Multiscale codependence analysis: an integrated approach to analyze relationships across scales

Abstract

The spatial and temporal organization of ecological processes and features and the scales at which they occur are central topics to landscape ecology and metapopulation dynamics, and increasingly regarded as a cornerstone paradigm for understanding ecological processes. Hence, there is need for computational approaches which allow the identification of the proper spatial or temporal scales of ecological processes and the explicit integration of that information in models. For that purpose, we propose a new method (multiscale codependence analysis, MCA) to test the statistical significance of the correlations between two variables at particular spatial or temporal scales. Validation of the method (using Monte Carlo simulations) included the study of type I error rate, under five statistical significance thresholds, and of type II error rate and statistical power. The method was found to be valid, in terms of type I error rate, and to have sufficient statistical power to be useful in practice. MCA has assumptions that are met in a wide range of circumstances. When applied to model the river habitat of juvenile Atlantic salmon, MCA revealed that variables describing substrate composition of the river bed were the most influential predictors of parr abundance at 0.4-4.1 km scales whereas mean channel depth was more influential at 200-300 m scales. When properly assessed, the spatial structuring observed in nature may be used purposefully to refine our understanding of natural processes and enhance model representativeness.

Permanent residents or temporary lodgers: characterizing intracellular bacterial communities in the siphonous green algaBryopsis

“…The environmental component was represented by seven macro-ecological variables (figure 2) extracted from Bio-ORACLE [33]. The geographical component was represented by a set of orthogonal spatial variables extracted from geographical coordinates by Moran's Eigenvector Maps (MEM) analysis [34] using 'codep' in R [35]. The geographical matrix was represented by the first two eigenvectors, which were the only ones having positive eigenvalues (6.54 and 1.52).…”

Statistical methods for temporal and space–time analysis of community composition data

“…For linear relationships, a significant correlation is interpreted as support for the hypothesis that x may affect y. Because y may react to different environmental factors at different scales, one may be interested in determining at which scale(s) x is an important predictor of y. Guénard et al [17] developed multiscale codependence analysis (MCA) to address that question and test the signicance of the correlations between two variables at different scales. The method is based on spatial eigenfunctions, MEM or AEM, which correspond to different and identiable scales.…”

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

“…To quantify the joint spatial dependence of a response and an explanatory data table, MCA requires a set of spatial eigenvectors (Borcard & Legendre, ; Dray et al., ; Griffith & Peres‐Neto, ; U ) suitable to represent spatial patterns of variation in the data (Guénard et al., ). These variables have to be centred (i.e., their values have to sum to 0) and orthonormal (i.e., their cross‐product to one another for all i ≠ j , and the sum of squares for all i , where ⊤ denotes the matrix transpose).…”

“…To test for statistical significance, Guénard et al. () proposed to use the τ statistic, defined as the product of two Student's t statistics corresponding to the two correlations coefficients whose product is (eq. 6 in Guénard et al., ).…”