I will present recent results from my group that pertain to spatio-temporal patterns formed by social foragers. Starting from work on chemotaxis by Lee A. Segel (who was my PhD thesis supervisor), I will discuss why simple taxis of foragers and randomly moving prey cannot lead to spontaneous emergence of patchiness. I will then show how a population of foragers with two types of behaviours can do so. I will discuss conditions under which one or another of these behaviours leads to a winning strategy in the sense of greatest food intake. This problem was motivated by social foraging in eiderducks overwintering in the Belcher Islands, studied by Joel Heath. The project is joint with post-doctoral fellows, Nessy Tania, Ben Vanderlei, and Joel Heath.
In diverse contexts, populations of cells and animals disperse and invade a spatial region over time. Frequently, the individuals that make up the population undergo a transition from a motile to an immotile state. A steady-state spatial distribution evolves as all the individuals settle. Moreover, there may be multiple releases of motile subpopulation. If so, the interactions between motile and immotile subpopulations may affect the final spatial distribution of the various releases. The development of the brain cortex and the translocation of threatened Maud Island frog are two applications we have considered.
The eventual equilibrium global mean temperature associated with a given stabilization level of atmospheric greenhouse gas concentrations remains uncertain, complicating the setting of stabilization targets to avoid potentially dangerous levels of global warming. Similar problems apply to the carbon cycle: observations currently provide only a weak constraint on the response to future emissions. These present fundamental challenges for the statistical community, since the non-linear relationship between quantities we can observe and the response to a stabilization scenario makes estimates of the risks associated with any stabilization target acutely sensitive to the details of the analysis, prior selection etc. Here we use ensemble simulations of simple climate-carbon-cycle models constrained by observations and projections from more comprehensive models to simulate the temperature response to a broad range of carbon dioxide emission pathways. We find that the peak warming caused by a given cumulative carbon dioxide emission is better constrained than the warming response to a stabilization scenario and hence less sensitive to underdetermined aspects of the analysis. Furthermore, the relationship between cumulative emissions and peak warming is remarkably insensitive to the emission pathway (timing of emissions or peak emission rate). Hence policy targets based on limiting cumulative emissions of carbon dioxide are likely to be more robust to scientific uncertainty than emission-rate or concentration targets. Total anthropogenic emissions of one trillion tonnes of carbon (3.67 trillion tonnes of CO2), about half of which has already been emitted since industrialization began, results in a most likely peak carbon-dioxide induced warming of 2○C above pre-industrial temperatures, with a 5-95% confidence interval of 1.3-3.9○C.
The 2011 IGTC (International Graduate Training Centre) Summit was held as part of the Applied Mathematics Perspectives thematic program at the University of Victoria. There was a poster session, research discussion session where students and experts interacted, and an education session for IGTC students.