This thesis is centered around the fundamental inquiry of ecology, which is to understand the relationships between organisms and their environment. Two core themes run and intertwine throughout the following work, beginning in parallel and then moving steadily towards synthesis in the concluding chapter. The first is concerned with developing and testing novel mathematical and computational methods which provide richer understanding of these species-environmental relationships. The second draws on emerging research from branches of the environmental social sciences and humanities, using the mathematical and scientific analyses in the earlier chapters as the entry into a more holistic engagement with ecology than is possible from any one disciplinary perspective alone.
We begin in Chapter 2 with the realm of community ecology and species distribution modelling, where we introduce the 'smoothing function' and the 'environmental manifold'. These two concepts provide new techniques for mapping the Hutchinsonian niche and working with the nonlinear and multivariate patterns emerging within and strongly influencing the quantitative relationships between species and environment. The following three chapters then shift focus to animal movement and landscape connectivity, each working from a different angle to provide more depth and breadth in addressing salient questions from this increasingly influential field of ecology. Chapter 3 introduces 'Pathwalker', a new individual-based computational method for modelling animal movement and connectivity, which is then used in Chapter 4 to provide the simulated data required for a comparative evaluation of major models in landscape connectivity.
Chapter 5 then keeps one foot in ecological science and places the other amongst areas of environmental geography, in order to analyse and overcome epistemological and methodological limitations in scientific studies of animal movement and landscape connectivity. This sufficiently motivates and widens the aperture of the thesis for disciplinary boundaries to dissolve in the heartfelt investigation of the final chapter, where we conclude by painting the possibility of an 'ecological mathematics'
