Evolution of Genes Neighborhood within Reconciled Phylogenies: An Ensemble Approach

Abstract

Context: The reconstruction of evolutionary scenarios for whole genomes in terms of genome rearrangements is a fundamental problem in evolutionary and comparative genomics. The DeCo algorithm, recently introduced by Bérard et al., computes parsimonious evolutionary scenarios for gene adjacencies, from pairs of reconciled gene trees. However, as for many combinatorial optimization algorithms, there can exist many co-optimal, or slightly sub-optimal, evolutionary scenarios that deserve to be considered. Contribution:We extend the DeCo algorithm to sample evolutionary scenarios from the whole solution space under the Boltzmann distribution, and also to compute Boltzmann probabilities for specific ancestral adjacencies. Results: We apply our algorithms to a dataset of mammalian gene trees and adjacencies, and observe a significant reduction of the number of syntenic conflicts observed in the resulting ancestral gene adjacencies.

The SCJ Small Parsimony Problem for Weighted Gene Adjacencies

“…Our main contributions are the introduction of the Small Parsimony Problem under the SCJ model with adjacency weights, together with an exact parameterized algorithm for the optimization and sampling versions of the problem. The motivation for this problem is twofold: incorporating sequence signal from aDNA data when it is available, and recent works showing that the reconstruction of ancestral genomes through the independent analysis of adjacencies is an interesting approach [15], [16], [18], [34].…”

“…BðsÞ ¼ e À pðsÞ kT , where kT is a given constant. If we denote the set of all possible evolutionary scenarios for the adjacency fx; yg by Sðx; yÞ, the partition function of the adjacency and its Boltzmann probability are defined as The weight of the adjacency at internal node v is then the sum of the Boltzmann probabilities of all scenarios where the adjacency is present at node v. All such quantities can be computed in polynomial time [16]. Parameter kT is useful to skew the Boltzmann probability distribution: If kT tends to zero, parsimonious scenarios are heavily favored and the Boltzmann probability distribution tends to the uniform distribution over optimal scenarios, while when kT tends to 1, the Boltzmann distribution tends toward the uniform distribution over the whole solution space.…”

“…We compare results of our implementation PHYSCA for different values of a 2 f0; 0:3; 0:5; 0:8; 1g with the tools RINGO [28], MGRA [29], Fitch-SCJ [30], ROCOCO [31], [32] (dense approach for signed adjacencies) and ANGES [33] (adjacencies only). We computed adjacency weights as described in Section 3.7 with the software DeClone [16] and parameter kT 2 f0:1; 1g.…”

“…To weight an adjacency at all internal nodes of the tree, we relied on evolutionary scenarios for each single adjacency, in terms of gain/loss, independently of the other adjacencies (i.e., without considering consistency of ancestral marker orders). We obtain these weights using the software DeClone [16], and we refer to them as DeClone weights. We considered two values of the DeClone parameter kT , 0.1 and 1, the former ensuring that only adjacencies appearing in at least one optimal adjacency scenario have a significant DeClone weight, while the latter samples adjacencies outside of optimal scenarios.…”

“…The contribution of the discarded adjacencies to the objective function is then the sum of their weights. These adjacency weights can e.g., be obtained as probabilities computed by sampling scenarios for each potential adjacency independently [16] or can be based on ancient DNA sequencing data providing direct prior information assigned to certain ancestral nodes. It follows that the phylogenetic framework we present can then also assist in scaffolding fragmented assemblies of aDNA sequencing data [10], [17].…”