Biological invasions are devastating ecosystems and economies world-wide, while many native species' survival depends on their ability to track climate change. Characterising the spread of biological populations is therefore of utmost importance, and can be studied with spatially explicit, discrete-time integro-difference equations (IDEs), which reflect numerous species' processes of demography and dispersal. While spatial variation has often been ignored when implementing IDE models, real landscapes are rarely spatially uniform and environmental variation is crucial in determining biological spread. To address this, we use novel methods to characterise population spread in heterogeneous landscapes. Asymptotic analysis is used for highly fragmented landscapes, where habitat patches are isolated and smaller than the dispersal scale, and in landscapes with low environmental variation, where the ecological parameters vary by no more than a small factor from their mean values. We find that the choice of dispersal kernel determines the effect of landscape structure on spreading speed, indicating that accurately fitting a kernel to data is important in accurately predicting speed. For the low-variation case, the spreading speeds in the heterogeneous and homogeneous landscapes differ by ϵ<sup>2</sup>, where ϵ governs the degree of variation, suggesting that in many cases, a simpler homogeneous model gives similar spread rates. For irregular landscapes, analytical methods become intractable and numerical simulation is needed to predict spread. Accurate simulation requires high spatial resolution, which, using existing techniques, requires prohibitive amounts of computational resources (RAM, CPU etc). We overcome this by developing and implementing a novel algorithm that uses adaptive mesh refinement. The approximations and simulation algorithm produce accurate results, with the adaptive algorithm providing large improvements in efficiency without significant losses of accuracy compared to non-adaptive simulations. Hence, the adaptive algorithm enables faster simulation at previously unfeasible scales and resolutions, permitting novel areas of scientific research in species spread modelling.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:730116 |
| Date | January 2016 |
| Creators | Gilbert, Mark |
| Contributors | Bullock, James ; Gaffney, Eamonn ; White, Steven |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ora.ox.ac.uk/objects/uuid:944d15d3-257a-47e5-acb9-9bdfba26985b |
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