Biodiversity Measures and the Role of Species Similarity

Here are the title, abstract and slides for my talk. Much of what I’m going to say exists in the following Ecology paper co-authored with Tom Leinster.

• Christina Cobbold, Biodiversity measures and the role of species similarity.

Abstract. Biodiversity is associated to properties of ecosystem function and productivity or at the molecular level it can describe genetic diversity with connections to quantities such as host-pathogen fitness. Diversity is clearly an important concept and it begs the question how should one measure diversity. There are literally dozens of measures of diversity in the literature, perhaps one of the most common examples being species richness or simply the number of species in the community concerned. Even such a simple definition raises questions, what defines a species? Sometimes this question is simple to answer, but for microbial communities, for example, there is no simple definition of a species and yet we still wish to quantify diversity.

To address this issue we present a natural family of diversity measures which not only takes into account relative abundance of species, but also accounts for differences or similarities between species. This latter point allows us to deal with communities where the notion of species is unclear. The family of measures are closely related to Rényi’s generalised entropies and I will illustrate how the formulas introduced by Tobias Fritz in his talk relate to our family of diversity measures.

We demonstrate that our new measure of diversity is not simply an addition to the already long list of indices: instead, a single formula subsumes many of the most popular indices, including Shannon’s, Simpson’s, species richness, and Rao’s quadratic entropy. These popular indices can then be used and understood in a unified way, and the relationships between them are made plain. The new measures are, moreover, effective numbers, so that percentage changes and ratio comparisons of diversity value are meaningful.