Compositional Data in Community Ecology: The Paradigm or Peril of Proportions?

Ecologists are often restricted to using or choose to use proportional- or percentage-type data with the view that it helps standardize for differences in variable totals among sampling units or individuals. This standardization to compositional data leads to constraints in the covariance and correlation structure that profoundly affect subsequent analysis and interpretation. This is another form of the problem related to the use of ratios in statistical analyses. Using simulated and zooplankton data I demonstrate the effect of using compositional data vs. the original data in correlation, ordination, and cluster analysis, which are common analytical methods in community ecology. Interpretations about the relatedness of various taxa or sites may reverse when using compositions relative to the unstandardized data. In addition, the selection of subcompositions (i.e., one or more variables are excluded when calculating the composition) may have profound and unpredictable consequences for the results. I examine some approaches proposed to deal with such data, e.g., centered log-ratio analysis, and recommend the use of correspondence analysis in multivariate studies to avoid the problems associated with differing solutions.