A Mathematically Robust Model of Exotic Pine Invasions

Abstract: Invasive pine trees pose a threat to biodiversity in a variety of Southern Hemisphere countries, but understanding of the dynamics of invasions and the factors that retard or accelerate spread is limited. Here, we consider the past models of wilding pine spread and develop a new model of pine invasion. We show that many prior models feature parameter estimates which are not biologically supported and rely on a conjecture to obtain an asymptotic spread speed of invasive pine populations, the main output of these models. In contrast to prior approaches, we use partial differential equations to model an invasion. We show that invasions are almost static for a significant period of time before rapidly accelerating to spread at a constant rate, matching observed behaviour in at least some field sites. Our work suggests that prior methods for estimating invasion speeds may not accurately predict spread and are sensitive to assumptions about the distribution of parameters. However, we present alternative estimation methods and suggest directions for further research.