The α value was 1.909 and number of invariable sites 0.011.
We call this remarkable topological invariable the connectivity number of P a,b,c,μ,ω) and denote it Ω a,b,c).
To cover the different sizes of these modules, we constructed five controls, four of which are composed of the gene sets with an invariable size, the number of genes in each gene set in the four controls ranging from 20 to 50 in ascending order; while the fifth control consisted of the gene sets with variable size from 20 to 50 which was randomly determined.
A Maximum Likelihood tree was derived using PhyML [ 53] with the following parameters: model, HKY; transition/transversion ratio; estimated; proportion of invariable sites, estimated; number of relative substitution rate categories, 4; gamma distribution parameter, estimated; starting tree, BIONJ; optimize tree topology, yes; optimize branch lengths and rate parameters, yes.
Next, a maximum likelihood tree is built from the alignment by PHYML (substitution model: HKY; Transition/transversion ratio∶4.0; Proportion of invariable sites: program estimated; Number of substitution rate categories: 1; Gamma distribution parameter∶1.0; Starting tree: BIONJ distance-based tree; No starting tree optimization) [41].
The alpha value and number of invariable sites were calculated from the datasets.
ML trees were drawn with PhyML using model JTT, proportion of invariable sites = 0, number of substitution rate categories = 6 and estimating the gamma distribution parameter.
Phylogenies were subsequently derived using the program PhyML [ 77] using the HKY model and an estimated number of invariable sites with four substitution rate categories.
Phylogenies were subsequently derived using the program PHYML [ 45] using the JTT model and an estimated number of invariable sites with four substitution rate categories.
Both alignments were also used to construct bootstrapped maximum likelihood (ML) trees using PhyML (Guindon and Gascuel 2003) under the LG + I + G model with four substitution rate categories, estimated gamma distribution parameter, and number of invariable sites employing 100 bootstrap replicates.
