TL;DR: In this paper, the authors focus on the pressure humanity is placing on the natural world, and on the continued ability of ecosystems to deliver the services on which we all depend, and develop strategies to ameliorate its impact.
Abstract: Summary As prehistoric cave paintings illustrate, our species has had an enduring appreciation of the variety and abundance of life on Earth. Today, however, concern is focused on the pressure humanity is placing on the natural world, and on the continued ability of ecosystems to deliver the services on which we all depend. To understand the extent of this ‘biodiversity crisis’ and develop strategies to ameliorate its impact, it is essential to be able to accurately measure biological diversity (a term often contracted to biodiversity) and make informed predictions about how and why this diversity varies over space and time.
TL;DR: Three commonly used measures of diversity, Simpson's index, Shannon's entropy, and the total number of species, are related to Renyi's definition of a generalized entropy, according to which there is a continuum of possible diversity measures.
Abstract: Three commonly used measures of diversity, Simpson's index, Shannon's entropy, and the total number of species, are related to Renyi's definition of a generalized entropy. A unified concept of diversity is presented, according to which there is a continuum of possible diversity measures. In a sense which becomes apparent, these measures provide estimates of the effective number of species present, and differ only in their tendency to include or to ignore the relatively rarer species. The notion of the diversity of a community as opposed to that of a sample is examined, and is related to the asymptotic form of the species—abundance curve. A new and plausible definition of evenness is derived.
TL;DR: Calculation of PD for different population subsets shows that protection of populations at either of two extremes of the geographic range of the group can significantly increase the phylogenetic diversity that is protected.