Abstract
The first part of the paper briefly overviews the problem of gene and species trees reconciliation with the focus on defining and algorithmic construction of the evolutionary scenario. Basic ideas are discussed for the aspects of mapping definitions, costs of the mapping and evolutionary scenario, imposing time scales on a scenario, incorporating horizontal gene transfers, binarization and reconciliation of polytomous trees, and construction of species trees and scenarios. The review does not intend to cover the vast diversity of literature published on these subjects. Instead, the authors strived to overview the problem of the evolutionary scenario as a central concept in many areas of evolutionary research. The second part provides detailed mathematical proofs for the solutions of two problems: (i) inferring a gene evolution along a species tree accounting for various types of evolutionary events and (ii) trees reconciliation into a single species tree when only gene duplications and losses are allowed. All proposed algorithms have a cubic time complexity and are mathematically proved to find exact solutions. Solving algorithms for problem (ii) can be naturally extended to incorporate horizontal transfers, other evolutionary events, and time scales on the species tree.
Highlights
This section of the paper does not intend to cover the vast diversity of published literature on the problem of trees reconciliation
The authors strived to overview the problem of defining algorithmic construction of the evolutionary scenario as a central concept in many areas of evolutionary research
The evolution of the genome, apart from the mutation process, is an entangled complex of individual and concerted evolutions of genes, their regulations, gene content and arrangement on chromosomes, genetic flows between the genome and intracellular organelles, and so forth. Their evolutionary histories often do not coincide with each other and with patterns of speciation giving the rise to a variety of evolutionary events, such as gene duplications, losses, gains, horizontal transfers, chromosome rearrangements, and others
Summary
This section of the paper does not intend to cover the vast diversity of published literature on the problem of trees reconciliation. An extensive corpus of studies is devoted to the reconstruction of ancestral molecular characters and properties, rather than inferring discrete evolutionary events on the species tree Such can be ancestral sequences, their lengths, primary and secondary regulatory structures, the tree areas with potential genetic transfers, and so forth [55,56,57,58,59]. Deterministic and probabilistic models (in particular, the Gibbs field approach) to reconstruct ancestral sequences and secondary structures are discussed in [60,61,62] presents a dedicated web service These works remain out of the scope, as do studies of the mutation process and various reconciliation applications. The reader is referred to the original cited works for further details
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