Optimization of exergy and implications of body sizes of phytoplankton and zooplankton in an aquatic ecosystem model

Size appears to be an important parameter in ecological processes. All physiological processes vary with body size ranging from small microorganisms to higher mammals. In this model, five state variables — phosphorus, detritus, phytoplankton, zooplankton and fish are considered. We study the implications of body sizes of phytoplankton and zooplankton for total system dynamics by optimizing exergy as a goal function for system performance indicator. The rates of different sub-processes of phytoplankton and zooplankton are calculated, by means of allometric relationships of their body sizes. We run the model with different combinations of body sizes of phytoplankton and zooplankton and observe the overall biomass of phytoplankton, zooplankton and fish. The highest exergy values in different combinations of phytoplankton and zooplankton size indicate the maximum biomass of fish with relative proportions of phytoplankton and zooplankton. We also test the effect of phosphorus input conditions corresponding to oligotrophic, mesotrophic, eutrophic system on its dynamics. The average exergy to be maximized over phytoplankton and zooplankton size was computed when the system reached a steady state. Since this state is often a limit cycle, and the exergy copies this behaviour, we averaged the exergy computed for 365 days (duration of 1 year) in the stable period of the run. In mesotrophic condition, maximum fish biomass with relative proportional ratio of phytoplankton, zooplankton is recorded for phytoplankton size class 3.12 (log V μm3 volume) and zooplankton size 4 (log V μm3 volume). In oligotrophic condition the highest average exergy is obtained in between phytoplankton size 1.48 (log V μm3 volume) and zooplankton size 4 (log V μm3 volume), whereas in eutrophic condition the result shows the highest exergy in the combination of phytoplankton size 5.25 (log V μm3 volume) and zooplankton size 4 (log V μm3 volume).