On what to permute in test-based approaches for variable importance measures in Random Forests

Motivation In bioinformatics applications, it is currently customary to permute the outcome variable in order to produce inference on covariates to test novel methods or statistics whose distributions are poorly known. The seminal publication of Altmann et al. in Bioinformatics uses the same permutation scheme to obtain P-values that can be treated as corrected measure of feature importance to rectify the bias of the Gini variable importance in Random Forests. Since then, such method has been used in applied work to also draw statistical conclusions on variable importance measures from resulting P-values. Results In this paper, we show that permuting the outcome may produce unexpected results, including P-values with undesirable properties and illustrate how more refined permutation schemes can be appropriate to obtain desirable results, including high power in discovering relevant variables. Supplementary information Supplementary data are available at Bioinformatics online.

A statistical method for analysing cospeciation in tritrophic ecology using electrical circuit theory

We introduce a new method to test efficiently for cospeciation in tritrophic systems. Our method utilises an analogy with electrical circuit theory to reduce higher order systems into bitrophic data sets that retain the information of the original system. We use a sophisticated permutation scheme that weights interactions between two trophic layers based on their connection to the third layer in the system. Our method has several advantages compared to the method of Mramba et al. [Mramba, L. K., S. Barber, K. Hommola, L. A. Dyer, J. S. Wilson, M. L. Forister and W. R. Gilks (2013): “Permutation tests for analyzing cospeciation in multiple phylogenies: applications in tri-trophic ecology,” Stat. Appl. Genet. Mol. Biol., 12, 679–701.]. We do not require triangular interactions to connect the three phylogenetic trees and an easily interpreted