Data describing amounts of components of specimens are compositional
if the size of each specimen is constant or irrelevant. Ideally compositional data is
given by relative portions summing up to 1 or 100%. But more often compositional
data appear disguised in several ways: different components might be reported
in different physical units, different cases might sum up to different totals, and
almost never all relevant components are reported. Nevertheless, the constraints
of constant sum and relative meaning of the portions have important implications
for their statistical analysis, contradicting the typical assumptions of usual uni- and
multivariate statistical methods and thus rendering their direct application spurious.
A comprehensive statistical methodology, based on a vector space structure of the
mathematical simplex, has only been developed very recently, and several software
packages are now available to treat compositional data within it. This book is at the
same time a textbook on compositional data analysis from a modern perspective