Optimal Foraging Theory

Marginal Value Theorem (Charnov 1976): An optimal forager should leave a patch when the instantaneous intake rate equals the average rate for the environment. Graphically (Charnov's tangent construction): draw the intake function E(t) starting from -t_travel on the x-axis; the optimal departure time is where the tangent from origin touches the curve. Key prediction: foragers should stay longer in high-quality patches and when travel time is longer (because the cost of travel is relatively higher). The MVT has been confirmed in bees, birds, and parasitoid wasps. Deviations can signal state-dependent foraging or predation risk. The intake function is typically E(t) = E_max·(1 - e^(-λt)) — exponential saturation (diminishing returns in a patch).