Regression and Sensitivity Analyses of Degradation Data

Although the tests were performed in an exploratory manner and thus neither a complete factorial design nor a complete fraction of a factorial design was completed, a significant amount of revealing information was collected in the tests. Since the goal was to bracket allowable moisture and inoculum ranges, statistical analyses of the xylan and glucan degradation data were conducted by regression analysis and used to explore system sensitivity to initial moisture and inoculum contents.

Regression Analyses

The conversion data for all tests were combined into a single data set represented by 234 data points varying in inoculum amount (I, mg of P. ostreatus/g of stems), gravimetric moisture content (M, g of H2O/g of stems), and treatment time (t, d). A power series expansion of the three variables through the second-order terms was fitted using linear regres­sion; the expansion included the terms I, M, t, IM, It, Mt, I2, M2, and t2, with an intercept of zero. Note that this equation has no basis in theory and was chosen simply because its shape was appropriate. The primary goal of the regression analyses was to obtain statistically valid equations for both AX and AG, and to use these relationships to estimate the sensitivity of the system to inoculum, moisture, and treatment time.

The xylan conversion (AX) and glucan conversion (AG) data were fitted separately to the power series expansion, resulting in r2 values of 0.925 and 0.910, respectively. However, an analysis of variance indicated that the terms M, IM, M2 in both analyses were statistically insignificant and thus unnecessary to fit the data. The data were refitted after dropping those terms, resulting in statistically valid fits with r2 values of 0.924 and 0.909. The results of the regression analyses are presented for both fits in Table 5, and comparisons of the measured and predicted values of AX and AG are shown in Figs. 3 and 4, respectively. Relatively good fits to the data were obtained, indicating that the data were internally consistent and that the system behaved in a predictable manner. The fits were more accurate at higher values of inoculum and moisture, caused by the higher

Table 5

Regression Models for Xylan and Glucan Conversions

Regression Resultsa

AX = axI + Pxt + YxIt + SxMt + ExI2 + фхТ AG = a^I + в

gt + YgIt + SgMt + EgI2 + ф^2

DOFb

233

233

r2

0.924

0.909

ai

0.106

0.0551

Pi

0.514

0.408

Yi

1.68 x 10-3

1.43 x 10-3

Si

0.106

0.0770

Ei

-8.19 x 10-4

-4.45 x 10-4

Фі

-4.11 x 10-3

-2.89 x 10-3

a Variable definitions: AX (xylan conversion, %); AG (glucan conversion, %); I (inoculum amount, mg of P. ostreatus/g of stems); M (moisture content, g of H2O/g of stems); t (time, d). b DOF, degrees of freedom for the regression analysis.

image037

Fig. 3. Comparison of predicted and measured xylan conversions for fungal upgrad­ing tests. The line shown has a slope of 1.0 and represents a perfect fit to the data.

amount of variability in degradation data at lower inoculum levels and moisture contents. The predicted conversions of xylan (AX), glucan (AG), and the ratio AX/AG with time are shown for the ultimately selected treatment conditions (40 mg of P. ostreatus /g of stems, 1.60 g of H2O/g of stems) in Fig. 5. The percentages of degradation for the nearest experi­mentally observed combination (44.0 mg of P. ostreatus/g of stems, 1.60 g of H2O/g of stems) were under-predicted by 5-10% at later treat­ment times (not shown). It is clear from Fig. 5 that the time-rate of degra­dation had decreased substantially by 12 wk and thus harvesting at 10 or 14 wk would make little difference in the final composition. In addition, the selectivity for xylan degradation over glucan degradation is predicted to be initially about 2.0 and then to decrease with time to about 1.2. This suggests that shorter treatment times would be preferred with this organ­ism if a more selective degradation is desired, although the initially high rate of decline of AX/AG is most likely an artifact of higher measurement uncertainties in the data at lower moisture and inoculum.

image038

Fig. 4. Comparison of predicted and measured glucan conversions for fungal upgrad­ing tests. The line shown has a slope of 1.0 and represents a perfect fit to the data.

image039

Fig. 5. Predicted time courses of xylan conversion (AX, %), glucan conversion (AG, %), and the degradation ratio (AX/AG) for 40 mg of P. ostreatus/g of stems and 1.60 g of H2O/g of stems.