### Model analysis

#### Analysis on Growth Curve of 1. Algae Species

After preprocessing the experimental growth data of algae culture, the MATLAB was used for statistical analysis, and figure 1/2 was obtained. Fig .1 is a light condition exploration group. The constant environmental condition is set as a f/2 medium with nitrogen concentration of 75μmol/L, and artificial seawater is arranged according to the Harrison formula (salinity is 3.05% PSU).The Solar light condition is light intensity and period are natural light, Regulated light condition is light intensity 58.5μmol m-2s-1and the period is 12 h/12h, and the temperature is natural. Figure 2 shows the temperature exploration group, whose constant is about 58.5μmol m of illumination-2s-1The light-darkness ratio was 12 L ：12D, medium was the f/2 medium of artificial seawater, in which nitrogen concentration was 75μmol/L, artificial seawater was arranged according to the Harrison formula (salinity was 3.05% PSU). temperature conditions were 20℃,22℃,24℃,26℃, normal window group.

The preliminary analysis of the above pictures shows that Regulated light group is more suitable for algae growth than Solar light group. The algae species seemed to like 22℃~24℃ at temperature, but showed a significant decline in growth for 20 and 26℃.

#### Analysis of Ecological Model of 2. Algae Temperature

##### 2.1 Univariate ANOVA analysis

A single factor ANOVA analysis was proposed to further confirm the significant effect of temperature on the growth of algae species. The growth state of algae species should be evaluated by the maximum specific growth rate, that is:

One-way anova was performed for the maximum specific growth rate with respect to temperature,and Table 2was obtained.The results showed that temperature had an impact on the maximum specific growth rate of algae at the level of 0.01. this confirms our preliminary conjecture that temperature has a significant effect on the growth state of algae species.

##### 2.2 Estimation of ecological model parameters

In order to further understand the temperature attributes of algae species, according to the literature consulted, two commonly used formulas of the corresponding relationship between algae species, shown in formula (3),(4), are found, which are based on the law of Shelford tolerance. An empirical formula based on the trend of algae growth data.

The μ is the maximum specific growth rate of algae ,σ is the tolerance of environmental conditions, T(opt) is the optimum growth temperature of algae species, is the experimental temperature and the parameter.

Using the principle of least square optimization and Newton iterative algorithm to optimize the parameters, the results of the parameters are shown in Table 3，4, and the data fitting results are shown in figure 3，4.

By analyzing the fitting results, it is found that the data consistency is very high and the results are satisfactory. The analysis of the parameters shows that the response relation formula 4 is too large and contrary to its actual biological significance, so the formula 4 is excluded, and the formula 3 parameters accord with the specific biological significance, and the results are satisfactory.

#### 3. Model results

After a series of data analysis, a series of parameters are obtained. According to the principle of tolerance of algae species ecological amplitude, the temperature ecological amplitude attribute of algae species can be obtained as follows:

By comparing the above results with the culture literature of related algae species, it is found that the results are very consistent, which indicates that the model is very successful.