Model significance analysis
The regression equations of salinity and temperature on the digestive physiological indexes of P. fucata (each coefficient was the actual value) established in the experiment were as follows:
AMS = − 19.3181 + 0.6795 * T + 0.8290 * S - (9.8000E − 003) * T * S - (7.8316E − 003) * T^2 -0.0102 * S^2
LPS = + 2.0610 - (6.7933E − 003) * T + (5.0782E − 003) * S - (2.6280E − 005) * T * S + (2.4976E − 004) * T^2 - (5.4164E − 005) * S^2
PEP = − 0.6887 + 0.1467 * T + 0.0919 * S - (3.2000E − 003) * T * S - (7.5789E − 004) * T^2 - (2.5789E − 004) * S^2
TRYP = − 2854.8924 + 19.1371 * T + 247.3842 * S + 1.4045 * T * S − 1.0933 * T^2 -5.0919 * S^2
GPX-liver = + 16.8759 − 0.4343 * T − 0.8073 * S + (9.5500E − 003) * T * S + (4.4360E − 003) * T^2 + (9.9370E − 003) * S^2
SOD-liver = + 133.7362–4.1737 * T − 5.3563 * S + 0.0722 * T * S + 0.0385 * T^2 + 0.0590 * S^2
Variance analysis of digestive indexes and immune genes in liver were presented in Tables 1. The results showed that the established models of salinity and temperature on digestive physiology of P. fucata were significantly indigenous (P < 0.05), and the mismatch term was not significantly indigenous (P > 0.05), indicating that the regression model was significantly indigenous. The fitting between experimental data and the model was good, and the model was suitable. The experimental results caused by unknown factors had little interference. The R2 of the established model was 0.9543, 0.9396, 0.9271, 0.9558, 0.9322 and 0.9246, respectively; the AdjR2 was 0.9335, 0.9122, 0.8940, 0.9357, 0.9014 and 0.8904, respectively; and the PredR2 was 0.8530, 0.8276, 0.7687, 0.8611, 0.7323 and 0.7083, respectively, so the model was appropriate.
Table 1
Model variance analysis of digestive indexes
Response | Source | Quadratic sum | df | Mean square | F value | P value | |
AMS | model | 0.760 | 5 | 0.150 | 45.91 | < 0.0001 | significant |
| residual error | 0.037 | 11 | 3.327E-003 | | | |
| lack of fit | 0.016 | 3 | 5.439E-003 | 2.15 | 0.1726 | not significant |
| pure error | 0.020 | 8 | 2.535E-003 | | | |
| total deviation | 0.800 | 16 | | | | |
LPS | model | 5.474E-003 | 5 | 1.095E-003 | 34.23 | < 0.0001 | significant |
| residual error | 3.518E-004 | 11 | 3.198E-005 | | | |
| lack of fit | 1.331E-004 | 3 | 4.436E-005 | 1.62 | 0.2594 | not significant |
| pure error | 2.187E-004 | 8 | 2.734E-005 | | | |
| total deviation | 5.825E-003 | 16 | | | | |
PEP | model | 0.100 | 5 | 0.021 | 28.00 | < 0.0001 | significant |
| residual error | 8.072E-003 | 11 | 7.338E-004 | | | |
| lack of fit | 2.702E-003 | 3 | 9.006E-004 | 1.34 | 0.3277 | not significant |
| pure error | 5.370E-003 | 8 | 6.713E-004 | | | |
| total deviation | 0.110 | 16 | | | | |
TRYP | model | 82652.860 | 5 | 16530.570 | 47.60 | < 0.0001 | significant |
| residual error | 3820.370 | 11 | 347.310 | | | |
| lack of fit | 1053.460 | 3 | 351.150 | 1.02 | 0.4351 | not significant |
| pure error | 2766.910 | 8 | 345.860 | | | |
| total deviation | 86473.230 | 16 | | | | |
GPX | model | 1.190 | 5 | 0.240 | 30.26 | < 0.0001 | significant |
| residual error | 0.086 | 11 | 7.837E-003 | | | |
| lack of fit | 0.050 | 3 | 0.017 | 3.71 | 0.0614 | not significant |
| pure error | 0.036 | 8 | 4.508E-003 | | | |
| total deviation | 1.270 | 16 | | | | |
SOD | model | 49.010 | 5 | 9.800 | 26.99 | < 0.0001 | significant |
| residual error | 3.990 | 11 | 0.360 | | | |
| lack of fit | 1.890 | 3 | 0.630 | 2.39 | 0.1438 | not significant |
| pure error | 2.100 | 8 | 0.260 | | | |
| total deviation | 53.000 | 16 | | | | |
The regression equations of salinity and temperature on the respiratory and metabolic physiological indexes of P. fucata (each coefficient is the actual value) established in the experiment were as follows:
LDH = + 6477.9344–235.5640 * T -225.9151 * S + 1.6170 * T * S + 3.9368 * T^2 + 3.1262 * S^2
NKA = + 37.2763–0.7110 * T − 1.6076 * S + 0.0188 * T * S - (1.0868E -003) * T^2 + 0.0192 * S^2
AKP = + 2059.6119–109.0579 * T − 21.2943 * S -1.7825 * T * S + 3.2400 * T^2 + 0.9106 * S^2
GPX-gill = + 13.5320 − 0.3348 * T − 0.6105 * S + (6.9700E − 004) * T * S + (5.1916E − 003) * T^2 + 0.0111 * S^2
SOD-gill = + 32.6290–1.5447 * T − 0.8288 * S + 0.0213 * T * S + 0.0175 * T^2 + (4.9017E − 003) * S^2
Variance analysis was performed on respiratory metabolism indexes and immune genes in gill tissues (Table 2). The results showed that the established models of the effects of salinity and temperature on respiratory metabolism physiology of P. fucata were significantly indigenous (P < 0.05), and the mismatch term was not significantly indigenous (P > 0.05), indicating that the regression model was significantly indigenous, and the fitting between the experimental data and the model was good, the model was suitable, and the experimental results caused by unknown factors had little interference. The R2 of the established model was 0.9587, 0.9699, 0.9358, 0.9492 and 0.9294, respectively; the AdjR2 was 0.9400, 0.9562, 0.9066, 0.9262 and 0.8973, respectively; and the PredR2 was 0.8469, 0.8730, 0.7314, 0.8614 and 0.7794, respectively, indicating that the model was appropriate.
Table 2
Model variance analysis of respiratory metabolic indicators
Response | Source | Quadratic sum | df | Mean square | F value | P value | |
LDH | model | 1.074E + 005 | 5 | 21473.120 | 51.10 | < 0.0001 | significant |
| residual error | 4622.790 | 11 | 420.250 | | | |
| lack of fit | 2668.480 | 3 | 889.490 | 3.64 | 0.0639 | not significant |
| pure error | 1954.310 | 8 | 244.290 | | | |
| total deviation | 1.120E + 005 | 16 | | | | |
NKA | model | 14.200 | 5 | 2.840 | 70.87 | < 0.0001 | significant |
| residual error | 0.440 | 11 | 0.040 | | | |
| lack of fit | 0.260 | 3 | 0.088 | 3.95 | 0.0533 | not significant |
| pure error | 0.180 | 8 | 0.022 | | | |
| total deviation | 14.640 | 16 | | | | |
AKP | model | 84824.460 | 5 | 16964.890 | 32.07 | < 0.0001 | significant |
| residual error | 5818.580 | 11 | 528.960 | | | |
| lack of fit | 3318.580 | 3 | 1106.190 | 3.54 | 0.0678 | not significant |
| pure error | 2500.000 | 8 | 312.500 | | | |
| total deviation | 90643.040 | 16 | | | | |
GPX | model | 1.190 | 5 | 0.240 | 41.13 | < 0.0001 | significant |
| residual error | 0.064 | 11 | 5.777E-003 | | | |
| lack of fit | 0.018 | 3 | 5.848E-003 | 1.02 | 0.4345 | not significant |
| pure error | 0.046 | 8 | 5.750E-003 | | | |
| total deviation | 1.250 | 16 | | | | |
SOD | model | 3.150 | 5 | 0.630 | 28.97 | < 0.0001 | significant |
| residual error | 0.240 | 11 | 0.022 | | | |
| lack of fit | 0.088 | 3 | 0.029 | 1.54 | 0.2768 | not significant |
| pure error | 0.150 | 8 | 0.019 | | | |
| total deviation | 3.390 | 16 | | | | |
Model Coefficient Estimation
The established regression model of digestive and respiratory metabolism indexes were estimated by coefficients, and the results were shown in Table 3 and Table 4. The coefficients in Table 3 and Table 4 were coded values (elimination of units among coefficients), and their effects were directly reflected by numerical values. 95% confidence interval (C.I.) explained the change of coefficient coding value in 95% interval.
Table 3 showed that the minimum values of 95% C.I. prediction of digestive index intercept were 1.05, 2.12, 2.61, 841.85, 0.58 and − 0.19, respectively, and the maximum values were 1.15, 2.13, 2.66, 874.45, 0.74 and 0.86, respectively.
The test and analysis results of the model coefficients showed that the primary and secondary effects of salinity and temperature and their interaction effects had significant indigenous effects on AMS (P < 0.05). The primary and secondary effects of salinity and temperature had significant effects on LPS (P < 0.05), while the secondary effects of salinity and their interaction with temperature had no significant effects on LPS (P > 0.05). The primary effect of temperature and the interaction effect of temperature and salinity had significant influence on PEP (P < 0.05), while the primary effect of salinity and the secondary effect of temperature and salinity had no significant influence on PEP (P > 0.05). The primary, secondary and interactive effects of salinity and temperature had significant effects on TRYP (P < 0.05). The primary and secondary effects of temperature, the secondary effects of salinity and the interaction between temperature and salinity had significant effects on the relative gene expression of GPX in liver (P < 0.05), while the primary effect of salinity had no significant effect on the relative gene expression of GPX in liver (P > 0.05). The primary, secondary and interaction effects of temperature and salinity had significant effects on the relative gene expression of SOD in liver (P < 0.05).
Table 4 showed that the minimum values predicted by the 95% C.I. of the intercept of respiratory metabolism indexes were 288.61, 1.82, 207.92, 0.43 and 0.40, respectively, and the maximum values were 324.47, 2.17, 248.15, 0.56 and 0.65, respectively. The test results of the model coefficients showed that the primary, secondary and interaction effects of salinity and temperature had significant indigenous effects on LDH (P < 0.05). Primary effect of salinity and temperature and their interaction effect, secondary effect of salinity had significant indigenous effect on NKA (P < 0.05), secondary effect of temperature had no significant indigenous effect on NKA (P > 0.05). The primary effect of temperature and the secondary effect of salinity had no significant indigenous effect on AKP (P > 0.05), while the primary effect of salinity, the secondary effect of temperature and the interaction between temperature and salinity had significant indigenous effect on AKP (P < 0.05). The primary and secondary effects of salinity and temperature had significant effects on the relative expression of GPX gene in gill tissue (P < 0.05), and the interaction of salinity and temperature had no significant effect on the relative expression of GPX gene in gill tissue (P > 0.05). The primary and secondary effects of temperature and the interaction of salinity and temperature had significant effects on the relative expression of SOD gene in gill (P < 0.05), while the primary and secondary effects of salinity had no significant effects on the relative expression of SOD gene in gill (P > 0.05).
Table 3
Coefficient estimation of the digestive index prediction model equation
Response | Factor | Coefficient estimation | P value | Standard error | 95% C.I. |
Low | High |
AMS | Intercept | 1.100 | - | 0.023 | 1.050 | 1.150 |
| T | 0.067 | 0.0070 | 0.020 | 0.023 | 0.110 |
| S | 0.055 | 0.0208 | 0.020 | 0.010 | 0.100 |
| T*S | -0.25 | < 0.0001 | 0.029 | -0.310 | -0.180 |
| T2 | -0.20 | < 0.0001 | 0.028 | -0.260 | -0.130 |
| S2 | -0.26 | < 0.0001 | 0.028 | -0.320 | -0.190 |
LPS | Intercept | 2.130 | - | 2.247E-003 | 2.120 | 2.130 |
| T | 0.025 | < 0.0001 | 1.999E-003 | 0.020 | 0.029 |
| S | 6.940E-003 | 0.0052 | 1.999E-003 | 2.539E-003 | 0.011 |
| T*S | -6.570E-004 | 0.8205 | 2.828E-003 | -6.880E-003 | 5.566E-003 |
| T2 | 6.244E-003 | 0.0444 | 2.752E-003 | 1.865E-004 | 0.012 |
| S2 | -1.354E-003 | 0.6324 | 2.752E-003 | -7.412E-003 | 4.703E-003 |
PEP | Intercept | 2.640 | - | 0.011 | 2.610 | 2.660 |
| T | 0.096 | < 0.0001 | 9.577E-003 | 0.075 | 0.120 |
| S | -0.012 | 0.2185 | 9.577E-003 | -0.034 | 8.579E-003 |
| T*S | -0.080 | 0.0001 | 0.014 | -0.110 | -0.050 |
| T2 | -0.019 | 0.1785 | 0.013 | -0.048 | 0.010 |
| S2 | -6.447E-003 | 0.6344 | 0.013 | -0.035 | 0.023 |
TRYP | Intercept | 858.150 | - | 7.410 | 841.850 | 874.450 |
| T | 19.000 | 0.0149 | 6.590 | 4.500 | 33.500 |
| S | -13.230 | 0.0698 | 6.590 | -27.740 | 1.270 |
| T*S | 35.110 | 0.0031 | 9.320 | 14.600 | 55.620 |
| T2 | -27.330 | 0.0118 | 9.070 | -47.290 | -7.370 |
| S2 | -127.300 | < 0.0001 | 9.070 | -147.260 | -107.330 |
GPX | Intercept | 0.660 | - | 0.035 | 0.580 | 0.740 |
| T | 0.270 | < 0.0001 | 0.031 | 0.210 | 0.340 |
| S | -0.060 | 0.0799 | 0.031 | -0.130 | 8.515E-003 |
| T*S | 0.240 | 0.0002 | 0.044 | 0.140 | 0.340 |
| T2 | 0.110 | 0.0259 | 0.043 | 0.016 | 0.210 |
| S2 | 0.250 | 0.0001 | 0.043 | 0.150 | 0.340 |
SOD | Intercept | 0.330 | - | 0.240 | -0.190 | 0.860 |
| T | -1.120 | 0.0003 | 0.210 | -1.590 | -0.650 |
| S | -1.230 | 0.0001 | 0.210 | -1.700 | -0.760 |
| T*S | 1.810 | < 0.0001 | 0.300 | 1.140 | 2.470 |
| T2 | 0.960 | 0.0073 | 0.290 | 0.320 | 1.610 |
| S2 | 1.480 | 0.0004 | 0.290 | 0.830 | 2.120 |
Table 4
Coefficient estimation of the respiratory metabolic index prediction model equation
Response | Factor | Coefficient estimation | P value | Standard error | 95% C.I. |
Low | High |
LDH | Intercept | 306.540 | - | 8.150 | 288.610 | 324.470 |
| T | 32.760 | 0.0009 | 7.250 | 16.810 | 48.710 |
| S | -52.120 | < 0.0001 | 7.250 | -68.070 | -36.170 |
| T*S | 40.420 | 0.0023 | 10.250 | 17.860 | 62.990 |
| T2 | 98.420 | < 0.0001 | 9.980 | 76.460 | 120.380 |
| S2 | 78.150 | < 0.0001 | 9.980 | 56.200 | 100.110 |
NKA | Intercept | 2.000 | - | 0.080 | 1.820 | 2.170 |
| T | -1.200 | < 0.0001 | 0.071 | -1.360 | -1.050 |
| S | -0.310 | 0.0010 | 0.071 | -0.470 | -0.160 |
| T*S | 0.470 | 0.0007 | 0.100 | 0.250 | 0.690 |
| T2 | -0.027 | 0.7855 | 0.097 | -0.240 | 0.190 |
| S2 | 0.480 | 0.0004 | 0.097 | 0.270 | 0.690 |
AKP | Intercept | 228.030 | - | 9.140 | 207.920 | 248.150 |
| T | 15.150 | 0.0893 | 8.130 | -2.750 | 33.050 |
| S | -74.330 | < 0.0001 | 8.130 | -92.220 | -56.430 |
| T*S | -44.560 | 0.0026 | 11.500 | -69.870 | -19.250 |
| T2 | 81.000 | < 0.0001 | 11.190 | 56.360 | 105.630 |
| S2 | 22.760 | 0.0668 | 11.190 | -1.870 | 47.400 |
GPX | Intercept | 0.490 | - | 0.030 | 0.430 | 0.560 |
| T | -0.280 | < 0.0001 | 0.027 | -0.340 | -0.220 |
| S | 0.140 | 0.0003 | 0.027 | 0.080 | 0.200 |
| T*S | 0.017 | 0.6555 | 0.038 | -0.066 | 0.100 |
| T2 | 0.130 | 0.0049 | 0.037 | 0.048 | 0.210 |
| S2 | 0.280 | < 0.0001 | 0.037 | 0.200 | 0.360 |
SOD | Intercept | 0.520 | - | 0.059 | 0.400 | 0.650 |
| T | -0.360 | < 0.0001 | 0.052 | -0.470 | -0.240 |
| S | -0.110 | 0.0638 | 0.052 | -0.220 | 7.328E-003 |
| T*S | 0.530 | < 0.0001 | 0.074 | 0.370 | 0.700 |
| T2 | 0.440 | < 0.0001 | 0.072 | 0.280 | 0.600 |
| S2 | 0.120 | 0.1158 | 0.072 | -0.035 | 0.280 |
Response surface analysis of digestive and respiratory metabolism
Under all different combinations of salinity and temperature, the digestive enzyme activity and the relative expression of immune genes in liver tissue estimated according to the fitted response surface were shown in Fig. 1. By examining the response surface or contour, it was found that the relative expression levels of AMS, TRYP and liver SOD genes were unimodal. AMS and TRYP increased firstly and then decreased with the increasing of temperature or salinity, while the relative expression of SOD gene in liver decreased firstly and then increased with the increasing of temperature or salinity. LPS increased with the increasing of the two factors. PEP increased with the increasing of temperature and decreased with the increasing of salinity. The relative expression level of liver GPX gene showed an upward trend with the increasing of temperature, and decreased firstly and then increased with the increasing of salinity.
Under all different combinations of salinity and temperature, the activities of respiratory metabolic enzymes and the relative expression of immune genes in gill tissue estimated by the fitted response surface were shown in Fig. 2. By examining the response surface or contour, it was found that LDH was a single peak, and its activity showed a U-shaped trend with the increase of salinity or temperature. NKA showed a decreasing trend with the increase of temperature, and a U-shaped trend with the increase of salinity. AKP showed a U-shaped trend with the increase of temperature, and decreased with the increase of salinity. The relative expression of GPX gene in gill tissue showed a decreasing trend with the increase of temperature, and a U-shaped trend with the increase of salinity. The relative expression of SOD gene in gill tissue showed a U-shaped trend with the increase of temperature, and decreased with the increase of salinity.
Optimization
The results showed that the optimal combination of temperature and salinity was 26.288℃/28.272‰, and the maximum value of AMS, LPS, PEP and TRYP was 1.107, 2.136, 2.660 and 860.627, respectively. The minimum relative expression levels of GPX and SOD genes in liver were 0.740 and 0.070, respectively. The lowest relative expression levels of GPX and SOD genes in gill were 0.439 and 0.463, respectively, and the lowest values of LDH, NKA and AKP were 319.477, 1.677 and 232.716, respectively. The desirability was 0.832.