Abstract
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.
Highlights
The use of genetic distance matrices to estimate genetic diversity within and among populations offers a number of benefits, including the ability to accommodate different genetic distance coding schemes, and computational tractability for large datasets
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
We address a trio of additional questions: (4) How has evolutionary divergence within the complex been translated into genetic diversification within and between the two taxa? (5) Do responses to geographic or ecological challenges align with divergent patterns of diversity within the two organisms? (6) Do ‘different is different’ and ‘degree of difference’ treatments yield similar or disparate patterns of diversity within and between these close congeners?
Summary
The use of genetic distance matrices to estimate genetic diversity within and among populations offers a number of benefits, including the ability to accommodate different genetic distance coding schemes, and computational tractability for large datasets. (g-10); squared distances ðd2jk 1⁄4 0Þ if alleles are identical but ðd2jk 1⁄4 1Þ if different; analysis yields sample-frame dependent maximum Q*-values and their translations into maximum diversity estimates. The among-stratum components represent ‘effective numbers’ of non-overlapping allelic collections for (equi-frequent and equi-different) sub-strata: among individuals of a single population, among populations within a single species, and among species of the total collection These among-stratum components are explicitly defined so that aWP 1⁄4 ðεAI Þ ðoWI Þ sWS 1⁄4 ðbAP Þ ðaWP Þ g 1⁄4 ðdAS Þ ðsWS Þ: ð17Þ. For DR coding, ‘degree of difference’ matters, and if the novel variant in (P1) is beyond the ‘size range’ of previously represented alleles in (P1), the internal diversity (αWP1) of that population will increase If it is beyond the size range of the species (SA), within which it is nested, so will be (σWS) and (βAP), etc. Average & Bartlett’s Test aWP 1⁄4 0:455 ðP < 0:041Þ aWP 1⁄4 0:645 ðP < 0:001Þ aWP 1⁄4 0:836 ðP > 0:64Þ
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