## 2 Materials and Methods
### Validation of the Relationship between FR and Site Index
\begin{table}
\begin{tabular}{c l l c} \hline  & **Parameters** & **Meaning** & **Unit** & **Value** \\ \hline
1 & pFS2 & Ratio of foliage:stem partitioning at stem diameter = 2 cm & 0.40 \\
2 & pFS20 & Ratio of foliage:stem partitioning at stem diameter = 20 cm & 0.25 \\
3 & StemConst & Constant in stem mass diameter relationship & 0.10 \\
4 & StemPower & Power in stem massvdiameter relationship & 2.50 \\
5 & pRx & Maximum fraction of NPP to roots & 0.40 \\
6 & pRn & Minimum fraction of NPP to roots & 0.20 \\
7 & SLA0 & Projected specific leaf area at the beginning of plantation & m\({}^{2}\) Kg\({}^{-1}\) & 6.40 \\
8 & SLA1 & Projected specific leaf area for mature stand & m\({}^{2}\) Kg\({}^{-1}\) & 4.00 \\
9 & tSLA & Age at which SLA is mean of SLA0 and SLA1 & year & 6.00 \\
10 & k & Extinction coefficient for APAR by canopy & 0.69 \\
11 & fullCanAge & Age at full canopy cover & year & 4.00 \\
12 & MaxIntcptn & Maximum proportion of rainfall intercepted by canopy & & 0.20 \\
13 & LAImaxIntcptn & LAI for maximum rainfall interception & & 5.00 \\
14 & \(\alpha_{Cx}\) & Maximum canopy quantum efficiency & molC molPAR\({}^{-1}\) & 0.053 \\
15 & MaxCond & Maximum canopy conductance & m s\({}^{-1}\) & 0.006 \\
16 & LAIgcx & Canopy LAI for maximum canopy conductance & & 3.00 \\
17 & CoeffCond & Defines stomatal response to VPD & mbar\({}^{-1}\) & 0.02 \\
18 & BLcond & Canopy boundary layer conductance & m s\({}^{-1}\) & 0.10 \\
19 & wSx1000 & Maximum stem mass per tree at 1000 trees ha\({}^{-1}\) & kg tree\({}^{-1}\) & 235.00 \\
20 & thinPower & Power in self thinning law & & 1.60 \\
21 & mF & Fraction of mean foliage biomass per tree on dying trees & & 0.00 \\
22 & mR & Fraction of mean root biomass per tree on dying trees & & 0.20 \\
23 & mS & Fraction of mean stem biomass per tree on dying trees & & 0.40 \\
24 & fracBB0 & Branch and bark fraction at stand age 0 & & 0.40 \\
25 & fracBB1 & Branch and bark fraction for mature stand & & 0.10 \\
26 & tBB & Age at which brak fraction is mean of fracBB0 and fracBB1 & & 15.00 \\
27 & gammaFx & Maximum litterfall rate & month\({}^{-1}\) & 0.042 \\
28 & gammaF0 & Litterfall rate at age 0 & month\({}^{-1}\) & 0.001 \\
29 & tgammaF & Age at which litterfall rate is mean of gammaFx and gammaF0 & & 18.00 \\
30 & Rttover & Average monthly root turnover rate & & 0.0168 \\
31 & m0 & Value of m when FR is zero & & 0.10 \\ \hline \end{tabular}
\end{table} 
Table 2: 3-PG parameters and their values for loblolly pine used in this study. After the model performance was tested using data from the control plots at the 21 sites, the performance of 3-\(\mathrm{PG_{lob}}\) was evaluated against independent data not used in the FR model development. We used control plots at six sites of a loblolly pine mid-rotation fertilization trial located in the southern United States. This fertilization trial was established in the mid 1980s as a factorial design of N (0,112, 224, and 336 kg ha\({}^{-1}\)) and P (0, 28, and 56 kg ha\({}^{-1}\)) fertilization (see [43, 51]). These independent study sites included a wide range of stand ages, soil types, and climate across the southeastern US (Table 3). We used control plots on each study site to independently validate FR derived _a priori_ from SI in the 3-PG model.