A multiscale stochastic cellular automaton model for dispersion process with applications to Mountain Pine Beetle infestations

Dispersion, the collective spatial movement of individuals in a population, often plays a prominent role in the dynamics of the population. However, dispersion is a multiscale phenomena bridging processes affecting individuals with processes affecting collections of individuals while the processes affecting collections of individuals are often unknown or difficult to quantify. This raises the need to develop models of dispersion. In this thesis, we construct and investigate a multiscale model of dispersion. Dispersion of population density is modelled at a macroscale by a stochastic process inspired by cellular automata models. The dispersion model is coupled to microscale models of population that describe the local production of individuals in the population. Assuming that dispersion occurs on a slower time scale than the production of individuals, we construct a systematic approach to couple the macroscale dispersion model to the microscale population model. The resulting multiscale model uses relatively few parameters and those parameters have physical interpretations with respect to the population being modelled. The model is also flexible in that it can incorporate a wide range of microscale population models. We carry out a thorough numerical investigation of the properties of the multiscale model for dispersion. The analysis shows that the multiscale dispersion model can yield a wide range of spatial and dynamic behaviours depending on the choice of parameters. We also demonstrate that the model parameters can be calibrated using data from specific statistics that characterize the spatial patterns of dispersion. We apply the stochastic model of dispersion to mountain pine beetle infestations of forest in North America. Our results suggest that the model can produce patterns that are qualitatively similar to those infestations. We also calibrate the dispersion model using data consisting of images of an actual pine beetle infestation.