Quantifying the Fitness Benefit of Learning in Changing Environments

Abstract

The costs and benefits of learning for a foraging organism are difficult to quantify, and depend sensitively on the environment. We construct a minimal mathematical model of learning in which a forager learns the quality of different food types through experience. In our model, learning depends on two parameters: rate of memory updating and rate of exploration. Our method returns optimal learning parameters for environments in which the value and variance of food types may change in any fashion. We analyze the effect of five components of environmental change on the optimal memory and exploration parameters. The fitness outcomes from learning foragers are compared to the outcomes from following fixed strategies, explicitly quantifying the fitness benefit (or cost) of learning as a function of environmental change. 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. Learning is beneficial only if memory and exploration are optimized. The benefit of learning is largely determined by the ratio between the overall expected value of taking one resource compared to the overall expected value of taking the other: As these two expectations diverge, the fitness benefit of learning decreases, and can even become negative. In many environments, sub-optimal learning performs as bad or even worse than following a fixed strategy. SignificanceLearning is commonly observed in foraging organisms. However, measuring the fitness benefits (and costs) of learning is difficult, and depends critically on the environment in which an organism lives. We build a minimal model of learning in the context of optimal foraging and optimal diet choice theory, with two learning parameters: , corresponding to the duration of the foragers memory, and{epsilon} , corresponding to how much the forager explores the environment to learn more about it. We identify the optimal ,{epsilon} for different types of environmental change, and quantify the benefits and costs of learning. The benefit of learning is often surprisingly small, and in many environments, learning provides lower fitness than following a fixed strategy.