  We consider a spatial (line) model for invasion of a population by a single
mutant with a stochastically selectively neutral fitness landscape, independent
from the fitness landscape for non-mutants. This model is similar to those
considered in Farhang-Sardroodi et al. [PLOS Comput. Biol., 13(11), 2017; J. R.
Soc. Interface, 16(157), 2019]. We show that the probability of mutant fixation
in a population of size $N$, starting from a single mutant, is greater than
$1/N$, which would be the case if there were no variation in fitness
whatsoever. In the small variation regime, we recover precise asymptotics for
the success probability of the mutant. This demonstrates that the introduction
of randomness provides an advantage to minority mutations in this model, and
shows that the advantage increases with the system size. We further demonstrate
that the mutants have an advantage in this setting only because they are better
at exploiting unusually favorable environments when they arise, and not because
they are any better at exploiting pockets of favorability in an environment
that is selectively neutral overall.
