Evolving gene networks: Selection for evolvability and directional epistasis in variable environments

The effects of temporal heterogeneity on evolutionary dynamics has received considerable attention from both empiricists and theoreticians. A classic model prediction is that species should evolutionarily track temporally varying environmental conditions only when environmental noise exhibits a sufficient degree of positive autocorrelation (i.e., when the color spectra of fluctuations is “red shifted” or “reddened”). While this general prediction is well accepted, less understood is whether the capacity to adapt to changing environmental conditions (or “evolvability”) can itself be selected for under different noise regimes. Here we present results of a theoretical exploration of the effects of temporal heterogeneity on the evolution of evolvability. Using individual-based models of artificial gene networks, we show that evolvability is more strongly selected for in populations that are exposed to environmental noise that is reddened compared to populations in stable or randomly varying (white noise) environments. Evolvability emerged more readily in networks of lower complexity (fewer regulatory pathways) and in red noise environments in which large amplitude fluctuations had longer periods. Moreover, red noise selected for networks with stronger positive epistasis (i.e., genomes that exhibited weaker negative effects of accumulating mutations); these networks in turn harbored a greater capacity to produce additive genetic variation and thus adapted more rapidly in novel environments. Our results provide insight into the mechanisms potentially underlying rapid adaptation in nature as well as the environmental conditions that favor the evolution of complex genetic regulatory systems.