Fig 4.

(a) Crossing valleys can be faster. Despite the red-dashed path containing a fitness valley (cells at vertex 2 have a reduced growth rate compared to the root population), the target population is more likely to arise via this path if λ − λ(2) < 1, as derived in (11). This is confirmed by the simulations displayed in (b), where λ − λ(2) = 0.8 < 1 and the Monte-Carlo estimate for ${\mathbb{P}}_1(T^{\left(2\right)}>T^{\left(1\right)})$ (the probability path 1 seeds the target first) is 0.58, while the analytic result yields 0.56. (b) Stochastic simulations of system in (a) vs theory (11). Parameters α = 0.9, β = 0.3, λ = 0.6, α(2) = 0.2, β(2) = 0.4, λ(2) = −0.2, ν = 0.1, runs = 250.