Bridging the scale gap: From local data to predicting large scale dynamics in heterogenous landscapes
Spatial heterogeneity has long been known to shape population dynamics. Dynamics at a landscape scale can therefore differ significantly from those at the local habitat scale, with local habitat conditions and individual movement shaping the distribution and flow of a population through the landscape. Often ecologists are challenged by this mismatch of scales: how do we upscale from observations at the habitat scale to landscape-level models and predictions? I will present a general averaging approach for coarse-graining from local to landscape-scale reaction-diffusion equations. The resulting equations connect to fundamental ecological concepts of Turchin's residence index and Skellam's dynamic level that Mark first introduced to me to as postdoc in his lab. Connecting these concepts opens avenues to mechanistically understand what drives population dynamics at different scales. I will illustrate several unexpected nonlinear relationships that emerge, showing how invasion speeds and population persistence can by altered by local movement behaviour. In doing so I hope to show some of the ways in which Mark's philosophy of delving deep into ecological problems where mathematics is yet to be developed has influenced mathematical ecology.