PMC

Variable distribution is shown along the diagonal, Spearman rank correlation between the corresponding independent variables in the upper right quadrant.

An illustration of contact correlation analysis methods. Here, identical input information, an ensemble of contact matrices, is being digested two different ways. In explicit contact correlation analysis (E-PCA), specific contacts are treated as independent variables and their covariance matrix is calculated using the whole contact matrix as one sample (dotted red line). On the other hand, implicit contact correlation analysis (I-PCA) treats rows of the contact matrix (a contact pattern between one constituent of the polymer and the rest of the polymer) as independent variables and calculates the covariance matrix using each row as one sample (dotted red line).

An illustration of relative matrix dimensions in comparative analyses. n is the number of observations (independent contrasts) and p is the number of variables (characters) measured in each observation. (a) , so the independent contrasts matrix is larger than the covariance matrices and it is possible to uniquely estimate the true covariance matrix. This is the case for most comparative studies to date, which consider many more species than variables. (b) , so the independent contrasts matrix is smaller than the covariance matrices and it is not possible to uniquely estimate the true covariance matrix. This is the situation for phylogenetic comparative analyses of RNA-seq expression data, as well as other high-throughput phenotype data.

Analytical framework. (A) Data input. Matrix W of seven sites described by bird species abundance; matrix E of seven sites described by habitat descriptors; matrix B of bird species separated in food guilds; seven sites described by the time since the last fire event (TSF). (B) Trait information scaling-up. Matrix T with community-weighted mean trait values, obtained from matrix multiplication B’*W. (C) Derived variables and summarized analyses. TSF as independent variable for Linear Mixed-Effect Models (LME), with each dependent variable derived from data matrices. The first ordination axis of Matrix E (Habitat structure (PCA), in bold) was used as independent variable in separate models, with bird variables derived from matrices W and T as dependent variables. Finally, matrix E was used in Canonical Correspondence Analyses (CCA) with matrices W and T.