True Evolutionary Distance Research Articles

Estimation of the true evolutionary distance under the fragile breakage model

BackgroundThe ability to estimate the evolutionary distance between extant genomes plays a crucial role in many phylogenomic studies. Often such estimation is based on the parsimony assumption, implying that the distance between two genomes can be estimated as the rearrangement distance equal the minimal number of genome rearrangements required to transform one genome into the other. However, in reality the parsimony assumption may not always hold, emphasizing the need for estimation that does not rely on the rearrangement distance. The distance that accounts for the actual (rather than minimal) number of rearrangements between two genomes is often referred to as the true evolutionary distance. While there exists a method for the true evolutionary distance estimation, it however assumes that genomes can be broken by rearrangements equally likely at any position in the course of evolution. This assumption, known as the random breakage model, has recently been refuted in favor of the more rigorous fragile breakage model postulating that only certain “fragile” genomic regions are prone to rearrangements.ResultsWe propose a new method for estimating the true evolutionary distance between two genomes under the fragile breakage model. We evaluate the proposed method on simulated genomes, which show its high accuracy. We further apply the proposed method for estimation of evolutionary distances within a set of five yeast genomes and a set of two fish genomes.ConclusionsThe true evolutionary distances between the five yeast genomes estimated with the proposed method reveals that some pairs of yeast genomes violate the parsimony assumption. The proposed method further demonstrates that the rearrangement distance between the two fish genomes underestimates their evolutionary distance by about 20%. These results demonstrate how drastically the two distances can differ and justify the use of true evolutionary distance in phylogenomic studies.

Twisted trees and inconsistency of tree estimation when gaps are treated as missing data – The impact of model mis-specification in distance corrections

Statistically consistent estimation of phylogenetic trees or gene trees is possible if pairwise sequence dissimilarities can be converted to a set of distances that are proportional to the true evolutionary distances. Susko et al. (2004) reported some strikingly broad results about the forms of inconsistency in tree estimation that can arise if corrected distances are not proportional to the true distances. They showed that if the corrected distance is a concave function of the true distance, then inconsistency due to long branch attraction will occur. If these functions are convex, then two “long branch repulsion” trees will be preferred over the true tree – though these two incorrect trees are expected to be tied as the preferred true. Here we extend their results, and demonstrate the existence of a tree shape (which we refer to as a “twisted Farris-zone” tree) for which a single incorrect tree topology will be guaranteed to be preferred if the corrected distance function is convex. We also report that the standard practice of treating gaps in sequence alignments as missing data is sufficient to produce non-linear corrected distance functions if the substitution process is not independent of the insertion/deletion process. Taken together, these results imply inconsistent tree inference under mild conditions. For example, if some positions in a sequence are constrained to be free of substitutions and insertion/deletion events while the remaining sites evolve with independent substitutions and insertion/deletion events, then the distances obtained by treating gaps as missing data can support an incorrect tree topology even given an unlimited amount of data.

DISTANCE-BASED PHYLOGENETIC ALGORITHMS: NEW INSIGHTS AND APPLICATIONS

Phylogenetic methods have recently been rediscovered in several interesting areas among which immunodynamics, epidemiology and many branches of evolutionary dynamics. In many interesting cases the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence, a divergence arises between the true evolutionary distances and the distances between pairs of taxa as inferred from the available data, making the phylogenetic reconstruction a challenging problem. Mathematically this divergence translates in the non-additivity of the actual distances between taxa and the quest for new algorithms able to efficiently cope with these effects is wide open. In distance-based reconstruction methods, two properties of additive distances were extensively exploited as antagonist criteria to drive phylogeny reconstruction: on the one hand a local property of quartets, i.e. sets of four taxa in a tree, the four-point condition; on the other hand, a recently proposed formula that allows to write the tree length as a function of the distances between taxa, the Pauplin's formula. A deeper comprehension of the effects of the non-additivity on the inspiring principles of the existing reconstruction algorithms is thus of paramount importance. In this paper we present a comparative analysis of the performances of the most important distance-based phylogenetic algorithms. We focus in particular on the dependence of their performances on two main sources of non-additivity: back-mutation processes and horizontal transfer processes. The comparison is carried out in the framework of a set of generative algorithms for phylogenies that incorporate non-additivity in a tunable way.

A Stochastic Local Search Algorithm for Distance-Based Phylogeny Reconstruction

In many interesting cases, the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence, a divergence arises between the true evolutionary distances and the differences between pairs of taxa as inferred from available data, making the phylogenetic reconstruction a challenging problem. Mathematically, this divergence translates in a loss of additivity of the actual distances between taxa. In distance-based reconstruction methods, two properties of additive distances have been extensively exploited as antagonist criteria to drive phylogeny reconstruction: On the one hand, a local property of quartets, that is, sets of four taxa in a tree, the four-points condition; on the other hand, a recently proposed formula that allows to write the tree length as a function of the distances between taxa, Pauplin's formula. Here, we introduce a new reconstruction scheme that exploits in a unified framework both the four-points condition and the Pauplin's formula. We propose, in particular, a new general class of distance-based Stochastic Local Search algorithms, which reduces in a limit case to the minimization of Pauplin's length. When tested on artificially generated phylogenies, our Stochastic Big-Quartet Swapping algorithmic scheme significantly outperforms state-of-art distance-based algorithms in cases of deviation from additivity due to high rate of back mutations. A significant improvement is also observed with respect to the state-of-art algorithms in the case of high rate of horizontal transfer.

Estimating true evolutionary distances under rearrangements, duplications, and losses

BackgroundThe 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).ResultsTo 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.ConclusionWe 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.

Genome rearrangements with duplications

BackgroundFinding sequences of evolutionary operations that transform one genome into another is a classical problem in comparative genomics. While most of the genome rearrangement algorithms assume that there is exactly one copy of each gene in both genomes, this does not reflect the biological reality very well - most of the studied genomes contain duplicated gene content, which has to be removed before applying those algorithms. However, dealing with unequal gene content is a very challenging task, and only few algorithms allow operations like duplications and deletions, especially if the duplicated or deleted segments are of arbitrary size.ResultsWe recently proposed a heuristic algorithm for sorting unichromosomal genomes by reversals, block interchanges, tandem duplications, and deletions. In this paper, we extend this approach to multichromosomal genomes. We are now able to sort a multichromosomal ancestral genome into a genome of a descendant by a large set of different operations, including tandem duplications and deletions of segments of arbitrary size.ConclusionExperimental results show that our algorithm finds sorting sequences that have a weight close to the true evolutionary distance.

Sorting by reversals, block interchanges, tandem duplications, and deletions

BackgroundFinding sequences of evolutionary operations that transform one genome into another is a classic problem in comparative genomics. While most of the genome rearrangement algorithms assume that there is exactly one copy of each gene in both genomes, this does not reflect the biological reality very well – most of the studied genomes contain duplicated gene content, which has to be removed before applying those algorithms. However, dealing with unequal gene content is a very challenging task, and only few algorithms allow operations like duplications and deletions. Almost all of these algorithms restrict these operations to have a fixed size.ResultsIn this paper, we present a heuristic algorithm to sort an ancestral genome (with unique gene content) into a genome of a descendant (with arbitrary gene content) by reversals, block interchanges, tandem duplications, and deletions, where tandem duplications and deletions are of arbitrary size.ConclusionExperimental results show that our algorithm finds sorting sequences that are close to an optimal sorting sequence when the ancestor and the descendant are closely related. The quality of the results decreases when the genomes get more diverged or the genome size increases. Nevertheless, the calculated distances give a good approximation of the true evolutionary distances.

Estimating true evolutionary distances under the DCJ model

Motivation: Modern techniques can yield the ordering and strandedness of genes on each chromosome of a genome; such data already exists for hundreds of organisms. The evolutionary mechanisms through which the set of the genes of an organism is altered and reordered are of great interest to systematists, evolutionary biologists, comparative genomicists and biomedical researchers. Perhaps the most basic concept in this area is that of evolutionary distance between two genomes: under a given model of genomic evolution, how many events most likely took place to account for the difference between the two genomes?Results: We present a method to estimate the true evolutionary distance between two genomes under the ‘double-cut-and-join’ (DCJ) model of genome rearrangement, a model under which a single multichromosomal operation accounts for all genomic rearrangement events: inversion, transposition, translocation, block interchange and chromosomal fusion and fission. Our method relies on a simple structural characterization of a genome pair and is both analytically and computationally tractable. We provide analytical results to describe the asymptotic behavior of genomes under the DCJ model, as well as experimental results on a wide variety of genome structures to exemplify the very high accuracy (and low variance) of our estimator. Our results provide a tool for accurate phylogenetic reconstruction from multichromosomal gene rearrangement data as well as a theoretical basis for refinements of the DCJ model to account for biological constraints.Availability: All of our software is available in source form under GPL at http://lcbb.epfl.chContact: bernard.moret@epfl.ch

Approximating the true evolutionary distance between two genomes

As more and more genomes are sequenced, evolutionary biologists are becoming increasingly interested in evolution at the level of whole genomes, in scenarios in which the genome evolves through insertions, duplications, deletions, and movements of genes along its chromosomes. In the mathematical model pioneered by Sankoff and others, a unichromosomal genome is represented by a signed permutation of a multiset of genes; Hannenhalli and Pevzner showed that the edit distance between two signed permutations of the same set can be computed in polynomial time when all operations are inversions. El-Mabrouk extended that result to allow deletions and a limited form of insertions (which forbids duplications); in turn we extended it to compute a nearly optimal edit sequence between an arbitrary genome and the identity permutation. In this paper we generalize our approach to compute distances between two arbitrary genomes, but focus on approximating the true evolutionary distance rather than the edit distance. We present experimental results showing that our algorithm produces excellent estimates of the true evolutionary distance up to a (high) threshold of saturation; indeed, the distances thus produced are good enough to enable the simple neighbor-joining procedure to reconstruct our test trees with high accuracy.

Reconstructing Chromosomal Evolution

Chromosomes evolve through genome rearrangement events, including inversions, transpositions, and inverted transpositions, that change the order and strandedness of genes within chromosomes. In this paper we present a method for estimating evolutionary histories for chromosomes based upon such events. The fundamental mathematical challenge of our approach is to estimate the true evolutionary distance between every pair of chromosomes, where the true evolutionary distance is the number of rearrangement events that took place in the evolutionary history between the chromosomes. We present two techniques, Exact- and Approx-IEBP, for estimating true evolutionary distances and prove guarantees about the accuracy of these techniques under a very general stochastic model of chromosomal evolution. We then show how we can use these estimated distances to obtain highly accurate estimates of chromosomal evolutionary history, significantly improving upon the previous best techniques.