Linking power, efficiency, and bifurcations in consumer-resource systems

Three hypotheses help organize energetic thinking about living systems: Lotkas Maximum Power Principle, Odum-Pinkertons Intermediate Efficiency Principle, and Morowitzs Biological Cycling Principle. Here we show how these hypotheses fit together in consumer-resource systems, moving from qualitative principles to formal, testable statements. Using the Rosen-zweig-MacArthur model, we prove that the consumers maximum output power lies exactly on the Hopf boundary that separates stable points from cycles; at that point, the resulting power efficiency is intermediate. In the Rosenzweig-MacArthur model the Hopf is supercritical, so a stable limit cycle appears smoothly as the equilibrium loses stability. We treat the Hopf onset of time-periodic population oscillations as a population-level analogue of sustained cycling under energy flux. We then embed these energetic statements in adaptive dynamics: with convex trait costs, evolutionary singular strategies exist and are locally stable, but they coincide with the maximum-power state only under explicit marginal-cost conditions. Together, these results unify classic ideas in the concrete setting of consumer-resource systems and suggest measurements to evaluate when bifurcations, energetics, and evolution can converge.