomics, where exact probabilistic models have been favoured recently [16,17]. However, probabilistic models still pose computational challenges for large datasets, and so far a probabilistic model does not exist for gene adjacencies, which motivates our work.…”

Complexity Insights of the Minimum Duplication Problem

“…Reconciliation is a widely-investigated problem, and different approaches have been proposed in the past based on the duplication-loss model [5][6][7][8][9][10][11][12][13][14] and also extended to consider later gene transfer [15][16][17][18][19]. Some approaches are based on a probabilistic model that aims to infer how a gene tree evolves within a given species tree [5,6,17].…”

“…Some approaches are based on a probabilistic model that aims to infer how a gene tree evolves within a given species tree [5,6,17].…”