Range expansion with mutation and selection: dynamical phase transition in a two-species Eden model

The colonization of unoccupied territory by invading species, known
as range expansion, is a spatially heterogeneous non-equilibrium
growth process. We introduce a two-species Eden growth model to
analyze the interplay between uni-directional (irreversible)
mutations and selection at the expanding front. While the
evolutionary dynamics leads to coalescence of both wild-type and
mutant clusters, the non-homogeneous advance of the colony results
in a rough front. We show that roughening and domain dynamics are
strongly coupled, resulting in qualitatively altered bulk and front
properties. For beneficial mutations the front is quickly taken
over by mutants and growth proceeds Eden-like. In contrast, if
mutants grow slower than wild-types, there is an antagonism between
selection pressure against mutants and growth by the merging of
mutant domains with an ensuing absorbing state phase transition to
an all-mutant front. We find that surface roughening has a marked
effect on the critical properties of the absorbing state phase
transition. While reference models, which keep the expanding front
flat, exhibit directed percolation critical behavior, the exponents
of the two-species Eden model strongly deviate from it. In turn,
the mutation-selection process induces an increased surface
roughness with exponents distinct from that of the classical Eden
model.