Data from: Comparing two classes of alpha diversities and their corresponding beta and (dis)similarity measures, with an application to the Formosan sika deer (Cervus nippon taiouanus) reintroduction program

1. Diversity partitioning, which decomposes gamma diversity into alpha and
beta components, is commonly used to obtain measures that quantify
spatial/temporal diversity and compositional similarity or dissimilarity
among assemblages. We focus on the decomposition of diversity as measured
by Hill numbers (parameterized by a diversity order q≧0). 2. At least
three diversity-partitioning schemes based on Hill numbers have been
proposed. These schemes differ in the way they formulate alpha diversity.
We focus on comparing two classes of alpha diversities, developed
respectively by Routledge (1979) and Chiu et al. (2014). Both are defined
for all diversity orders q≧0. Because these two approaches to quantifying
alpha have not been compared in the literature; it has been unclear how to
choose a proper alpha formulation for practical applications. 3. We review
the two classes of alpha diversities and discuss the properties of their
corresponding beta and (dis)similarity measures. Our research offers clear
guidelines regarding the choice of an alpha formula: (i) If the goal is to
assess compositional (dis)similarity among (unweighted) species relative
abundance datasets, then the two alpha formulas are identical, leading to
the same beta and (dis)similarity measures. (ii) If the goal is to assess
compositional (dis)similarity among (unweighted) species raw abundance
datasets, then Chiu et al.’s approach should be used. Their beta can be
monotonically transformed to various (dis)similarity measures in the range
[0, 1]. (iii) If each assemblage is weighted by its absolute, total
abundance (i.e., assemblage size), but the goal is to assess compositional
(dis)similarity among species relative abundance datasets, then
Routledge’s approach should be used. In this case, construction of
legitimate (dis)similarity measures among species relative abundance
datasets for unequal assemblage sizes/weights, for any order q≧0, has not
been addressed in the literature. Here we propose non-monotonic
transformations of Routledge’s beta to fill this gap. 4. The extension of
our analysis to phylogenetic diversity partitioning is generally parallel.
We apply various species and phylogenetic dissimilarity measures to
Taiwan’s plant data; the results provide insights into the assessment of a
reintroduction program of Formosan sika deer into a forest area. Pertinent
sampling and related issues are also discussed.