## 4 Discussion
The relationship between plant productivity and soil nutrient concentration between the deficiency stage and sufficiency stages is linear [18, 38, 39, 40]. We used a linear function to define the relationship between FR and productivity, and a three parameter sigmoidal function to address three stages of relationship between soil nutrient concentration and plant productivity, namely, deficiency, sufficiency, and luxury consumption. Mortality has been ignored or considered zero in many previous studies with 3-PG, such as those in clonal eucalyptus stands [2, 3, 53]. 3-PG predicted mortality poorly in a study with _Pinus radiata_ in southeastern New Zealand [54]. [PERSON] _et al._ (2013) [6] also found poor predictions of mortality for loblolly pine in Georgia. In contrast, when used to simulate stocking in native eucalyptus forests in southeastern Australia, 3-PG performed well and explained about 89% of the variability in observed data [55]. Similar results were observed in our study, where the relationship between observed and predicted mortality had an \(R^{2}\) of 0.88. In the 21 study sites in this study, there were only 4 sites where large discrepancies were observed. Two of these sites suffered higher mortality due to causes not related to stand density. At 10 of 21 study sites 3-PG predicted stocking within \(\pm\)30 trees ha\({}^{-1}\). Results from this study also demonstrate that 3-PG can be used to accurately reproduce observed LAI in loblolly pine stands. Our model predictions of LAI as a function of FR were reasonable based on observed values [31, 56]. Good correspondence was obtained between simulated LAI across fertility gradients and reported LAIs. For example, LAI values of 5.5 on sites with higher FR values matched well with LAI values observed by [PERSON] _et al._ (2013) [31] and [PERSON] _et al._ (2012) [57]. LAI simulated on medium and low fertility ratings corresponded well with LAI reported by [PERSON] _et al._ (2012) [58] for loblolly pine. Both the maximum LAI and the time to reach it were observed to be functions of FR. Our results support the assertion from [PERSON] _et al._ (1994) [56] that slow growing stands reach maximum LAI later than fast growing stands. An average value for growth efficiency on control plots for loblolly pine in the southeastern United States is approximately 7.2 m\({}^{3}\) ha\({}^{-1}\) yr\({}^{-1}\) LAI\({}^{-1}\) [26, 59]. In this study, the sites with low fertility, such as the control plots in Oglethorpe, Georgia, had current annual increment (CAI) of 17 m\({}^{3}\) ha\({}^{-1}\) yr\({}^{-1}\) at age 11. The predicted LAI for this site was 2.40, which translates into a growth efficiency of 7.1 m\({}^{3}\) ha\({}^{-1}\) yr\({}^{-1}\) LAI\({}^{-1}\). The sites with high fertility such as the control plots in Marengo, Alabama had a CAI of 34 m\({}^{3}\) ha\({}^{-1}\) yr\({}^{-1}\) at age 9. The predicted LAI for this site was 5.4, which translates into a growth efficiency of 6.3 m\({}^{3}\) ha\({}^{-1}\) yr\({}^{-1}\) LAI\({}^{-1}\). Results from this study show that while predictions of loblolly pine aboveground biomass by 3-PG across the broader region were reasonably accurate, predictions at individual specific sites may be poorer. This result has been observed in other models of pine growth such as empirical growth and yield models [15]. In this study 3-PG performed well at most of the sites with finer textured Alfisols and Ultisols. 3-PG predictions of aboveground biomass were less accurate in sandy Spodosols and Entisols. On these soils 3-PG predictions were generally more accurate at younger ages and then declined with time. Temporal variation in nutrient availability may cause the poorer prediction on the sandy soils. Nutrient availability in pine plantations varies through time, especially for N, which is often the nutrient most limiting productivity [18] and therefore should be highly related to FR.