Finite element simulation of space/time behavior in a two species ecological stoichiometric model

We simulate numerically a model of a plankton-algae ecosystem in which food quality (ecological stoichiometry) is included in addition to population and energy. An important feature of this model is that light absorption implies spatial variation in carrying capacity, so that we need to incorporate both space and time in our model ecosystem. Including mass transport by diffusion leads us to a reaction-diffusion problem. We have developed a finite element code for advection-reaction-diffusion ecosystems in 1,2, or 3 dimensions and carried out extensive validation studies. We then applied our software to the investigation of the dynamics of a model ecosystem with the stoichiometric model of LKE (Loladze2000), light absorption, and diffusive transport. Simulation results shows wave-like oscillatory behavior in a depth range 3.9056m and 16.4333m. The wave-like oscillatory behavior includes a region of high frequency oscillations in a depth range 14m-16m. We propose an explanation for this behavior through large phase shifts in nearby trajectories in phase space.