## 3 Results
### Model Evaluation  
Using the FR values predicted from SI, 3-PG accurately predicted yield and mortality of loblolly pine in the control plots from the 21 sites in this study. Overall, using FR determined _a priori_ from site index using Equation (3), the aboveground biomass derived from DBH and Height (observed aboveground biomass) and predicted aboveground biomass from 3-PG had an \(R^{2}\) of 0.89 and the measured stand tree density and predicted stand tree density also had an \(R^{2}\) value of 0.89 (Figure 4). The model efficiency for aboveground biomass was 0.88. The slope of the relationship between observed aboveground biomass and predicted aboveground biomass was not significantly different from 1 (\(p<0.001\)). Similarly, the slope between measured values of stand density and modeled values of stand density was not different from 1 (\(p<0.001\)). Although 3-PG predited yield well at most sites, there was more variation when observed vs predicted growth was examined on individual sites. Figure 5 illustrates results from several study sites where predictions matched well with the observed values and the sites where predictions did not match well with the observed values. Among the sites where prediction did not match well with the observed values were the sites dominated by Spodosols in the Lower Coastal Plain and the sites where some stochastic events caused high level of mortality. Figure 3: Sigmoidal relationship between Fertility Rating (FR) and site index based on the relationship between stand volume and site index illustrated in Table 3.  
Figure 4: Relationship between observed aboveground biomass (Mg ha\({}^{-1}\)) and modeled aboveground biomass (left) and measured stem density (stem ha\({}^{-1}\)) and modeled stem density across the 48 control plots at the 21 study sites located across the southeastern United States. Solid lines represent linear fit between observed and predicted values and dotted lines represent the 1:1 line between observed and predicted values. Group of points around (1400,1000) in left diagram were due to lightning caused mortality. Figure 5: _Cont._  
3-PG also performed well when evaluated against the independent data from the mid-rotation stands not used to develop the relationship between site index and FR. The predicted values from 3-PG explained 73% of the variation in observed aboveground biomass and 86% of the variation in measured stand density in the independent data (Figure 6). However, there was a positive bias in the predicted aboveground biomass in the data set with a significant difference from the 1:1 line. The slope of the relationship between observed stand density and predicted stand density was not significantly different from 1 (\(p<0.001\)). 3-PG predicted stem density explained 88% of the variance in observed stem density. 3-PG predicted mortality accurately on the majority of the sites. The largest discrepancies in mortality predictions were observed in Kershaw, South Carolina; Brantley, Georgia; Vernon, Louisiana; and Sabine, Louisiana. The site in Kershaw, South Carolina suffered higher rates of mortality due to lightning, the site in Brantley Georgia suffered higher mortality due to unknown reasons, and the site in Vernon, Louisiana had no mortality. The predicted LAI value from 3-PG increased as FR increased, reaching a peak LAI of 5.5, 4, and 2 for FR values of 0.96, 0.64, and 0.21, respectively. LAI measurements were available on 4 of the 21 study sites; 3-PG predicted LAI reasonably well on these sites. About 53% of the variation in observed LAI was described by the predicted LAI (Figure 7). 3-PG also predicted a reasonable pattern for LAI development throught time. Predicted LAI increased as FR increased and the age of maximum LAI was a function of FR. Higher FR values tend to shorten the time to reach maximum LAI (Figure 7).