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 researc...