  Biological organisms exhibit diverse strategies for adapting to varying
environments. For example, a population of organisms may express the same
phenotype in all environments (`unvarying strategy'), or follow environmental
cues and express alternative phenotypes to match the environment (`tracking
strategy'), or diversify into coexisting phenotypes to cope with environmental
uncertainty (`bet-hedging strategy'). We introduce a general framework for
studying how organisms respond to environmental variations, which models an
adaptation strategy by an abstract mapping from environmental cues to
phenotypic traits. Depending on the accuracy of environmental cues and the
strength of natural selection, we find different adaptation strategies
represented by mappings that maximize the longterm growth rate of a population.
The previously studied strategies emerge as special cases of our model: the
tracking strategy is favorable when environmental cues are accurate, whereas
when cues are noisy, organisms can either use an unvarying strategy or,
remarkably, use the uninformative cue as a source of randomness to bet-hedge.
Our model of the environment-to-phenotype mapping is based on a network with
hidden units; the performance of the strategies is shown to rely on having a
high-dimensional internal representation, which can even be random.
