Bringing multivariate support to multiscale codependence analysis: assessing the drivers of community structure across spatial scales

1. Multiscale codependence analysis (MCA) quantifies the joint spatial distribution of a pair of variables in order to provide a spatially-explicit assessment of their relationships to one another. For the sake of simplicity, the original definition of MCA only considered a single response variable (e.g. a single species). However, that definition would limit the application of MCA when many response variables are studied jointly, for example when one wants to study the effect of the environment on the spatial organisation of a multi-species community in an explicit manner.
2. In the present paper, we generalize MCA to multiple response variables. We conducted a simulation study to assess the statistical properties (i.e. type I error rate and statistical power) of multivariate MCA (mMCA) and found that it had honest type I error rate and sufficient statistical power for practical purposes, even with modest sample sizes. We also exemplified mMCA by applying it to two ecological data set...