Minimizing Contradictions on Circular Order of Phylogenic Trees

Abstract

Distance-based approaches to phylogeny use estimations of the evolutionary distance between sequences to reconstruct an evolution tree. If the evolution can be represented by an X-tree, the different sequences can be ordered so that the distance matrix , n i j Y , representing the distance from a leaf n to the path (i, j ), is perfectly ordered meaning that ,After ordering of the sequences, the distance matrix Y i j n , permits to visualize phylogenetic relationships between taxa and to localize deviations from perfect order. The effect of perturbations resulting from lateral gene transfer or crossover can be modeled probabilistically. The order is shown to be quite robust against many perturbations. We have developed algorithms to minimize the level of contradiction in the order of the sequences. These algorithms are tested on the SSU rRNA data for Archaea. The degree of contradiction after optimization is for most taxa quite low. Regions in the taxa space with deviations from perfect order were identifi ed.

A six-parameter space to describe galaxy diversification

“…for any i, j, k n. The best order of a distance matrix is, by definition, the order minimizing the contradiction (Thuillard 2007(Thuillard , 2008. Thuillard & Fraix-Burnet (2009) showed that the perfect order is linked to the convexity of the variables in the parameter space, and is obtained for specific properties of the variables along the order.…”

“…The minimum contradiction analysis (Thuillard 2007, 2008 finds this best order. It is a powerful tool for ascertaining whether the parameters can lead to a tree-like arrangement of the objects (Thuillard & Fraix-Burnet 2009).…”

“…The requirement for the algorithm is that each group must contain at least one object and each object must belong to exactly one group, so there are at most as many groups as there are objects. Partitioning methods are applied (Whitmore 1984;Murtagh 1987;Chattopadhyay & Chattopadhyay 2006, 2007Babu et al 2009;Chattopadhyay et al 2009a;Chattopadhyay et al 2010), if one wishes to classify the objects into K clusters where K is fixed. Cluster centres were chosen based on a group average method, which ensures that the process is almost robust (Milligan 1980).…”

“…Many attempts to apply multivariate clustering methods have been made (e.g. Ellis et al 2005;Chattopadhyay & Chattopadhyay 2006, 2007Chattopadhyay et al , 2008Chattopadhyay et al , 2009aFraix-Burnet et al 2009;Sánchez Almeida et al 2010;Fraix-Burnet et al 2010). Sophisticated statistical tools are used in some areas of astrophysics and are being developed steadily, but multivariate analysis and clustering techniques have not yet been widely applied across the community.…”

Minimum Contradiction Matrices in Whole Genome Phylogenies

“…The corresponding circular order is defined as a perfect order. We have shown with a probabilistic model that perfect order is quite robust against lateral transfer and crossover (Thuillard, 2007). The search for the order minimizing a measure of the deviation from perfect order can be efficiently done with a multi-resolution algorithm (Thuillard, 2001, 2007).…”