Reconstructing Gene Trees From Fitch's Xenology Relation

Two genes are xenologs in the sense of Fitch if they are separated by at least one horizontal gene transfer event. Horizonal gene transfer is asymmetric in the sense that the transferred copy is distinguished from the one that remains within the ancestral lineage. Hence xenology is more precisely thought of as a non-symmetric relation: $y$ is xenologous to $x$ if $y$ has been horizontally transferred at least once since it diverged from the least common ancestor of $x$ and $y$. We show that xenology relations are characterized by a small set of forbidden induced subgraphs on three vertices. Furthermore, each xenology relation can be derived from a unique least-resolved edge-labeled phylogenetic tree. We provide a linear-time algorithm for the recognition of xenology relations and for the construction of its least-resolved edge-labeled phylogenetic tree. The fact that being a xenology relation is a heritable graph property, finally has far-reaching consequences on approximation problems associated with xenology relations

On Weighting Schemes for Gene Order Analysis

Gene order analysis aims at extracting phylogenetic information from the comparison of the order and orientation of the genes on the genomes of different species. This can be achieved by computing parsimonious rearrangement scenarios, i.e. to determine a sequence of rearrangements events that transforms one given gene order into another such that the sum of weights of the included rearrangement events is minimal. In this sequence only certain types of rearrangements, given by the rearrangement model, are admissible and weights are assigned with respect to the rearrangement type. The choice of a suitable rearrangement model and corresponding weights for the included rearrangement types is important for the meaningful reconstruction. So far the analysis of weighting schemes for gene order analysis has not been considered sufficiently. In this paper weighting schemes for gene order analysis are considered for two rearrangement models: 1) inversions, transpositions, and inverse transpositions; 2) inversions, block interchanges, and inverse transpositions. For both rearrangement models we determined properties of the weighting functions that exclude certain types of rearrangements from parsimonious rearrangement scenarios

Algorithmen zur Rekonstruktion kophylogenetischer Ereignisse

Das Problem der Rekonstruktion einer gemeinsamen evolutionären Entwicklung zwischen Wirts- und Parasitenspezies ist in der Forschung weit diskutiert. Dabei wird der Komplexität einer solchen Berechnung besondere Bedeutung beigemessen. In dieser Arbeit wird ein algorithmischer Ansatz vorgestellt, welcher auf Basis dynamischer Programmierung eine Rekonstruktion zweier phylogenetischer Stammbäume und einer gegebenen Abbildung von Parasiten auf zugehörige Wirte erzeugt. Grundlage dieser Berechnung ist ein ereignis-basiertes Modell der Koevolution, bei dem jedem Ereignis ein Kostenwert zugeordnet ist. Gesucht wird nach Rekonstruktionen, welche die Gesamtkosten der aufgetretenen Ereignisse minimieren. Es wird eine Vorgehensweise vorgestellt, mit welcher sich die Kosten der Ereignisse automatisch berechnen lassen. Dazu wurde ein Gütemaß entwickelt, um verschiedene Rekonstruktionen bezüglich der bei ihrer Berechnung verwendeten Ereigniskostenverteilung bewerten zu können. Im Gegensatz zu bisherigen Arbeiten unterstützt der vorgestellte Ansatz zudem die Verwendung von Stammbäumen mit mehrfach verzweigenden Knoten. Die algorithmischen Überlegungen wurden in einem Javaprogramm namens DynamicTreeMap umgesetzt.The problem of reconstructing the common evolutionary development between host- and parasite species has been strongly discussed in research. Hereby a special meaning has been attributed to the complexity of such a calculation. In this thesis an algorithmic approach based on dynamic programming will be introduced, that creates a reconstruction of two phylogenetic genealogical trees and a given mapping of parasites on appropriate hosts. The foundation of this calaculation is an event-driven model of coevolution where costs are assigned to each event. The algorithm searches for reconstructions, which minimize the total costs of all occurred events. A method will be introduced which calculates the event-costs automatically. Therefore a quality rate has been developed, to evaluate different reconstructions concerning the used event-costs. Unlike present approaches genealogical trees with multiple branching nodes can be considered. The described approach has been implemented in a java program named DynamicTreeMap

Forbidden Time Travel: Characterization of Time-Consistent Tree Reconciliation Maps

Motivation: In the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels considerably simplifies the problem of reconciling a gene tree T with a species trees S, relative to the reconciliation problem without prior knowledge of the event types. It is well-known that optimal reconciliations in the unlabeled case may violate time-consistency and thus are not biologically feasible. Here we investigate the mathematical structure of the event labeled reconciliation problem with horizontal transfer. Results: We investigate the issue of time-consistency for the event-labeled version of the reconciliation problem, provide a convenient axiomatic framework, and derive a complete characterization of time-consistent reconciliations. This characterization depends on certain weak conditions on the event-labeled gene trees that reflect conditions under which evolutionary events are observable at least in principle. We give an O(|V(T)|log(|V(S)|))-time algorithm to decide whether a time-consistent reconciliation map exists. It does not require the construction of explicit timing maps, but relies entirely on the comparably easy task of checking whether a small auxiliary graph is acyclic. The algorithms are implemented in C++ using the boost graph library and are freely available at https://github.com/Nojgaard/tc-recon. Significance: The combinatorial characterization of time consistency and thus biologically feasible reconciliation is an important step towards the inference of gene family histories with hor- izontal transfer from orthology data, i.e., without presupposed gene and species trees. The fast algorithm to decide time consistency is useful in a broader context because it constitutes an attractive component for all tools that address tree reconciliation problems