BACKGROUND: In a previous study we demonstrated that co-evolutionary information can be utilized for improving the accuracy of ancestral gene content reconstruction. To this end, we defined a new computational problem, the Ancestral Co-Evolutionary (ACE) problem, and developed algorithms for solving it. RESULTS: In the current paper we generalize our previous study in various ways. First, we describe new efficient computational approaches for solving the ACE problem. The new approaches are based on reductions to classical methods such as linear programming relaxation, quadratic programming, and min-cut. Second, we report new computational hardness results related to the ACE, including practical cases where it can be solved in polynomial time.Third, we generalize the ACE problem and demonstrate how our approach can be used for inferring parts of the genomes of non-ancestral organisms. To this end, we describe a heuristic for finding the portion of the genome ('dominant set') that can be used to reconstruct the rest of the genome with the lowest error rate. This heuristic utilizes both evolutionary information and co-evolutionary information.We implemented these algorithms on a large input of the ACE problem (95 unicellular organisms, 4,873 protein families, and 10, 576 of co-evolutionary relations), demonstrating that some of these algorithms can outperform the algorithm used in our previous study. In addition, we show that based on our approach a 'dominant set' cab be used reconstruct a major fraction of a genome (up to 79%) with relatively low error-rate (e.g. 0.11). We find that the 'dominant set' tends to include metabolic and regulatory genes, with high evolutionary rate, and low protein abundance and number of protein-protein interactions. CONCLUSIONS: The ACE problem can be efficiently extended for inferring the genomes of organisms that exist today. In addition, it may be solved in polynomial time in many practical cases. Metabolic and regulatory genes were found to be the most important groups of genes necessary for reconstructing gene content of an organism based on other related genomes.

MOTIVATION: The evolution of viruses is very rapid and in addition to local point mutations (insertion, deletion, substitution) it also includes frequent recombinations, genome rearrangements and horizontal transfer of genetic materials (HGTS). Evolutionary analysis of viral sequences is therefore a complicated matter for two main reasons: First, due to HGTs and recombinations, the right model of evolution is a network and not a tree. Second, due to genome rearrangements, an alignment of the input sequences is not guaranteed. These facts encourage developing methods for inferring phylogenetic networks that do not require aligned sequences as input. RESULTS: In this work, we present the first computational approach which deals with both genome rearrangements and horizontal gene transfers and does not require a multiple alignment as input. We formalize a new set of computational problems which involve analyzing such complex models of evolution. We investigate their computational complexity, and devise algorithms for solving them. Moreover, we demonstrate the viability of our methods on several synthetic datasets as well as four biological datasets. AVAILABILITY: The code is available from the authors upon request.