Directed Percolation with Rough Boundaries
In the absence of mutations, only a single species remains at long times.
This is an absorbing state; transitions to adsorbing states belong to the Directed Percolation universality class.
How is this picture modified due to roughness of the front?
Couplings between the fluctuations in height and the concentration fluctuations at the front:
The non-linear terms are relevant below 4 dimensions, pointing to perturbative renormalization group.
"Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation," PRE 99, 042134 (2019).
Jordan Horowitz & M.Kardar, arxiv:1901.07956. (off-line)