Stoichiometric Aquatic Food-Web Models Coupling Pelagic and Benthic Zones

Abstract

Ecological stoichiometry allows us to investigate how food quality affects food-web population dynamics. We consider periphyton, phytoplankton, and a shared Daphnia consumer in a closed system with separate benthic and pelagic phosphate pools. The producers have variable phosphorus-to-carbon ratios, while the consumer maintains a constant ratio. We construct the model, establish boundedness under stated conditions, characterize its grazer-free equilibrium families and their local spectra, derive conditions for positive consumer growth, and examine its numerical bifurcation structure as light-dependent carrying capacity varies. The bifurcation diagrams contain stable and unstable equilibrium branches together with a stable periodic family, revealing a more complex response to light enrichment than a single sequence of steady states and oscillations. A descending consumer equilibrium branch illustrates that greater light availability need not increase consumer biomass. We then introduce periodically varying carrying capacities and compare weak and strong seasonal forcing. Stronger forcing produces brief consumer rebounds in the high-light example, although the peaks diminish over the displayed interval. Together, the growth conditions and branch diagrams provide a framework for interpreting population dynamics in terms of food quantity and food quality. Independent numerical continuation identifies a Hopf crossing and a fold; the termination mechanism of the periodic branch remains unresolved.