Optimal Foraging Theory

The Marginal Value Theorem (Charnov 1976) states that a forager maximizes long-term energy intake by leaving a patch when its instantaneous gain rate equals the average gain rate for the environment. Graphically, the optimal patch time is found by drawing a tangent line from the point (−t_travel, 0) to the cumulative energy gain curve. Longer travel times → spend more time in each patch (because travel is costly). Better environments (short travel, high quality patches) → leave sooner. This exact solution has been verified empirically in starlings, bumblebees, and parasitoid wasps.