Inversion-based genomic signatures

<p>Abstract</p> <p>Background</p> <p>Reconstructing complete ancestral genomes (at least in terms of their gene inventory and arrangement) is attracting much interest due to the rapidly increasing availability of whole genome sequences. While modest successes have been reported for mammalian and even vertebrate genomes, more divergent groups continue to pose a stiff challenge, mostly because current models of genomic evolution support too many choices.</p> <p>Results</p> <p>We describe a novel type of genomic signature based on rearrangements that characterizes evolutionary changes that must be common to all minimal rearrangement scenarios; by focusing on global patterns of rearrangements, such signatures bypass individual variations and sharply restrict the search space. We present the results of extensive simulation studies demonstrating that these signatures can be used to reconstruct accurate ancestral genomes and phylogenies even for widely divergent collections.</p> <p>Conclusion</p> <p>Focusing on genome triples rather than genomes pairs unleashes the full power of evolutionary analysis. Our genomic signature captures shared evolutionary events and thus can form the basis of a robust analysis and reconstruction of evolutionary history.</p

Listing all sorting reversals in quadratic time

We describe an average-case O(n2) algorithm to list all reversals on a signed permutation π that, when applied to π, produce a permutation that is closer to the identity. This algorithm is optimal in the sense that, the time it takes to write the list is Ω(n2) in the worst case

Rapidly Computing the Phylogenetic Transfer Index

Given trees T and T_o on the same taxon set, the transfer index phi(b,T_o) is the number of taxa that need to be ignored so that the bipartition induced by branch b in T is equal to some bipartition in T_o. Recently, Lemoine et al. [Lemoine et al., 2018] used the transfer index to design a novel bootstrap analysis technique that improves on Felsenstein\u27s bootstrap on large, noisy data sets. In this work, we propose an algorithm that computes the transfer index for all branches b in T in O(n log^3 n) time, which improves upon the current O(n^2)-time algorithm by Lin, Rajan and Moret [Lin et al., 2012]. Our implementation is able to process pairs of trees with hundreds of thousands of taxa in minutes and considerably speeds up the method of Lemoine et al. on large data sets. We believe our algorithm can be useful for comparing large phylogenies, especially when some taxa are misplaced (e.g. due to horizontal gene transfer, recombination, or reconstruction errors)

Weighted Minimum-Length Rearrangement Scenarios

We present the first known model of genome rearrangement with an arbitrary real-valued weight function on the rearrangements. It is based on the dominant model for the mathematical and algorithmic study of genome rearrangement, Double Cut and Join (DCJ). Our objective function is the sum or product of the weights of the DCJs in an evolutionary scenario, and the function can be minimized or maximized. If the likelihood of observing an independent DCJ was estimated based on biological conditions, for example, then this objective function could be the likelihood of observing the independent DCJs together in a scenario. We present an O(n^4)-time dynamic programming algorithm solving the Minimum Cost Parsimonious Scenario (MCPS) problem for co-tailed genomes with n genes (or syntenic blocks). Combining this with our previous work on MCPS yields a polynomial-time algorithm for general genomes. The key theoretical contribution is a novel link between the parsimonious DCJ (or 2-break) scenarios and quadrangulations of a regular polygon. To demonstrate that our algorithm is fast enough to treat biological data, we run it on syntenic blocks constructed for Human paired with Chimpanzee, Gibbon, Mouse, and Chicken. We argue that the Human and Gibbon pair is a particularly interesting model for the study of weighted genome rearrangements

Estimating true evolutionary distances under rearrangements, duplications, and losses

Background: The rapidly increasing availability of whole-genome sequences has enabled the study of whole-genome evolution. Evolutionary mechanisms based on genome rearrangements have attracted much attention and given rise to many models; somewhat independently, the mechanisms of gene duplication and loss have seen much work. However, the two are not independent and thus require a unified treatment, which remains missing to date. Moreover, existing rearrangement models do not fit the dichotomy between most prokaryotic genomes (one circular chromosome) and most eukaryotic genomes (multiple linear chromosomes). Results: To handle rearrangements, gene duplications and losses, we propose a new evolutionary model and the corresponding method for estimating true evolutionary distance. Our model, inspired from the DCJ model, is simple and the first to respect the prokaryotic/eukaryotic structural dichotomy. Experimental results on a wide variety of genome structures demonstrate the very high accuracy and robustness of our distance estimator. Conclusions: We give the first robust, statistically based, estimate of genomic pairwise distances based on rearrangements, duplications and losses, under a model that respects the structural dichotomy between prokaryotic and eukaryotic genomes. Accurate and robust estimates in true evolutionary distances should translate into much better phylogenetic reconstructions as well as more accurate genomic alignments, while our new model of genome rearrangements provides another refinement in simplicity and verisimilitude

Heuristics for the inversion median problem

Background: The study of genome rearrangements has become a mainstay of phylogenetics and comparative genomics. Fundamental in such a study is the median problem: given three gene arrangements, find a fourth that minimizes the sum of the evolutionary distances between itself and the given three. Many exact algorithms and heuristics have been developped for the inversion median problem, of which the best known is MGR. Results: We present a unifying framework for median heuristics, which enables us to clarify existing strategies and to place them in a partial ordering. Analysis of this framework leads to a new insight: the best strategies continue to refer to the input data rather than just to updated estimates. Using this insight, we develop a new heuristic for inversion medians that uses input data to the end of its computation and leverages our previous work with DCJ medians. Finally, we present the results of extensive experimentation showing that our new heuristic outperforms all others in accuracy and, especially, in running time: the heuristic typically returns solutions within 1 % of optimal and runs in seconds to minutes even on genomes with 25’000 genes—in contrast, MGR can take days on instances of 200 genes and cannot be used beyond 1’000 genes. Conclusions: Finding good rearrangement medians, in particular inversion medians, had long been regarded as the computational bottleneck in whole-genome studies. Our new heuristic for inversion medians, ASM, which dominates all others in our framework, puts that issue to rest by providing near-optimal solutions within seconds to minutes on even the largest genomes