Self-optimization in a phytoplankton model

EXTREMAL PRINCIPLES WITH SPECIAL EMPHASIS ON EXERGY AND ASCENDENCY — THE MODERN APPROACH IN THEORETICAL ECOLOGY

Extremal principles or ecological orientors or goal functions are the most modern approach in theoretical ecology. There are many such principles proposed by different theoretical ecologists. In this paper, the most important extremal principles are discussed based on their theoretical backgrounds. Two widely accepted goal functions, i.e. exergy and ascendency are optimized and treated in a quantitative manner in an aquatic ecosystem model of planktonic and fish systems for their appropriateness. In the model varied body sizes of phytoplankton and zooplankton are considered. Parameter values varied according to the allometric principle with the body sizes. For self-organization of the model system two goal functions predict different results, however both are realistic.

EVALUATION OF SYSTEM PERFORMANCE THROUGH OPTIMIZING ASCENDENCY IN AN AQUATIC ECOSYSTEM MODEL

We develop a six-compartment model consisting of phosphorus, detritus, phytoplankton, zooplankton, planktonivorous fish and pisciphagous fish. In this model, we study the implications that the body sizes of phytoplankton and zooplankton have on the system dynamics. We use ascendency as a goal function or indicator of system performance. Ascendency quantifies growth and development of an ecosystem as a product of total system throughflow and the mutual information inherent in the pattern of internal system flows. Different physiological rate parameters of phytoplankton and zooplankton are assessed by means of allometric relationships applied to their body sizes. We let the phytoplankton body size range from 10 μm3to 107μm3and the zooplankton body size range from 10 μm3to 104μm3in volume. We also investigate the effects of phosphorus input conditions, corresponding to oligotrophic, mesotrophic and eutrophic systems on system dynamics. Ascendency (to be maximized over phytoplankton and zooplankton sizes) was computed after the system had reached a steady state. Since it always was a seasonal cycle, and the ascendency followed this behavior, we averaged the ascendency over 365 successive days (duration of one year) in the oscillatory phase. Under all types of nutrient conditions, the smallest phytoplankton size yielded the maximal values of the ascendency, while the corresponding zooplankton size varied. Under oligotrophic conditions, a phytoplankton size of 10 μm3combined with a zooplankton size of 101.25μm3to give the maximum value of the ascendency. Under mesotrophic and eutrophic conditions, maxima were obtained for zooplankton sizes 102.26μm3and 103.20μm3, respectively.