Test algae and culture condition
Microcystis sp. and C. meneghiniana isolated from Lake Tega [17] were used as test algae in this study. Wright’s cryptophytes (WC) medium [18] at pH 8.0 was used as culture medium because it can cultivate both diatoms and cyanobacteria [19]. The initial nitrate-nitrogen (N) and phosphate-phosphorus (P) concentrations of the WC medium were 14 mg-N L-1 and 1.55 mg-P L-1, which were adjusted by dissolving sodium nitrate (NaNO3) and dipotassium hydrogen phosphate (K2HPO4) in distilled water, respectively. The concentration of silicate-silicon (Si) in medium supplied by sodium metasilicate (Na2SiO3) was increased from 2.8 mg-Si L-1 to 11 mg-Si L-1, which the same concentration with that in the Tone River water. For subculture, Microcystis sp. and C. meneghiniana were separately cultured in 100 mL WC medium in a 300 mL Erlenmeyer flask, at 25oC and 135 μmol photons m-2 s-1 with cool-white fluorescent light with the light-dark circle for 14 hours:10 hours. The both cultured species were transferred and inoculated to fresh medium every two or three weeks. All the media used were sterilized by autoclaving at 121oC for 20 minutes, and both inoculation and sampling transfer were conducted in a clean bench to minimum bacterial contamination.
Growth characteristics of Microcystis sp.and C. meneghiniana.
Under sufficient N concentration, the competitive experiment between M. aeruginosa and Cyclotella sp. showed that the limitation of phosphorus could not lead to the domination of Cyclotella sp.[11], which implies that cyanobacteria could still form blooms possibly in actual condition. Meanwhile, the appropriate dilution rate could inhibit the growth of M. aeruginosa effectively. Therefore, to determine the dominant characteristics of Microcystis sp. and C. meneghiniana under various dilution rates with the phosphorus limitation, a competitive culture experiment was performed with limited phosphorus concentration.
Prior to the competitive experiment, both species were precultured in a nitrogen- and phosphorus-free medium for 7 days to deplete intracellular N and P, so that they would not grow with the intracellular nutrient under nutrient limited condition. In the competitive experiment, both precultured species were inoculated together in the 100 mL sterilized medium in a 300 mL Erlenmeyer flask. The initial cell densities of Microcystis sp. and C. meneghiniana were adjusted to 1.0 × 104 and 3.98 × 102 cells mL-1, respectively, which were equivalent to the same cell volume of 105 μm3.
In many lakes, there was continuous water inflow from river, which could be modeled as a continuous culture system. The dilution rate (D) was used to represent the continuous inflow of the water per day. In this study, the culture medium was diluted with fresh medium once a day, which should be modeled as a semi-continuous culture system. The daily renewal rate (d) was used to describe the medium replacement in this culture system. This is because the daily renewal rate (d) in the semi-continuous culture system can be converted to the dilution rate (D) by the following equation [20] : see formula 1 in the supplementary files.
Three experimental groups with different daily renewal rates were set as 0%, 5% and 15%, in the competitive experiment. An appropriate volume of culture medium was removed and as soon an equal volume of fresh medium was added to each flask once a day. In addition to the different daily renewal rates, the P concentration of each group was limited to 0.1 mg-P L-1, which was same as the minimum P concentration in Lake Tega in recent five years [10]. The initial N concentration of 14 mg-N L-1 was adequate for the growth of both two species [19]. The cell density and nutrient concentration were measured every 2-5 days and continued until the growth rate became constant. The experiment was conducted in triplicates and the results were presented as [the mean value] ± [standard deviation].
Measurements and statistical analysis
The cell density of samples was measured by counting in a plankton counting plate (MPC-200, Matsunami Glass Industry, Japan) using an optical microscope (ECLIPSE E100, Nikon, Japan) after appropriately diluted.
Concentrations of nitrogen were measured by ion chromatography (ICS-1100, Nippon Dionex, Japan), and molybdenum blue method (Japanese Standard Association, 2016) was used to measure phosphorus concentration. The solution pH was monitored by a pH meter (D-51, Horiba, Japan).
Differences in experimental parameters of Microcystis sp. and C. meneghiniana in each condition were analyzed by a one-way analysis of variance (ANOVA) with a post hoc comparison being performed with Turkey’s test, via SPSS Statistics (Ver. 23, IBM Corporation, USA). The results were considered to be a significant difference at p < 0.05.
Mathematical model and simulation of cyanobacterial bloom appearance
In order to predict the cell densities of Microcystis sp. andC. meneghiniana and the trends of the appearance of cyanobacterial blooms under the various nutrient concentrations and daily renewal rates, the model constructed by Chujo et al. [4] was used. Then the effective dilution rate for suppressing cyanobacteria was discussed based on the simulated values. The equations of the model are tabulated in Table 1.
The accuracy of Mikawa’s model [16] tended to decrease under high nutrient concentrations. Because the growth rate term of the model was formulated based on the Droop equation, the growth rate values in a longer period would be close to μmax, which led to the excess of cell densities. For this reason, the carrying capacity term was introduced in the model by Chujo et al. [4] to limit the growth rate. The way to determine the limiting nutrient in the improved model was also different from that in the previous one. While in Mikawa’s model, the limiting nutrient was determined as the relationship between the mass ratio of minimum cell quota of assimilated N:P (the optimum N:P ratio) and the external dissolved N:P mass ratio. The relationship between the mass ratio of cell quota of assimilated N:P (Qn:Qp) and the optimum N:P ratio was taken as the determination of the limiting nutrient (as shown in the tag of Table 1) in the Chujo’s model.
The model equations were calculated via a fourth-order form of the Runge-Kutta method with the time step of Δt = 0.01 day, using Microsoft Excel. Furthermore, to investigate the accuracy of the predicted competitive growth patterns, the growth curves of both species were simulated under the same condition as the competitive experiment mentioned above.
In the case of model simulation, the initial N and P concentrations were adjusted from 0 to 5.0 mg-N L-1 and 0 to 0.5 mg-P L-1, respectively, reflecting the nutrient concentration in Lake Tega. The daily renewal rate (d) was increased from 0% to 20% with a 2.5% interval for each step. Since the two species always reached saturation around 20 days [4], the cell density in the 30th day was used as final result for prediction to ensure the simulated.