We verified this intuition by comparing the analytical results for cases where (p2 is increased by a set factor (so that only R2 is changed by this rescaling), to outcomes where 02 is scaled (which will not just affect R2 but will also increase p by the same factor, as outlined above).

Comparison of analytical results with simulations data

3(c)-(f) demonstrates that the analytical results slightly underestimate the simulation results to a small degree, especially if the mutated strain’s growth rate is high and R2 is close to K, but becomes more accurate as R2 increases and generally provides a good approximation.