A new adaptive system approach to predator–prey modeling

A computable general equilibrium approach can effectively model adaptive ecological systems, and here it is applied to a predator–prey system. Features of the model include: (1) predators and prey maximize net energy intake by responding to energy expenditures for capturing prey and for avoiding capture; (2) the expenditures are determined system-wide by the interaction of all predators and prey; (3) predator consumption is negatively related to its expenditures on prey; (4) prey biomass given up to predators is negatively related to the predator’s expenditure owing to predation risk; (5) when there is but one prey species, the steady-state predator consumption and expenditure are independent of the prey density because any advantage of a larger prey density is competed away by the predators; (6) when there are two prey species, the steady-state predator consumptions and expenditures are not independent of the densities, because there are many combinations of consumptions and expenditures that yield a steady state, and the combinations are differentiated by prey densities; (7) no a priori assumptions are made about functional responses, and the functional response observed depends on whether the prey consumption is allowed to vary and on the numerical response of the predator; (8) functional and numerical responses tend to be negatively related; (9) predator switching behavior depends on the relative expenditures for the prey species, and the predator may specialize in one prey or switch gradually between prey; (10) population difference equations depend on individual net energies and not on aggregated species parameters, while oscillations in a population depend on average lifespan.