Mathematical and computational study of dispersal in mixed landscapes

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My research program aims to understand how populations disperse and persist in mixed landscapes, particularly those disturbed by anthropogenic activity including agriculture, forestry, and climate change. For this proposal, I am focussing on developing the mathematical theory for intelligent dispersers operating in landscapes periodically disturbed by agriculture or forestry. In particular, I am interested in understanding how persistence is affected by the three interacting timescales of organism dynamics (generation time, multi-annual population cycles), anthropogenic activity (agriculture, forestry), and recolonisation (populations dispersing back into habitat that has become habitable after, e.g., harvest or planting). Bumblebees and tree squirrels both search for resources along circular forays that demonstrate a high degree of cognition: The organisms remember locations where they found resources earlier, and can learn about new resource patches from targeted communication with others. In agricultural landscapes, the synchronisation of bloom time over large portions of the landscape creates a strong external forcing in the distribution of resources that is a challenge for bumblebees, indeed, wild bee populations are in decline globally. In managed forests, dispersing organisms are being asked to recolonise an increasing proportion of the landscape: at what point do harvesting schedules make it no longer possible for the recolonisation process to be completed? In order for us to understand how intelligent dispersers locate new resources, and whether or not this can be done quickly enough on disturbed landscapes to ensure population persistence, we need mathematical models for their movement patterns. Current continuum models do not take memory into account, and communication between conspecifics is limited to olfactory cues deposited in the environment or carried by chemical signals. My research program will develop new mathematical models for intelligent dispersal, and then analyse them numerically to determine species persistence in the presence of anthropogenic disturbance that is periodic in space and time. The result will be the development of novel PDE models that have never before been studied, and their analysis will expand our understanding of dynamical systems, both in terms of the behaviours that can be observed, and in the analytic and numerical techniques used. Finally, these models lend important insights into the effect of anthropogenic activity in managed ecosystems, particularly with regard to species persistence for species of economic and/or esthetic concern.