Application of hypercorrelated matrices in ecological research

Abstract

Ecological data matrices often require some form of pre-processing so that any undesirable effects (e.g. the variable size effect) may be removed from multivariate analyses. This paper describes hypercorrelation, a simple data transformation that improves ordination methods significantly. Hypercorrelated matrices efficiently eliminate the ‘arch’ (or Guttman) effect, a spurious polynomial relation between ordination axes. These matrices reduce the sensitivity of correspondence analysis to outliers. Canonical analyses (canonical correspondence analysis and redundancy analysis) of hypercorrelated matrices are resistant to undesirable effects of missing data. Finally, the hypercorrelation extends applicability of “linear ordination method” (principal components analysis and redundancy analysis) to sparse (high beta diversity) matrices.