Inventory, differentiation, and proportional diversity: a consistent terminology for quantifying species diversity.

Almost half a century after Whittaker (Ecol Monogr 30:279-338, 1960) proposed his influential diversity concept, it is time for a critical reappraisal. Although the terms alpha, beta and gamma diversity introduced by Whittaker have become general textbook knowledge, the concept suffers from several drawbacks. First, alpha and gamma diversity share the same characteristics and are differentiated only by the scale at which they are applied. However, as scale is relative--depending on the organism(s) or ecosystems investigated--this is not a meaningful ecological criterion. Alpha and gamma diversity can instead be grouped together under the term "inventory diversity." Out of the three levels proposed by Whittaker, beta diversity is the one which receives the most contradictory comments regarding its usefulness ("key concept" vs. "abstruse concept"). Obviously beta diversity means different things to different people. Apart from the large variety of methods used to investigate it, the main reason for this may be different underlying data characteristics. A literature review reveals that the multitude of measures used to assess beta diversity can be sorted into two conceptually different groups. The first group directly takes species distinction into account and compares the similarity of sites (similarity indices, slope of the distance decay relationship, length of the ordination axis, and sum of squares of a species matrix). The second group relates species richness (or other summary diversity measures) of two (or more) different scales to each other (additive and multiplicative partitioning). Due to that important distinction, we suggest that beta diversity should be split into two levels, "differentiation diversity" (first group) and "proportional diversity" (second group). Thus, we propose to use the terms "inventory diversity" for within-sample diversity, "differentiation diversity" for compositional similarity between samples, and "proportional diversity" for the comparison of inventory diversity across spatial and temporal scales.