From pairs of most similar sequences to phylogenetic best matches

Background Many of the commonly used methods for orthology detection start from mutually most similar pairs of genes (reciprocal best hits) as an approximation for evolutionary most closely related pairs of genes (reciprocal best matches). This approximation of best matches by best hits becomes exact for ultrametric dissimilarities, i.e., under the Molecular Clock Hypothesis. It fails, however, whenever there are large lineage specific rate variations among paralogous genes. In practice, this introduces a high level of noise into the input data for best-hit-based orthology detection methods. Results If additive distances between genes are known, then evolutionary most closely related pairs can be identified by considering certain quartets of genes provided that in each quartet the outgroup relative to the remaining three genes is known. A priori knowledge of underlying species phylogeny greatly facilitates the identification of the required outgroup. Although the workflow remains a heuristic since the correct outgroup cannot be determined reliably in all cases, simulations with lineage specific biases and rate asymmetries show that nearly perfect results can be achieved. In a realistic setting, where distances data have to be estimated from sequence data and hence are noisy, it is still possible to obtain highly accurate sets of best matches. Conclusion Improvements of tree-free orthology assessment methods can be expected from a combination of the accurate inference of best matches reported here and recent mathematical advances in the understanding of (reciprocal) best match graphs and orthology relations. Availability Accompanying software is available at https://github.com/david-schaller/AsymmeTree

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