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Our results prove that the time-heterogeneous approach produces improved likelihood values with improved branch lengths estimates and more realistic, though not perfect (see below), topology estimates.
While partial or full augmentation of gene sampling generally improved branch support for deep nodes, other nodes at the superfamily level are not robustly supported even with > 14 kb of sequence data (Table 2).
Augmenting data set C with sequence data for 11 genes for just over half the number of taxa greatly improved branch support (all five analyses resulted in > 50% BP; data set C versus D, Table 2).
Using PAML software, the likelihood ratio test was applied to examine the following two hypotheses: (1) the K A / K S ratio was significantly higher in the branch of interest than in the background branch (tests B and D in [ 17]) and (2) positive selection acted on the branch of interest (improved branch site model; test 2 in [ 18]).
The majority of our analyses indicate that increased dataset size results in improved branch length estimates.
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By replacing the lower level linear programs with their KKT conditions, we transform the bilevel MINLP into a single-level nonconvex MINLP, which is further globally optimized using an improved branch-and-refine algorithm.
It deviates in various aspects from the approaches proposed for related rate-maximization problems in[37, 38], e.g., it allows for an optimization over all subcarriers including a non-convex constraint set, and uses improved branching and bounding techniques.
In the present study, we also used an improved branch-site likelihood method to detect positive selection at the amino acid sites [28], [40], [47].
An improved branch-site model A [64], [65] was used to extrapolate the sites under positive selection (dN/dS>1 in one lineage and dN/dS < = 1 in other lineages).
Furthermore, overexpression of DGKβ in the primary cultured hippocampal neurons from KO mice improved branching; the number of branches was restored to the control level (Fig. 7A and B).
PSGs were then identified using the improved branch-site model as implemented in CODEML.
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