Fig 3. Evolutionary trajectory of a population adapting to a fast fluctuating environment displays selection for high nonlinearity.

The initial population started from a non-optimal genotype (θ₀) where k = 80, n_H = 1, K_D = 10 with evolutionary parameters N = 10000, ν = 0.1, s_t = 40, u = 0.03, and M = 1.1 both under (A) the original model and (B) in the absence of biochemical noise (CONTROL). The average K_D (〈K_D〉_cycle) versus the average Hill coefficient (〈n_H〉_cycle) are shown for each environmental cycle simulated, colored given the geometric mean of the population fitness per environmental cycle ($W_{\text{cycle}}=\sqrt[2/\nu ]{{\Pi }_{g=\left\{\text{cycle}\right\}}{w}_g}$), and the marker size corresponds to the average percentage of bistable genotypes in the population (see legend). The traces of other nine replicas are shown in gray as a reference. Each cycle spans a LOW (dark green) and HIGH (light green) epoch and there are 500 environmental cycles over 10,000 generations for each of these simulations. The population fitness w per generation for the first and last cycles, as well as the cycle with the minimum and maximum W_cycle are shown in the bottom for comparison, and colored according to their W_cycle value. In both simulations (A-B), the population evolved to higher nonlinearity values 〈n_H〉_cycle and W_cycle.