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Modeling spatial evolution of multi-drug resistance under drug environmental gradients
Fig 3
Competitive exclusion everywhere in space, but the ultimately winning strain depends on parameters of gi(z) variation.
A. In this piece-wise growth rate example, the g1(z) and g2(z) are such that the mean growth rates for both strains are the same 
for b = 1/2 and gmax = 0.5, gmin = 0.3. Yet, even with equal spatially-averaged growth rates, starting from equal initial distributions, the strain with the central advantage will be the winner. When b changes, the final winner is a result of b as well as (max(g) − min(g)) magnitude. B. In this example, the winner can be overturned by modulating the width of the interval where g1(z) > g2(z), while keeping the shape of the two functions. We assume the growth rates are non-monotonic functions of space, represented by a concave and a convex parabola with vertices near the middle of the domain:g1(z) = m − σ(z − L/2)2 + h and g2(z) = m + 2σ(z − L/2)2 with m = 0.3, σ = 0.4, D = 0.015 and h varied. The critical value of h for overturning the final outcome is h = 0.04. Mutant 1 loses if h < 0.04 but it wins if h > 0.04, when its fitness advantage in the center of the domain is sufficiently high to compensate for its disadvantage near the boundaries. This cannot be predicted with the mean growth rate difference 
but can be predicted with λ1 difference for mutants 1 and 2. See also S1 Mathematica Notebook.
doi: https://doi.org/10.1371/journal.pcbi.1012098.g003