The Orthology Road: Theory and Methods in Orthology Analysis

The evolution of biological species depends on changes in genes. Among these changes are the gradual accumulation of DNA mutations, insertions and deletions, duplication of genes, movements of genes within and between chromosomes, gene losses and gene transfer. As two populations of the same species evolve independently, they will eventually become reproductively isolated and become two distinct species. The evolutionary history of a set of related species through the repeated occurrence of this speciation process can be represented as a tree-like structure, called a phylogenetic tree or a species tree. Since duplicated genes in a single species also independently accumulate point mutations, insertions and deletions, they drift apart in composition in the same way as genes in two related species. The divergence of all the genes descended from a single gene in an ancestral species can also be represented as a tree, a gene tree that takes into account both speciation and duplication events. In order to reconstruct the evolutionary history from the study of extant species, we use sets of similar genes, with relatively high degree of DNA similarity and usually with some functional resemblance, that appear to have been derived from a common ancestor. The degree of similarity among different instances of the “same gene” in different species can be used to explore their evolutionary history via the reconstruction of gene family histories, namely gene trees. Orthology refers specifically to the relationship between two genes that arose by a speciation event, recent or remote, rather than duplication. Comparing orthologous genes is essential to the correct reconstruction of species trees, so that detecting and identifying orthologous genes is an important problem, and a longstanding challenge, in comparative and evolutionary genomics as well as phylogenetics. A variety of orthology detection methods have been devised in recent years. Although many of these methods are dependent on generating gene and/or species trees, it has been shown that orthology can be estimated at acceptable levels of accuracy without having to infer gene trees and/or reconciling gene trees with species trees. Therefore, there is good reason to look at the connection of trees and orthology from a different angle: How much information about the gene tree, the species tree, and their reconciliation is already contained in the orthology relation among genes? Intriguingly, a solution to the first part of this question has already been given by Boecker and Dress [Boecker and Dress, 1998] in a different context. In particular, they completely characterized certain maps which they called symbolic ultrametrics. Semple and Steel [Semple and Steel, 2003] then presented an algorithm that can be used to reconstruct a phylogenetic tree from any given symbolic ultrametric. In this thesis we investigate a new characterization of orthology relations, based on symbolic ultramterics for recovering the gene tree. According to Fitch’s definition [Fitch, 2000], two genes are (co-)orthologous if their last common ancestor in the gene tree represents a speciation event. On the other hand, when their last common ancestor is a duplication event, the genes are paralogs. The orthology relation on a set of genes is therefore determined by the gene tree and an “event labeling” that identifies each interior vertex of that tree as either a duplication or a speciation event. In the context of analyzing orthology data, the problem of reconciling event-labeled gene trees with a species tree appears as a variant of the reconciliation problem where genes trees have no labels in their internal vertices. When reconciling a gene tree with a species tree, it can be assumed that the species tree is correct or, in the case of a unknown species tree, it can be inferred. Therefore it is crucial to know for a given gene tree whether there even exists a species tree. In this thesis we characterize event-labelled gene trees for which a species tree exists and species trees to which event-labelled gene trees can be mapped. Reconciliation methods are not always the best options for detecting orthology. A fundamental problem is that, aside from multicellular eukaryotes, evolution does not seem to have conformed to the descent-with-modification model that gives rise to tree-like phylogenies. Examples include many cases of prokaryotes and viruses whose evolution involved horizontal gene transfer. To treat the problem of distinguishing orthology and paralogy within a more general framework, graph-based methods have been proposed to detect and differentiate among evolutionary relationships of genes in those organisms. In this work we introduce a measure of orthology that can be used to test graph-based methods and reconciliation methods that detect orthology. Using these results a new algorithm BOTTOM-UP to determine whether a map from the set of vertices of a tree to a set of events is a symbolic ultrametric or not is devised. Additioanlly, a simulation environment designed to generate large gene families with complex duplication histories on which reconstruction algorithms can be tested and software tools can be benchmarked is presented