Initial conditions and their effect on invasion velocity across heterogeneous landscapes

Accurate, time dependent control options are required to halt biological invasions prior to equilibrium establishment, beyond which control efforts are often impractical. Although invasions have been successfully modeled using diffusion theory, diffusion models are typically confined to providing simple range expansion estimates. In this work, we use a Susceptible/Infected cellular automaton (CA) to simulate diffusion. The CA model is coupled with a network model to track the speed and direction of simulated invasions across heterogeneous landscapes, allowing for identification of locations for targeted control in both time and space. We evaluated the role of the location of initial establishment insofar as it affected the pattern and rate of spread and how these are influenced by patch attributes such as size. Our results show that the location of initial establishment can significantly affect the temporal dynamics of an invasion. Traditional network metrics such as degree and measures of topological distance were insufficient for predicting the direction and speed of the invasion. Our coupled models allow the dynamic tracking of invasions across fragmented landscapes for both theoretical and practical applications.