The apportionment of quadratic entropy: a useful alternative for partitioning diversity in ecological data

Many methods that study the diversity within hierarchically structured populations have been developed in genetics. Among them, the analysis of molecular variance (AMOVA) (Excoffier et al., 1992) has the advantage of including evolutionary distances between individuals. AMOVA is a special case of a far more general statistical scheme produced by Rao (1982a; 1986) and called the apportionment of quadratic entropy (APQE). It links diversity and dissimilarity and allows the decomposition of diversity according to a given hierarchy. We apply this framework to ecological data showing that APQE may be very useful for studying diversity at various spatial scales. Moreover, the quadratic entropy has a critical advantage over usual diversity indices because it takes into account differences between species. Finally, the differences that can be incorporated in APQE may be either taxonomic or functional (biological traits), which may be of critical interest for ecologists.