Evolution in alternating environments with tunable inter-landscape correlations

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in periodically or stochastically modulated environments have been extensively studied, both theoretically and experimentally, though understanding the effects of temporally varying selection pressures remains challenging. Here we investigate how periodic cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. Inspired by collateral sensitivity that frequently arises between antibiotics, we construct pairs of fitness landscapes that share global fitness features (i.e. identical mean and variance) but are correlated with one another in a tunable way, resulting in landscape pairs that range from perfectly anti-correlated to perfectly correlated. We find that switching between these landscape pairs can drive the system to different regions of genotype space and, depending on the ruggedness of the landscape and the inter-landscape correlation, can either increase or decrease steady-state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anti-correlated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub-optimal local fitness maximums that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between strongly anti-correlated paired landscapes leads to ergodic-like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady-state fitness in comparison to single landscape evolution.