Biological invasions are are an important part of mathematical biology and have historically been modelled with deterministic continuous reaction-diffusion equations. Recent work has pre- sented alternative discrete stochastic models of biological invasions. In particular, cellular au- tomata models have been popular studies in studies of epidemics and invasions. Many of these models have been shown to have interesting properties. In particular, they have been demonstrated to belong in the KPZ universality class.
In this thesis, we present an alternative lattice-free model of biological invasion. We consider an extension of this model to two-dimensions which has exciting properties. In particular, we show using simulation that it, despite having completely different mechanics than the cellular automata models, belongs in the KPZ universality class as well.
