  The development of John Aitchison's approach to compositional data analysis
is followed since his paper read to the Royal Statistical Society in 1982.
Aitchison's logratio approach, which was proposed to solve the problematic
aspects of working with data with a fixed sum constraint, is summarized and
reappraised. It is maintained that the properties on which this approach was
originally built, the main one being subcompositional coherence, are not
required to be satisfied exactly -- quasi-coherence is sufficient, that is near
enough to being coherent for all practical purposes. This opens up the field to
using simpler data transformations, such as power transformations, that permit
zero values in the data. The additional property of exact isometry, which was
subsequently introduced and not in Aitchison's original conception, imposed the
use of isometric logratio transformations, but these are complicated and
problematic to interpret, involving ratios of geometric means. If this property
is regarded as important in certain analytical contexts, for example
unsupervised learning, it can be relaxed by showing that regular pairwise
logratios, as well as the alternative quasi-coherent transformations, can also
be quasi-isometric, meaning they are close enough to exact isometry for all
practical purposes. It is concluded that the isometric and related logratio
transformations such as pivot logratios are not a prerequisite for good
practice, although many authors insist on their obligatory use. This conclusion
is fully supported here by case studies in geochemistry and in genomics, where
the good performance is demonstrated of pairwise logratios, as originally
proposed by Aitchison, or Box-Cox power transforms of the original compositions
where no zero replacements are necessary.
