| Abstract: |
| The role of memory and cognition in the movement of individuals (e.g. animals) within a population, is thought to play an important role in population dispersal. In response, there has been increasing interest in incorporating spatial memory effects into classical partial differential equation (PDE) models of animal dispersal. However, the specific detail of the transport terms, such as diffusion and advection terms, that ought to be incorporated into PDE models to accurately reflect the memory effect remains unclear. To bridge this gap, we propose a straightforward lattice-based model where the movement of individuals depends on both on crowding effects and the historic distribution within the simulation. The advantage of working with the individual-based model is that it is straightforward to propose and implement memory effects within the simulation in a way that is more intuitive than proposing extensions of classical PDE models. Through deriving the continuum limit description of our stochastic model we obtain a novel nonlinear diffusion equation which encompasses memory-based diffusion terms. In this talk I will show the relationship between memory-based diffusion and the individual-based movement mechanisms that depend upon memory effects. |
|