The null distributions of statistic under the competitive hypothesis are generated by gene sampling; the null distributions under the self-contained hypothesis are generated by subject-sampling.
Nestedness analyses were run using the nestedness function as implemented in the R library Bipartite57 and the null model 3 as suggested by Rodríguez‐Gironés and Santamaría64, which is a constrained null model that accounts for the frequency of genera (column totals) and the genus richness of fossil sites (row totals) while sampling the null space uniformly, which minimises type I and II errors.
The mean maps were summated to a joint likelihood map and 10,000 permutations used to sample the null distribution and test the probability that any given voxel of the joint likelihood map was significant.
The identification of metabolic fluxes obeying the steady-state condition, <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0012383.e005.PNG" class= inline-graphic"/>,with S as the stoichiometric matrix, was accomplished by sampling the null space of S by an Artificial Center Hit and Run Algorithm (ACHR) [41], [42].
The paper describes a novel and efficient method for sampling the null distributions that calibrate the significance of nestedness scores.
Because it is based on the relative enrichment, this test did not deal well with background noise and led to a high false positive rate: when in a given region, few random reads (a couple) were present in the nucleosome sample but not in the control sample, the null hypothesis (equal enrichment in both samples) was rejected and the region declared as nucleosome.
The function compares the medians of the samples, testing the null hypothesis that all samples are drawn from the same population (or equivalently, from different populations with the same distribution), as a nonparametric one-way ANOVA and an extension of the Wilcoxon rank-sum test to more than two groups.
We also generated Monte-Carlo P-values for the similarity values by generating 50 000 samples from the null distribution as follows: each null sample was generated by creating a random tree topology with the same number of leaves as the dataset, and we then calculated the cluster similarity with the manual grouping.
The number of overlapping base pairs between the two tracks was calculated for the real data, as well as for 50 000 Monte Carlo samples from the null model.
The FPR was computed as the proportion of pairs of samples from the null tests incorrectly identified as coming from different communities.
