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