The effects of spatiotemporal disturbances on the goshawk squirrel dynamics in coniferous forests

Historically wildfires have been the major natural stand replacing disturbance and many ecosystems have developed with adaptation to a certain range of wildfire frequencies. While clearcutting frequencies that mimic natural disturbance frequencies may be able to sustain healthy forests, research has shown that forest conditions differ after wildfires and after clearcuts, even though most of those differences disappear over time. As climate change progresses, however, the fire frequency (as well as magnitude and severity) are predicted to increase, changing the dynamics in formerly stable ecosystems. My work focuses on the effects of disturbance frequency and size on the American goshawk - North American red squirrel predator-prey system in the coniferous forests of western North America. To investigate how changes in disturbance dynamics affect the goshawk-squirrel system I developed a PDE model reflecting important properties of this system. These properties include a spatially and temporally varying carrying capacity that depends on forest age, density-dependent dispersal of red squirrels as a result of territorial behaviour, and both periodic (harvesting) and stochastic (wildfire) forest disturbances. I ran simulations varying the size and frequency of both types of disturbance, keeping all other factors constant and at values consistent with the goshawk-squirrel system. I also conducted a linear stability analysis to determine the general behaviour of the non-spatial model under a wide range of parameter values. The stability analysis shows that the system has at least one stable positive coexistence steady state under a wide range of possible parameter values. For some parameter values, the system exhibits bistability. The simulations results show that increased disturbance frequency generally has a negative effect on species persistence and eventually leads to local extinction. The effects of disturbance size are non-linear and, non-monotonic. Very small and very large disturbance sizes have strong nega- tive effects, whereas small increases in disturbance size at the lower end of the size spectrum can have positive effects. A possible explanation for those non-linear dynamics could be fragmentation effects. I conclude with possible extensions to the model, e.g., including more realistic fire dynamics.