Success probability for selectively neutral invading species in the line model with a random fitness landscape

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