Competition at the edge of expanding populations

Microbes, cancer cells, and invasive species often spread across space forming a continuous two-dimensional population in a process known as range expansion. At the edge of this growth, mutants are likely to arise and rapidly colonize new territory. These mutants may colonize new territory either faster or slower than their wildtype ancestors, leading to a nontrivial morphology of the expansion front near the mutant colony. In this work, we couple a model of surface growth to a model of one-dimensional competition to describe this behavior. In silico, we find that the colony morphologies generated by new mutants in this model match those seen in microbial invasion experiments. We also make analytical predictions for how the speed of mutant invasion depends on the speed at which the population colonizes new territory. We summarize our results into three general classes. The mutant can either invade the wildtype purely due to its competitive advantage, or due to an overwhelming colonization advantage. Finally, we uncover a third case where the effects of colonization rate and competitive ability become mixed. Taken together our results not only elucidate many subtleties associated with mutant establishment, but also pave the way for a more universal description of evolutionary and ecological processes in growing populations that is also very amenable to theoretical analyses.