Spatial analysis of compositional data: A historical review

• Regionalised compositions treated as raw data are prone to spurious correlation.
• Regionalised compositions can be analysed using isometric logratio transformations.
• Problems related to the alr-transformation are solved recognising the space structure of the sample space.
• Modelling of cross-variograms can be afforded through the variation variogram.

Like the statistical analysis of compositional data in general, spatial analysis of compositional data requires specific tools. A historical overview of their development is presented in three steps: (a) the recognition of the problem, known as spurious spatial covariance, (b) first attempts to use the logratio approach, and (c) the application of the principle of working in coordinates using isometric logratio representations. Also mentioned are the use of matrix-valued variation-variograms as a tool to model crossvariograms, and the simplicial approach to indicator kriging, that solves inconsistencies in the standard approach to indicator kriging.