## 1 Introduction  
The 3-PG model [1], Physiological Principles Predicting Growth, is a process model that predicts forest productivity based on radiation use efficiency, carbon balance, and partitioning. 3-PG and its variants have been calibrated and tested on many commercially important tree species around the globe. Work with eucalypt (_Eucalyptus grandis_ [PERSON]) [2,3], patula pine (_Pinus patula_ [PERSON].) [4], loblolly pine (_Pinus taeda_ L.) [5,6], radiata pine (_Pinus radiata_ [PERSON]) [7], slash pine (_Pinuselliotti_ Engelm. var. _elliotti_) [8], and ponderosa pine (_Pinus ponderosa_ Dougl. ex. [PERSON].) [9] have found that 3-PG can accurately predict growth under a variety of management regimes and climatic and edaphic conditions. 3-PG calculates the amount of photosynthetically active radiation (PAR, \(\phi_{p}\)) intercepted by a stand (APAR, \(\phi_{pa}\)) which is then converted into gross primary productivity (GPP,P\({}_{G}\)) using canopy quantum efficiency (\(\alpha_{c}\)), constrained by environmental factors such as vapor pressure deficit (D), mean temperature (T), soil moisture (\(\theta_{s}\)), frost days, and site nutrient status [2]. Canopy quantum efficiency, \(\alpha_{c}\), is calculated as:  
\[\alpha_{c}=f_{T}\;f_{N}\;f_{f}\;\varphi\;\alpha_{Cx}\]  
where \(\alpha_{Cx}\) is the theoretical maximum canopy quantum efficiency, f\({}_{\rm T}\), f\({}_{\rm N}\), f\({}_{\rm f}\), and \(\varphi\) are temperature, nutrition, frost, and physiology related modifiers, respectively. The physiology related modifier (\(\varphi\)) is defined by the multiplication of an age-dependent modifier (f\({}_{\rm Age}\)) and the most restrictive of the vapor pressure deficit (f\({}_{\rm D}\)) and soil water modifiers (f\({}_{\rm\theta}\)); such that \(\varphi=\) f\({}_{\rm Age}\) min\(\{\rm f_{D}f_{\rm\theta}\}\). Under non-limiting conditions, all these modifiers have values of 1 [1,2,10]. Net primary productivity (NPP, P\({}_{n}\)) is calculated as a fixed proportion of P\({}_{\rm G}\) that accounts for autotrophic respiration. P\({}_{n}\) is then allocated to aboveground and belowground biomass production. Fertility rating (FR), is a site-specific variable in 3-PG that relates soil fertility to stand productivity. FR is used in 3-PG as an index of nutrient availability and the effects of FR on P\({}_{\rm G}\) are determined by the impact of FR on leaf area index (LAI) which in turn affects APAR, canopy light use efficiency, and canopy conductance. The nutrient modifier (f\({}_{\rm N}\)) in 3-PG is calculated as: \({\rm f_{N}=1-(1-f_{N0})(1-FR)^{n_{N}}}\), where f\({}_{\rm N0}\) is the value of f\({}_{\rm N}\) when FR = 0 and \(n_{fN}\) determines the shape of the response. In 3-PG, \(f_{N0}\) is set at 0.5 [6] and \(n_{fN}\) is set to 1 so that the fertility modifier is a linear function of FR [11]. FR also has a direct effect on the partitioning coefficient, m, which is used to calculate partitioning to roots [1]. It is calculated as: \({\rm m=m_{0}+(1-m_{0})FR}\), where \({\rm m_{0}}\) is set to 0.1 [6]. Therefore when FR = 0, m = 0.1 and when FR = 1, m = 1. Several studies have attempted to use the relationship between soil properties and tree growth to estimate FR. [PERSON] _et al_. (2008) [12] used clay and sand percentage obtained from State Soil Geographic Survey (STATSGO) database to predict FR. [PERSON] _et al_. (2013) [13] used clay content and Ca, K, and Na in the soil profile to predict FR. [PERSON] _et al_. (2011) [14] used fertility limitation, water limitation, oxygen limitation, management limitation, and topographic limitation to calibrate FR. In all three cases 3-PG predictions of stand growth using the estimated FR values closely matched the observed data. However, they were not validated on independent sites. [PERSON] _et al_. (2004) [3] used a different approach based on the observed growth response following fertilization topredict FR in clonal eucalyptus stands.