Optimal Foraging Revisited through the Three Response Laws: A First-Principles Reconstruction of Behavioral Ecology

Classic Optimal Foraging Theory (OFT) maximizes net energy intake but rests on three idealized assumptions: unbounded internal capacity, instantaneous decision-making, and empirically chosen gain curves. We reconstruct OFT from first principles by enforcing three universal response laws: (i) finite energetic capacity, (ii) a non-zero causal delay, and (iii) low-order dynamical stability. Substituting the uniform delay factor with its Padé-(1,1) surrogate confines every admissible gain curve to a two-pole, strictly concave family that subsumes Holling Type II, Michaelis–Menten, and hyperbolic discounting. This family is -dense in the physically feasible set and uniquely minimizes a quadratic dissipation functional. The resulting framework yields a delay-corrected Marginal Value Theorem—predicting systematically longer patch residence times than the classical rule—and a latency-aware prey-switching threshold. Thus, optimal foraging emerges as a special case of the response-law grammar, providing energy-bounded, delay-aware predictions without ad hoc curve fitting.