An important issue in evolutionary molecular biology is to discover genomic duplication episodes and their correspondence to the species tree. Existing approaches vary in the two fundamental aspects: the choice of evolutionary scenarios that model allowed locations of duplications in the species tree, and the rules of clustering gene duplications from gene trees into a single multiple duplication event. Here we study the method of clustering called minimum episodes for several models of allowed evolutionary scenarios with a focus on interval models in which every gene duplication has an interval consisting of allowed locations in the species tree. We present mathematical foundations for general genomic duplication problems. Next, we propose the first linear time and space algorithm for minimum episodes clustering jointly for any interval model and the algorithm for the most general model in which every evolutionary scenario is allowed. We also present a comparative study of different models of genomic duplication based on simulated and empirical datasets. We provided algorithms and tools that could be applied to solve efficiently minimum episodes clustering problems. Our comparative study helps to identify which model is the most reasonable choice in inferring genomic duplication events.

The duplication-loss-coalescence (DLC) parsimony model is invaluable for analyzing the complex scenarios of concurrent duplication loss and deep coalescence events in the evolution of gene families. However, inferring such scenarios for already moderately sized families is prohibitive owing to the computational complexity involved. To overcome this stringent limitation, we make the first step by describing a flexible integer linear programming (ILP) formulation for inferring DLC evolutionary scenarios. Then, to make the DLC model more scalable, we introduce four sensibly constrained versions of the model and describe modified versions of our ILP formulation reflecting these constraints. Our simulation studies showcase that our constrained ILP formulations compute evolutionary scenarios that are substantially larger than scenarios computable under our original ILP formulation and the original dynamic programming algorithm by Wu et al. Furthermore, scenarios computed under our constrained DLC models are remarkably accurate compared with corresponding scenarios under the original DLC model, which we also confirm in an empirical study with thousands of gene families.

BackgroundDiscovering the location of gene duplications and multiple gene duplication episodes is a fundamental issue in evolutionary molecular biology. The problem introduced by Guigó et al. in 1996 is to map gene duplication events from a collection of rooted, binary gene family trees onto theirs corresponding rooted binary species tree in such a way that the total number of multiple gene duplication episodes is minimized. There are several models in the literature that specify how gene duplications from gene families can be interpreted as one duplication episode. However, in all duplication episode problems gene trees are rooted. This restriction limits the applicability, since unrooted gene family trees are frequently inferred by phylogenetic methods.ResultsIn this article we show the first solution to the open problem of episode clustering where the input gene family trees are unrooted. In particular, by using theoretical properties of unrooted reconciliation, we show an efficient algorithm that reduces this problem into the episode clustering problems defined for rooted trees. We show theoretical properties of the reduction algorithm and evaluation of empirical datasets.ConclusionsWe provided algorithms and tools that were successfully applied to several empirical datasets. In particular, our comparative study shows that we can improve known results on genomic duplication inference from real datasets.

Transposable elements (TEs) can be found in virtually all known genomes; plant genomes are exceptionally rich in this kind of dispersed repetitive sequences. Current knowledge on TE proliferation dynamics places them among the main forces of molecular evolution. Therefore efficient tools to analyze TE distribution in genomes are needed that would allow for comparative genomics studies and for studying TE dynamics in a genome. This was our main motivation underpinning TIRfinder construction—an efficient tool for mining class II TEs carrying terminal inverted repeats. TIRfinder takes as an input a genomic sequence and information on structural properties of a TE family, and identifies all TEs in the genome showing the desired structural characteristics. The efficiency and small memory requirements of our approach stem from the use of suffix trees to identify all DNA segments surrounded by user-specified terminal inverse repeats (TIR) and target site duplications (TSD) which together constitute a mask. On the other hand, the flexibility of the notion of the TIR/TSD mask makes it possible to use the tool for de novo detection. The main advantages of TIRfinder are its speed, accuracy and convenience of use for biologists. A web-based interface is freely available at http://bioputer.mimuw.edu.pl/tirfindertool/.

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