Animal Guts as Ideal Chemical Reactors: Maximizing Absorption Rates

I solved equations that describe coupled hydrolysis in and absorption from a continuously stirred tank reactor (CSTR), a plug flow reactor (PFR), and a batch reactor (BR) for the rate of ingestion and/or the throughput time that maximizes the rate of absorption (=gross rate of gain from digestion). Predictions are that foods requiring a single hydrolytic step (e.g., disaccharides) yield ingestion rates that vary inversely with the concentration of food substrate ingested, whereas foods that require multiple hydrolytic and absorptive reactions proceeding in parallel (e.g., proteins) yield maximal ingestion rates at intermediate substrate concentrations. Counterintuitively, then, animals acting to maximize their absorption rates should show compensatory ingestion (more rapid feeding on food of lower concentration), except for the lower range of diet quality for complex diets and except for animals that show purely linear (passive) uptake. At their respective maxima in absorption rates, the PFR and BR yield only modestly higher rates of gain than the CSTR but do so at substantially lower rates of ingestion. All three ideal reactors show milder than linear reduction in rate of absorption when throughput or holding time in the gut is increased (e.g., by scarcity or predation hazard); higher efficiency of hydrolysis and extraction offset lower intake. Hence adding feeding costs and hazards of predation is likely to slow ingestion rates and raise absorption efficiencies substantially over the cost-free optima found here.