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

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

Relative Timing Information and Orthology in Evolutionary Scenarios

Evolutionary scenarios describing the evolution of a family of genes within a collection of species comprise the mapping of the vertices of a gene tree $T$ to vertices and edges of a species tree $S$. The relative timing of the last common ancestors of two extant genes (leaves of $T$) and the last common ancestors of the two species (leaves of $S$) in which they reside is indicative of horizontal gene transfers (HGT) and ancient duplications. Orthologous gene pairs, on the other hand, require that their last common ancestors coincides with a corresponding speciation event. The relative timing information of gene and species divergences is captured by three colored graphs that have the extant genes as vertices and the species in which the genes are found as vertex colors: the equal-divergence-time (EDT) graph, the later-divergence-time (LDT) graph and the prior-divergence-time (PDT) graph, which together form an edge partition of the complete graph. Here we give a complete characterization in terms of informative and forbidden triples that can be read off the three graphs and provide a polynomial time algorithm for constructing an evolutionary scenario that explains the graphs, provided such a scenario exists. We show that every EDT graph is perfect. While the information about LDT and PDT graphs is necessary to recognize EDT graphs in polynomial-time for general scenarios, this extra information can be dropped in the HGT-free case. However, recognition of EDT graphs without knowledge of putative LDT and PDT graphs is NP-complete for general scenarios. In contrast, PDT graphs can be recognized in polynomial-time. We finally connect the EDT graph to the alternative definitions of orthology that have been proposed for scenarios with horizontal gene transfer. With one exception, the corresponding graphs are shown to be colored cographs

Gene Family Histories: Theory and Algorithms

Detailed gene family histories and reconciliations with species trees are a prerequisite for studying associations between genetic and phenotypic innovations. Even though the true evolutionary scenarios are usually unknown, they impose certain constraints on the mathematical structure of data obtained from simple yes/no questions in pairwise comparisons of gene sequences. Recent advances in this field have led to the development of methods for reconstructing (aspects of) the scenarios on the basis of such relation data, which can most naturally be represented by graphs on the set of considered genes. We provide here novel characterizations of best match graphs (BMGs) which capture the notion of (reciprocal) best hits based on sequence similarities. BMGs provide the basis for the detection of orthologous genes (genes that diverged after a speciation event). There are two main sources of error in pipelines for orthology inference based on BMGs. Firstly, measurement errors in the estimation of best matches from sequence similarity in general lead to violations of the characteristic properties of BMGs. The second issue concerns the reconstruction of the orthology relation from a BMG. We show how to correct estimated BMG to mathematically valid ones and how much information about orthologs is contained in BMGs. We then discuss implicit methods for horizontal gene transfer (HGT) inference that focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of an undirected graph, the later-divergence-time (LDT) graph. We explore the mathematical structure of LDT graphs and show how much information about all HGT events is contained in such LDT graphs

Ko Un and the poetics of postcolonial identity

Ko Un is one of South Korea\u27s most important writers of the past 50 years, and a poet whose work provides important insights into crucial linkages between language, identity and community. He lived through, chronicled and critically engaged most of the traumatic events his nation faced during the last century: a brutal colonial occupation by Japan; the division of the peninsula into communist North and capitalist South; an unusually devastating fraternal war; the integration of the divided peninsula into global Cold War politics; periods of authoritarian rule on both sides; and the more recent challenge to promote reconciliation. Some of these episodes challenged the very existence of Korea as a people, nation and state. Ko Un\u27s poetry was part of a larger effort to regain a sense of being and national identity in the face of turmoil, war and globalisation. We argue that by engaging with these highly political issues Ko Un\u27s work provides important clues about how to articulate notions of identity and community in a way that empathetically portrays other people and their identities. In doing so he offers an alternative to the prevailing inside/outside logic that often leads to problematic forms of nationalism. <br /