On hierarchical diversity decomposition

Question: According to Whittaker's proposal,ecologists have traditionally viewed beta-diversity as the ratio between gamma-diversity and average alpha-diversity. More recently, all alternative way of partitioning diversity has been 'rediscovered' for which beta-diversity is obtained as the difference between diversity and average alpha-diversity. This additive way of partitioning diversity has rapidly become a very popular framework for hierarchical diversity decomposition at various spatial scales. The question for this study is: Can we highlight any relation between these two ways of partitioning diversity, or do these methods really capture different facets of spatial turnover in species composition? Methods: First the properties that a diversity measure should possess for enabling additive decomposition into alpha-, beta-, and gamma-components are reviewed. Next, attention is drawn to the relationships between additive and multiplicative diversity decomposition. Results: It is shown that the additive model is closely related to its multiplicative counterpart through a simple logarithmic transformation. Conclusions: Contrary to the current assumption, both methods for partitioning diversity are not as different as they appear. Hence, the supposed superiority of additive diversity partition over multiplicative diversity decomposition is largely unjustified.