Converting quadratic entropy to diversity: Both animals and alleles are diverse, but some are more diverse than others

• DOI: 10.1371/journal.pone.0185499
• Publication Date: 2017-10-31T17:27:48Z
• Authors: Peter E. Smouse; Sam C. Banks; Rod Peakall
• Keywords: Genetic Markers; Rao’s quadratic entropy; 0301 basic medicine; Science; Q; 590; R; Biodiversity; Permanova; 15. Life on land; Hill numbers; Scaled diversity; Antechinus; Phylogenetic diversity; Amova; 03 medical and health sciences; Marsupialia; Medicine; Animals; Gamova; Alleles; Research Article; Microsatellite Repeats

The use of diversity metrics has a long history in population ecology, while population genetic work has been dominated by variance-derived metrics instead, a technical gap that has slowed cross-communication between the fields. Interestingly, Rao’s Quadratic Entropy (RQE), comparing elements for ‘degrees of divergence’, was originally developed for population ecology, but has recently been deployed for evolutionary studies. We here translate RQE into a continuous diversity analogue, and then construct a multiply nested diversity partition for alleles, individuals, populations, and species, each component of which exhibits the behavior of proper diversity metrics, and then translate these components into [0,1] - scaled form. We also deploy non-parametric statistical tests of the among-stratum components and novel tests of the homogeneity of within-stratum diversity components at any hierarchical level. We then illustrate this new analysis with eight nSSR loci and a pair of close Australian marsupial (Antechinus) congeners, using both ‘different is different’ and ‘degree of difference’ distance metrics. The total diversity in the collection is larger than that within either species, but most of the within-species diversity is resident within single populations. The combined A. agilis collection exhibits more diversity than does the combined A. stuartii collection, possibly attributable to localized differences in either local ecological disturbance regimes or differential levels of population isolation. Beyond exhibiting different allelic compositions, the two congeners are becoming more divergent for the arrays of allele sizes they possess.