A minimal model of learning: quantifying the cost and benefit of learning in changing environments

Many organisms have the ability to learn, but the costs and benefits of learning are difficult to quantify. We construct a minimal mathematical model of learning in which a forager attempts to maximize the amount of resources (food) it collects in a changing environment. Our model has two learning parameters: α, corresponding to the duration of the forager's memory, and [Formula: see text], corresponding to how much the forager explores the environment to learn more about it. We analyse the effect of different regimes of environmental change on the optimal memory and exploration parameters [Formula: see text]. By comparing the fitness outcomes from learning foragers to the outcomes from foragers following fixed strategies, we explicitly quantify the fitness benefit (or cost) of learning as a function of environmental change. We find that in many environments, the marginal benefit of learning is surprisingly small. In every environment, it is possible to implement learning in such a way that performance is as bad or worse than following a fixed strategy. In some environments, even the best implementations of our minimal model of learning perform worse than the best fixed strategy. Finally, we find that variance in resource values negatively biases foragers' estimates for those values, potentially explaining experimental results showing that animals prefer less variable resources.