Constructing stability: optimal learning in noisy ecological niches

Organisms can learn in response to environmental inputs as well as actively modify their environments through niche construction on slower evolutionary time scales. How quickly should an organism respond to a changing environment, and when possible, should organisms adjust the time scale of environmental change? We formulate these questions using a model of learning costs that considers optimal time scales of both memory and environment. We derive a general, sublinear scaling law for optimal memory as a function of environmental persistence. This encapsulates a trade-off between remembering and forgetting. We place learning strategies within a niche construction dynamics in a game theoretic setting. Niche construction is found to reduce or stabilize environmental volatility when learned environmental resources can be monopolized. When learned resources are shared, niche destructors evolve to degrade the shared environment. We integrate these results into a metabolic scaling framework in order to derive learning strategies as a function of body size.