Fast algorithm to reconstruct a species supertree from a set of protein trees

Abstract

The problem of reconstructing a species supertree from a given set of protein, gene, and regulatory site trees is the subject of this study. Under the traditional formulation, this problem is proven to be NP hard. We propose a reformulation: to seek for a supertree, most of the clades of which contribute to the original protein trees. In such a variant, the problem seems to be biologically natural and a fast algorithm can be developed for its solution. The algorithm was tested on artificial and biological sets of protein trees, and it proved to be efficient even under the assumption of horizontal gene transfer. When horizontal transfer is not allowed, the algorithm correctness is proved mathematically; the time necessary for repeating the algorithm is assessed, and, in the worst case scenario, it is of the order n 3 ⋅ |V 0 | 3 , where n is the number of gene trees and |V 0 | is the number of tree species. Our software for supertree construction, examples of computations, and instructions can be freely accessed at

Cubic time algorithms of amalgamating gene trees and building evolutionary scenarios

“…Trees contain 50,932 leaves in total. The method used to generate gene trees on a given species tree is described in [8], p. 166. As mentioned below, the procedure of trees simulation along a topology needs further study and justification.…”

“…Namely, the supertree S is sought for as a global minimum of (1) but S runs over a set of such species trees that mostly contain clades present in input trees G j , [3,7,8]. A set of species names assigned to leaves of a subtree in G j with the root v is called a clade (of vertex v in G j ) and denoted by cl ( v ).…”

“…A relevant biological discussion of our approach is provided in [8]. The mapping cost in [3] is similar to the cost from [2] in the case of standard event set.…”

“…A rigorous comparison using artificial data implies having a sound algorithm to simulate gene trees on a known species tree topology. This problem needs further research and justification, however a particular algorithm was proposed in [8]. …”

Reconciliation of Gene and Species Trees

“…Important information contained in the discrepancies between these evolutions can be extracted and studied with the methods of trees reconciliation. Knowledge of ancestral genomic events provides efficient instruments in a range of fields, like establishing orthology/paralogy relationships between gene families [ 11 – 14 ], functional gene annotations [ 15 – 18 ], reconstruction of ancestral genes and genomes and their dating [ 19 , 20 ], accurate reconstruction of gene and species trees [ 18 , 21 – 27 ], construction of phylogenies based on whole genome data [ 22 , 23 ], event-based reconstruction of coevolution [ 28 ] and its applications in ecology and biogeography [ 29 – 31 ], phylogenetic approaches to predict protein interactions [ 32 ], and so forth. A particularly intriguing problem is the coevolution of species, genes, and their regulatory systems, including binding sites, protein and RNA factors, DNA and RNA secondary structures, and RNA triplexes, which is poorly understood even in its statement.…”