Characterizing Interactions Across Large-Scale Point Process Populations

Many ecological and other scientific datasets take the form of recorded events, such as time points of significant occurrences, or spatial locations of objects of interest. In statistical terms, such data represent point processes. The purpose of this research project is to study sets of interactions across multiple point processes, introducing novel statistical estimation methods for these interactions, with a specific focus on methods for applications at the forefront of ecology.

In ecological settings it is particularly important to model the interactions between multiple sets of point processes. Understanding an ecosystem requires models of how occurrences of multiple species interact spatially, potentially across several time instances. The current lack of theoretical understanding in this area is exacerbated by the sizes of modern datasets, which typically involve appreciable numbers and types of species, across multiple spatial scales, but also where many of the most important species are quite rare.

Novel methodology in this area is urgently needed, and will be developed via two work packages: first, in the high-dimensional setting, estimating many measures of very heterogeneous interactions; and second, introducing scale-based analysis of large sets of interactions. These approaches will adapt and extend tools from time series analysis - the subject of the PI's current fellowship - and the decade of recent developments in random matrix theory, adapted to collections of measures of interactions. The project thus falls in the remit of both statistics and intradisciplinary research; both highlighted under current EPSRC fellowship priority areas.

The outcomes of the project will directly impact specific ecological inference applications (such as the ecological Barro Colorado Island tree data set) and the theory of multiple point processes, as well as more generally the important contemporary area of high-dimensional statistical data analysis.

The work proposed in this project is fundamental research in statistics, and also directly impacts ecology. Statistics has an additional impact on society via collaborations and users of developed technologies. Statistical methodology underpins all study and interpretation of data, and point processes are ubiquitous in applications.

Impact will also follow via other statisticians who engage with ecologists and institutes that study biodiversity for monitoring purposes. We shall host a workshop at UCL to ensure dissemination of our work to point process experts and statisticans, and present our work at scientific meetings. We also aim to disseminate via the numerous ecology and diversity institutes at UCL.

We will have an impact on the study of biodiversity directly via collaboration with Dr David Murrell, a UCL plant ecologist. Dr Murrell will present work at ecology conferences, and disseminate to other relevant avenues. We shall use our other existing collaborations such as the Sir Alister Hardy Foundation for Ocean Science, for a broader interface, as well as UCL ecology institutes. Web resources with code and preprints will also be developed, so that researchers can easily access our achieved results.