## 4 Discussion  
Our hypothesis that FR can be estimated from SI and used as a fixed parameter in 3-PG was supported by the results of these simulations. When the independent estimate of FR from SI was input into 3-PG\({}_{\mathrm{lob}}\), the simulated value of yield matched the observed yield well, with an \(R^{2}\) value of 0.89. The slope of the relationship between observed aboveground biomass and predicted aboveground biomass was not significantly different from 1. Previous work on 3-PG to predict loblolly pine growth and yield by [PERSON] _et al._ (2001) [5] at a single location in North Carolina and by [PERSON] _et al._ (2013) [6] on multiple locations across Georgia also showed that 3-PG could predict loblolly pine growth and yield accurately. The present study was carried out on a wider range of sites across the South. This study used 48 control plots located at 21 study sites across 9 states in the southeastern United States and found that aboveground biomass and mortality were predicted reasonably well in the majority of sites in all the physiographic regions. The model also performed well when used against the independent data from mid-rotation stands not used in the model development. The predicted values from the model explained 73% of the variance in the observed aboveground biomass and 86% of the variance in measured stem density, which indicates that the model can be applied across a wide range of ages and stand conditions. The model to predict FR from site index provided _a priori_ estimates of FR in 3-PG. This is an improvement over previous work with 3-PG that has used FR as a tunable parameter to match 3-PG simulations to observed data [10]. Tuning FR makes detecting the proper value of FR a subjective decision. The validity of 3-PG growth predictions would be improved if a quantitative method could be developed to determine FR based on measured input parameters [6,13]. Determining soil fertility by measuring soil profiles will not always be practical, affordable or accurate for management applications [52]. It is also difficult to quantify soil fertility from soil properties in forested ecosystems because of the complex relationship between soil properties and stand productivity, deep rooting systems of trees that can explore soil deep into the profile, and variability in soil properties and characteristics within relatively small geographic areas [10,16]. 3-PG\({}_{\mathrm{lob}}\) is highly sensitive to FR. For example, FR value of 0, 0.5, and 1 for 12-years-old loblolly pine stand at 1677 stems ha\({}^{-1}\) in Brunswick, Virginia corresponded to 16.4 Mg ha\({}^{-1}\), 90.0 Mg ha\({}^{-1}\), and 167.2 Mg ha\({}^{-1}\) of aboveground biomass, respectively. FR was also accurately estimated from the SI values in the SSURGO dataset and used in 3-PG to model productivity of loblolly pine across the landscape. The 3-PG model produced realistic values of aboveground productivity when FR values were derived using SI values from the SSURGO dataset. For example in Kemper County, Mississippi 3-PG predicted aboveground productivity ranging from 40-85 Mg ha\({}^{-1}\) at 12 years. These values corresponded well with the previously reported range in the southeastern US [57,66,67]. The maximum site index for loblolly pine at base age 25 is approximately 30.5 m [47] and some of the infertile sites in the southeastern United States can have site index values as low as 10.7 m [45,46]. Conceptually, the relationship between soil nutrient concentration and plant growth can be classified into four steps: nutrient deficiency, sufficiency, luxury consumption, and toxicity in plants [38, 39, 40] and the relationship between soil nutrient supply and plant growth is curvilinear [39,40]. Plant productivity is low when soil nutrient concentrations are low but increases considerably at higher concentrations until nutrients no longer limits growth. After reaching the sufficiency stage, additionalnutrient applications result in luxury consumption.