  Evolving systems, be it an antibody repertoire in the face of mutating
pathogens or a microbial population exposed to varied antibiotics, constantly
search for adaptive solutions in time-varying fitness landscapes. Generalists
correspond to genotypes that remain fit across diverse selective pressures;
cross-reactive antibodies are much wanted but rare, while multi-drug resistant
microbes are undesired yet prevalent. However, little is known about under what
conditions such solutions with a high capacity to adapt would be efficiently
discovered by evolution, as environmental changes alter the relative fitness
and accessibility of neighboring genotypes. In addition, can epistasis --- the
source of landscape ruggedness and path constraints --- play a different role,
if the environments are correlated in time? We present a generative model to
estimate the propensity of evolving generalists in rugged landscapes that are
tunably related and cycling relatively slowly. We find that environment cycling
can substantially facilitate the search for fit generalists by dynamically
enlarging their effective basins of attraction. Importantly, these high
performers are most likely to emerge at an intermediate level of both
ruggedness and environmental relatedness, trading diversity for fitness and
accessibility. Our work provides a conceptual framework to study evolution in
correlated varying complex environments, and offers statistical understanding
that suggests general strategies for speeding up the generation of broadly
neutralizing antibodies or preventing microbes from evolving multi-drug
resistance.
