Combination of Logistic and modified Monod functions to study Microcystis aeruginosa growth stimulated by fish feed

The ecological health of aquaculture water is threatened by wasted fish feed and herbicides. In order to study the effect of prometryn and fish feed on Microcystis aeruginosa growth based on Monod and Logistic functions, four different concentrations of prometryn (0, 50, 100 and 200 μg L^-1) and two different dosages of fish feed (0.075 g, 0.15 g; d < 0.85 mm) were added into the culture medium, and the fish feed was the source of nitrogen and phosphorus in the MII medium. Results showed that Microcystis aeruginosa growth can be fitted well by Logistic and modified Logistic functions with 0-200 μg L^-1 prometryn (R² = 0.981-0.998 and R² = 0.989-0.999, respectively). With the same concentration of prometryn, the maximum algae density (N_max) of Microcystis aeruginosa calculated by both Logistic and modified Logistic functions increased with increasing dosage of fish feed and with the same dosage of fish feed, N_max declined with increasing concentrations of prometryn. Inhibition of prometryn on algae growth stimulated by fish feed is of double concentration-dependence, inhibition rates (I) are lower in 0.15 g fish feed medium than 0.75 g ones generally, implying that more nutrients can alleviate the stress caused by prometryn on algae. Derived formula for the specific growth rate, growth rate and inhibition rate using modified Logistic function agreed reasonably well with measured data. Jointly application of modified Monod and Logistic functions can better describe the relationship between specific growth rates and nutrients concentrations compared to combination of Monod and Logistic functions. In addition, equations for describing variations of nutrients concentrations (PO₄^3--P and NH₄⁺-N) with time were also derived based on both modified Monod and Logistic functions, which agree reasonably well with the measured data. In sum, the combination of modified Monod and Logistic functions provides a promising and robust method in studying algal growth stimulated by fish feed in incubator experiments.