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Table 1 Flow processes and major centrality measures Duplication Transfer Parallel duplication Serial duplication Geodesics Closeness Closeness Betweenness Closeness Paths Degree Closeness Trails Degree Closeness Walks Degree Eigenvector PageRank *Adapted from Borgatti [36], p.63.
Let PΔ, PΘ and Ploss denote the costs associated with duplication, transfer and loss events respectively.
In the context of gene family evolution, the two trees are the gene tree and the species tree, and in the well-studied Duplication-Transfer-Loss model (DTL), the events are speciation, duplication, transfer and loss.
Algorithms that capture duplication, transfer and ILS in a single, integrated model are of increasing importance (Degnan and Rosenberg, 2009).
This problem of gene tree species tree reconciliation by duplication, transfer and loss simultaneously is referred to as the duplication TL (DTL) reconciliation problem.
In our DTLI model, divergence in a gene tree arises through one of four events: duplication, transfer, speciation and deep coalescence.
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Exact algorithms with exponential time complexity have been presented for the duplication-transfer (DT) (Tofigh et al., 2011) and duplication-transfer-loss (DTL) models (David and Alm, 2011), under a parsimony criterion.
This reconciliation problem is referred to as duplication-transfer-loss (DTL) reconciliation and has been extensively studied in the literature.
Next, we define what constitutes a valid DTL reconciliation; specifically, we define a Duplication-Transfer-Loss scenario (DTL-scenario) (Bansal et al., 2012; Tofigh et al., 2011) for T and S that characterizes the mappings of T into S that constitute a biologically valid reconciliation.
MowgliNNI progressively reduced the number of predicted duplications, transfers and losses as the threshold increased.
This is achieved by studying the proportion of true positive (TP), false positive (FP) and false negative (FN) separately for duplications, transfers and losses [ 2].
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