Topology and Geometry in Wildlife Conservation

The proposed research idea for my DPhil is to use and develop modern and advanced methods from algebraic topology and geometry to study and understand mathematical structures within particular wildlife conservation data sets. The aim is to understand mathematical patterns and structures in such data sets, and their ecological implications (e.g. laws governing community organisation; how wildlife populations are affected by human and environmental impact).
The Wildlife Conservation Research Unit (WildCRU) at Oxford University has state-of-the-art data sets on wildlife from Southeast Asia, Africa and South America, which are the largest and richest of their kind in the world. The Southeast Asia data set, for example, is a multi-species data set (upwards of 75 species) gathered from approximately 3000 camera stations across southeast Asia (ranging from Nepal to Borneo), from which roughly 2 million species occurrences have been recorded. I have had the pleasure of meeting Prof. David Macdonald (the director of WildCRU) and his colleague Dr. Samuel Cushman (who has carried out extensive analysis of these data sets), and it is through them that I have been given the opportunity to work with WildCRU's data sets.
The research in understanding these data sets to date has been undertaken using statistical/linear methods: in particular, cluster analysis, linear models, regression and correlations. The applications as such of these linear methods have led to new insights relating to the wildlife studied, but have also had their limitations. The methods used thus far have not addressed the temporal, geographical, or multi-species nature of the data set. It has also been difficult to upscale to a global level the individual models based on local studies, for which the current methods have been inadequate. The proposed DPhil will apply advanced methods from topology and geometry to study these complex n-dimensional structures. This research would be cutting-edge in that it would provide novel and deep understanding of the structures within these ecological data sets. The important ecological insights gained from the application of topological and geometric methods would include a better grasp of environmental predictors such as abiotic gradients (e.g. climate, topography), ecological conditions (e.g. forest cover), and human impact.
As a mathematics student who enjoys working in the field of algebraic topology and geometry, and as someone who is passionate about wildlife conservation and the natural world, I am excited to apply and explore modern mathematical methods from these areas to work on problems in conservation. I have had the fortunate opportunity over the summer to work on an interdisciplinary project with Dr. Heather Harrington studying algebraic geometry in phylogenetics, which revolved around analysing three seminal papers on the subject. Methods from topology and geometry have recently been applied to problems in the life sciences (for example, the areas of DNA topology and topological data analysis). But the proposed research would provide an entirely new approach to studying problems in wildlife conservation and ecology, and would affirm and develop recent advanced methods from topology and geometry into a new area of study, thus benefiting both subjects.

This project relates to various EPSRC areas, including Algebra, Geometry & Topology, and Statistics and Applied Probability.