Practice question

The marginal value theorem predicts how long a forager should remain in a resource patch when travel between patches consumes time. Within a patch, cumulative gain rises but usually decelerates because preferred items are depleted, prey hide, or interference increases. The instantaneous, or marginal, gain rate therefore falls with residence time. Leaving too early wastes travel investment, whereas staying too long yields returns below those available elsewhere. The optimal departure point occurs where the tangent from the travel-time intercept touches the cumulative gain curve; equivalently, current marginal gain equals the long-term average gain rate for the habitat. The theorem predicts longer residence in richer patches and, all else equal, longer residence when travel time between patches increases. It does not explain predator extinction, population oscillations, or mimicry, which operate at different biological levels. Tests often measure departure from artificial food patches or giving-up densities. Risk, information, and nutritional balance can modify behavior, but patch-residence optimization is the theory’s central mechanism.