Abstract
Hybridization and horizontal gene transfer are two major mechanisms of reticulate evolution. Both of them allow for a creation of new species by recombining genes or chromosomes of the existing organisms. An effective detection of hybridization events and estimation of their evolutionary significance have been recognized as main hurdles of the modern computational biology. In this article, we underline common features characterizing horizontal gene transfer and hybridization phenomena and describe a new algorithm for the inference and validation of the diploid hybridization events, when the newly created hybrid has the same number of chromosomes as the parent species. A simulation study was carried out to examine the ability of the proposed algorithm to infer correct hybrids and their parents in various practical situations.
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Appendix
Appendix
This appendix includes the definition of the subtree constraint (Fig. 10) used in the hybrid detection algorithm (Algorithm 1). This constraint, originally formulated in [6], allows one to take into account all evolutionary rules that should be satisfied when inferring horizontal gene transfers. This appendix also includes Theorems 2 and 3 allowing one to select optimal transfers during the execution of the hybrid detection algorithm (Algorithm 1) (see [6] for their proofs).
Subtree constraint: the transfer between the branches (x, y) and (z, w) in the species tree T is allowed if and only if the cluster rooted by the branch (x, a), and regrouping both affected subtrees, is present in the gene tree. A single tree branch is depicted by a plane line and a path is depicted by a wavy line
Theorem 2.
If the newly formed subtree Sub yw resulting from the HGT (horizontal gene transfer) is present in the gene tree T′, and the bipartition vector associated with the branch (x,x 1 ) in the transformed species tree T 1 (Fig. 11 ) is present in the bipartition table of T′, then the HGT from (x,y) to (z,w), transforming T into T 1 , is a part of a minimum-cost HGT scenario transforming T into T′ and satisfying the subtree constraint.
HGT from the branch (x,y) to the branch (z,w) is a part of a minimum-cost HGT scenario transforming the species tree T into the gene tree T′ if the bipartition corresponding to the branch (x,x 1) in the transformed species tree T 1 is present in the bipartition table of T′ and the subtree Sub yw is present in T′
Theorem 3.
If the newly formed subtree Sub yw resulting from the HGT is present in the gene tree T′, and all the bipartition vectors associated with the branches of the path (x′,z′) in the transformed species tree T 1 (Fig. 12 ) are present in the bipartition table of T′, and the path (x′,z′) in T 1 consists of at least three branches, then the HGT from (x,y) to (z,w), transforming T into T 1 , is a part of any minimum-cost HGT scenario transforming T into T′ and satisfying the subtree constraint.
HGT from the branch (x,y) to the branch (z,w) is a part of any minimum-cost HGT scenario transforming the species tree T into the gene tree T′ if all the bipartitions corresponding to the branches of the path (x′,z′) in the transformed species tree T 1 are present in the bipartition table of T′ and the subtree Sub yw is present in the tree T′
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Makarenkov, V., Boc, A., Legendre, P. (2014). A New Algorithm for Inferring Hybridization Events Based on the Detection of Horizontal Gene Transfers. In: Aleskerov, F., Goldengorin, B., Pardalos, P. (eds) Clusters, Orders, and Trees: Methods and Applications. Springer Optimization and Its Applications, vol 92. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0742-7_17
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DOI: https://doi.org/10.1007/978-1-4939-0742-7_17
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