Rapidly fluctuating environments constrain coevolutionary arms races by impeding selective sweeps.

Although pervasive, the impact of temporal environmental heterogeneity on coevolutionary processes is poorly understood. Productivity is a key temporally heterogeneous variable, and increasing productivity has been shown to increase rates of antagonistic arms race coevolution, and lead to the evolution of more broadly resistant hosts and more broadly infectious parasites. We investigated the effects of the grain of environmental heterogeneity, in terms of fluctuations in productivity, on bacteria-phage coevolution. Our findings demonstrate that environmental heterogeneity could constrain antagonistic coevolution, but that its effect was dependent upon the grain of heterogeneity, such that both the rate and extent of coevolution were most strongly limited in fine-grained, rapidly fluctuating heterogeneous environments. We further demonstrate that rapid environmental fluctuations were likely to have impeded selective sweeps of resistance alleles, which occurred over longer durations than the fastest, but not the slowest, frequency of fluctuations used. Taken together our results suggest that fine-grained environmental heterogeneity constrained the coevolutionary arms race by impeding selective sweeps.