Computing additive beta-diversity from presence and absence scores: a critique and alternative parameters.

Whittaker first proposed to measure the variation in species composition among plots or -diversity as the ratio between regional diversity( -diversity) and average local diversity (-diversity). More recently, an alternative way of partitioning diversity for which -diversity is obtainedas the difference between -diversity and average -diversity has become very popular for linking the structure of species assemblages toecosystem functioning in a spatially explicit manner. Unfortunately, additive -diversity computed from species presences and absences suffersfrom the major drawback of being dependent on regional species richness. For instance, if the separation between -diversity and -diversityis incomplete, so that variation in species composition is affected by species richness, then differences in -diversity values among differentsets of plots could reflect differences in the species count rather than any fundamental difference in species composition among the plots. Basedon the above observation, in this paper I will first propose a basic requirement for -diversity measures that adequately captures our intuitivenotion of independence of species richness. Next, I will show that additive -diversity computed from species presence and absence scores can beinterpreted within the framework of fuzzy set theory. Finally, based on this unusual “fuzzy” interpretation of additive -diversity, I will introducetwo families of parametric -diversity measures whose members have varying sensitivities to the presence of rare and frequent species.