On Exploring Genome Rearrangement Phylogenetic Patterns

The study of genome rearrangement is much harder than the corresponding problems on DNA and protein sequences, because of the occurrences of numerous combinatorial structures. By explicitly exploring these combinatorial structures, the recently developed adequate subgraph theory shows that a family of these structures, adequate subgraphs, are informative in finding the optimal solutions to the rearrangement median problem. Its extension gives rise to the tree scoring method GASTS, which provides quick and accurate estimation of the number of rearrangement events, for any given topology. With a similar motivation, this paper discusses and provides solid but somewhat initial results, on combinatorial structures that are informative in phylogenetic inference. These structures, called rearrangement phylogenetic patterns, provide more insights than algorithmic approaches, and may provide statistical significance for inferred phylogenies and lead to efficient and robust phylogenetic inference methods on large sets of taxa. We explore rearrangement phylogenetic patterns with respect to both the breakpoint distance and the DCJ distance. The latter has a simple formulation and well approximates other edit distances. On four genomes, we prove that a contrasting shared adjacency, where a gene forms one adjacency in two genomes and a different adjacency in the other two genomes, is a rearrangement phylogenetic pattern. Phylogenetic inferences based on the numbers of this pattern, are very accurate and robust against short internal edges, tested on 55,000 datasets simulated by random inversions. Further analysis shows that the numbers of this pattern well explain the variations in the number of rearrangement events over different topologies.