Partitioning diversity for conservation analyses

Aim  Differentiation of sites or communities is often measured by partitioning regional or gamma diversity into additive or multiplicative alpha and beta components. The beta component and the ratio of within-group to total diversity (alpha/gamma) are then used to infer the compositional differentiation or similarity of the sites. There is debate about the appropriate measures and partitioning formulas for this purpose. We test the main partitioning methods, using empirical and simulated data, to see if some of these methods lead to false conclusions, and we show how to resolve the problems that we uncover.
Location  South America, Ecuador, Orellana province, Rio Shiripuno.
Methods  We construct sets of real and simulated tropical butterfly communities that can be unambiguously ranked according to their degree of differentiation. We then test whether beta and similarity measures from the different partitioning approaches rank these datasets correctly.
Results  The ratio of within-group diversity to total diversity does not reflect compositional similarity, when the Gini–Simpson index or Shannon entropy are used to measure diversity. Additive beta diversity based on the Gini–Simpson index does not reflect the degree of differentiation between N sites or communities.
Main conclusions  The ratio of within-group to total diversity (alpha/gamma) should not be used to measure the compositional similarity of groups, if diversity is equated with Shannon entropy or the Gini–Simpson index. Conversion of these measures to effective number of species solves these problems. Additive Gini–Simpson beta diversity does not directly reflect the differentiation of N samples or communities. However, when properly transformed onto the unit interval so as to remove the dependence on alpha and N , additive and multiplicative beta measures yield identical normalized measures of relative similarity and differentiation.