Evolutionary dynamics of unstable populations invading healthy populations

Typical studies of spatial population genetics look at the dynamics of populations as they evolve in an isolated environment. In reality, when a population is evolving and spreading into new territory, it must compete with any other populations who already occupy that space. An invasive animal species, for example, must compete with the species already present in the ecological habitat; similarly, a cancerous tumor which starts out as a small cluster of rapidly growing and mutating cells must compete with surrounding healthy tissue. We look at spatial mutational meltdown models of a mutagenic population in the presence of a neutral bystander species with which it interacts only via competition. In particular we focus on the critical dynamics of the phase transition between the mutagenic population surviving for long times or dying out. We see that the roughness of domain walls between mutagenic and neutral populations becomes enhanced near the phase transition, consistent with the enhancement seen in isolated mutagenic models which have a rough, undulating growth front. Studying how these undulating domain walls couple to the critical dynamics of our model may provide valuable insight into what the shape of a cancerous tumor tells us about its long term survival probability.