Mathematical Diversity

Mathematical Diversity

Why study diversity?

Diversity is a ubiquitous feature of the world around us, with applications including:

  • guiding policy for biodiversity offsetting;
  • selecting the most efficacious vaccines; and
  • the prioritisation of biodiversity in conservation management.

Unfortunately, the measurement of diversity has been difficult to define in practice. Numerous measures have been developed across a wide range of fields, and applied with varying success. This is most evident when a review of literature reveals general disagreement, widespread confusion, and misinterpretation of results. It is clear that we would benefit from a unification of these measures, which is suitably robust and easily interpretable. 

What do we do?

A new framework of measures has recently been developed (Reeve, et al. in press) that considers diversity in a robust and innovative way, by 

  • partitioning the diversity of a supercommunity into it's constituent subcommunities;
  • capturing similarity between individuals; and
  • providing a framework that is invariant under shattering.

These measures are a generalisation of recently developed similarity-sensitive ecosystem diversity measures, which are in turn a generalisation of traditional ecosystem descriptors such as species richness, Simpson’s index, Shannon entropy, and Hill numbers.

The application of these measures give valuable insight into the underlying substructure of a community, exposing interesting features associated with subcommunity structure, such as:

contribution to ecosystem diversity;species redundancy, concentration;representativeness; andthe number of distinct communities present.

What next?

Our current work examines these measures across a range of applications (taxonomic, functional, genetic, phylogenetic, and so on), to provide a greater understanding of the underlying properties and utility of the measure of diversity. 


Contact: Sonia Mitchell