Marginal value theorem

The marginal value theorem (MVT) is the central result of optimal foraging theory, predicting that a forager should leave a resource patch when the instantaneous rate of gain in that patch drops to the average rate across all available patches. The theorem transforms a spatial problem — where to forage — into a temporal one: when to leave. It was first derived by Eric Charnov in 1976 and has been extended to predict everything from patch residence times in bees to human dating behavior.

The theorem assumes that foragers have perfect information about average patch quality and that travel time between patches is significant. When these assumptions are violated — when patches are cryptic, when predators create risk gradients, or when information sharing among foragers alters the effective patch distribution — the predictions fail in revealing ways that expose the hidden social and ecological structure of foraging.