UAlberta Math Biology Seminar: Jane Shaw MacDonald

The Earth is warming and temperature isoclines are shifting. Empirical evidence suggests that shifting speeds of temperature isoclines are accelerating, are elevation- dependent, and that there is annualvariation around the expected location of the temperature isoclines. In response, many species have shifted or will need to shift their geographical ranges to stay within their suitable temperature regime. Individuals may be able to bias their movement towards their suitable habitat, and their movement rates can depend on habitat quality. We present a mathematical tool to study transient behaviour of population dynamics within such moving habitats to discern between populations at high and low risk of extinction. We introduce a system of reaction– diffusion equations, in one-dimensional space, to study the impact of varying shifting speeds on the persistence and distribution of a single species. Unique to our model includes habitat dependent movement behaviour and habitat preference of individuals. These assumptions result in a jump in density across habitat types and generalise previous studies. We build and validate a numerical finite difference scheme to solve the resulting equations. Our numerical scheme uses a coordinate system where the location of the moving suitable habitat is fixed in space and a modification of a finite difference scheme to capture the jump in density. We explore a variety of shiftingspeed scenarios and contribute insights into the mechanisms that support population persistence through time in shifting habitats. One common finding is that a strong bias for the suitable habitat helps the population persist at faster shifting speeds, yet sustains a smaller total population at slower shifting speeds. Two-dimensional space gives a more accurate description of land or shallow water habitat. We present a two- dimensional analogue of our one-dimensional system and introduce the on-going work to advance the study in a more realistic setting.