"Forwards and backwards in spatially heterogeneous populations"Etheridge, AlisonWe introduce a broad class of individual based models that might describe how spatially heterogeneous populations live, die, and reproduce. Our primary interest is in understanding how genetic ancestry spreads across geography when looking back through time in these populations. A novelty is that by explicitly splitting reproduction into two phases (production of juveniles and their maturation) we produce a framework that not only captures models which when suitably scaled converge to classical reaction diffusion equations, but also ones with nonlinear diffusion that exhibit quite different behaviour. This is joint work with Tom Kurtz (Madison), Peter Ralph (Oregon) and Ian Letter and Terence Tsui (both formerly Oxford). |
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