Other criteria can be used to reconcile gene trees to species trees such as the sum of duplications plus losses or, for recently diverged lineages, coalescent depth [ 75].
The algorithm described in [ 70] has a linear time complexity, and, given a polytomous gene tree G, binary species tree S, and their mapping α, searches for a binarization G* of G by first minimizing the total sum of duplications and then the total sum of losses in the obtained set of binarizations.
The total sum of duplications and losses (the "embedding cost") has the minimal value on α among all costs of possible mappings f of gene tree G into species tree S. The embedding cost of mapping α is denoted c; the analogous cost of f is denoted c(f); that is, c = min{ c(f) | f} (where f is a variable).
We ground on an approach to find the tree S by minimizing the total cost of mappings α j of individual gene trees G j into S. Traditionally, this cost is defined basically as a sum of duplications and gaps in each α j.
In pioneer papers [ 2], the cost c0(G S) is defined through the mapping α(G, S) of a given tree G into S basically as a sum of duplications (pairs < x, z>, where α(x)= α z)) and gaps (vertices y, where there is no x for which y= α(x)).
In considering the evolution of the soybean genome, it is noteworthy that all soybean LGs related to three or four Chrs of L. japonicus (LGs C1, D1b, D2, E, G, J, and K) exhibited links with Chr 4. It has been demonstrated that polyoloidy is more than the sum of its gene duplications, since this process duplicates the members of entire regulatory networks.
Total for each subpopulation is a sum of deletions and duplications in each subpopulation The genes affected by CNVRs in all Qataris were evaluated by standard pathway analysis against the KEGG pathway database using the DAVID bioinformatics suite [ 31– 31].
Total deletions and duplications are a sum of CN classes 0, 1 and 3, 4+, respectively.
The score of a reconciliation under this model is the weighted sum of the number of duplications, losses, and transfers : (1) where δ, λ and τ, respectively, are the costs of duplication, loss and transfer.
Museum officials acknowledge the risk of duplication.
