Additive partitioning of diversity including species differences: a comment on Hardy & Senterre (2007)

Summary The distribution of biodiversity at multiple spatial scales has been traditionally investigated through the additive partitioning of γ‐biodiversity (regional) into α‐(within‐site) and β‐(among‐site) components. However, this decomposition is almost exclusively applied using species turnover among communities while two communities with no species in common can be very similar because they share some ‘biological’ similarity. To overcome this limitation, Hardy & Senterre (2007) (J. Ecol., 95, 493–506) presented a new statistical framework partitioning the phylogenetic diversity into α‐ and β‐components using the Rao's quadratic entropy. We show that their decomposition is correct only when sites have the same total abundance, otherwise it may lead to negative β‐diversity values. As an alternative, we provided a general decomposition of the quadratic entropy into α‐, β‐ and γ‐diversities. Synthesis. We suggest that the ‘biological’ turnover quantified by the β‐component of the regional quadratic entropy may help, at least, to disentangle dispersal vs. niche influences on biodiversity patterns.