. 2023 Aug 21;18(8):e0289679. doi: 10.1371/journal.pone.0289679

Table 4. Best fit models.

Response	Best model	Equation^b^, ^c	Adj. R²	RMSE
Aboveground Biomass, Robinia pseudoacacia	D²H×t	$A G B = \exp (- 6.4678 t_{C} - 4.5032 t_{10} - 4.3952 t_{15} - 2.6261 t_{15 + P} + 1.4730 \ln (D^{2} H) t_{C} + 1.1393 \ln (D^{2} H) t_{10} + 1.0992 \ln (D^{2} H) t_{15} + 0.8934 \ln (D^{2} H) t_{15 + P})$	0.997	6%
Aboveground Biomass, Betula nigra	D×H+t	$A G B = \exp (- 3.9685 t_{C} - 4.5197 t_{10} - 4.1638 t_{15} - 4.1651 t_{15 + P} + 1.6614 \ln (D) + 1.9429 \ln (H) - 0.1963 \ln (D) \ln (H))$	0.989	14%
Aboveground Biomass, Gliricidia sepium	D²H×A	$A G B = \exp (- 3.1365 + 0.4930 \ln (D^{2} H) + 0.5685 \ln (A) + 0.0658 \ln (D^{2} H) \ln (A))$	0.984	33%
Aboveground Biomass, Casuarina equisetifolia	D²H+A	$A G B = \exp (- 2.5574 + 0.5856 \ln (D^{2} H) + 0.3754 \ln (A))$	0.918	35%
Aboveground Biomass, Psidium cattleianum	D+H+A×t	$A G B = \exp (- 0.5735 t_{C} - 0.6268 t_{10} - 0.2870 t_{15} - 0.6349 t_{15 + P} - 0.1764 \ln (D) + 1.2340 \ln (H) + 1.2708 \ln (A) t_{C} + 0.9806 \ln (A) t_{10} + 0.5058 \ln (A) t_{15} + 0.6404 \ln (A) t_{15 + P})$	0.928	26%
Aboveground Biomass, Acacia koa	D ² HA	$A G B = \exp (- 2.7031 + 0.6224 \ln (D^{2} H A))$	0.971	29%
Aboveground Biomass, Morella faya	D²H×A×t	$A G B = \exp (- 1.8949 t_{C} + 0.1149 t_{10} - 3.2917 t_{15} - 1.2393 t_{15 + P} + 0.6439 \ln (D_{2} H) t_{C} - 0.0540 \ln (D_{2} H) t_{10} + 1.0310 \ln (D_{2} H) t_{15} + 0.4438 \ln (D_{2} H) t_{15 + P} + 0.6031 \ln (A) t_{C} + 1.3206 \ln (A) t_{10} + 0.2671 \ln (A) t_{15} + 0.6183 \ln (A) t_{15 + P} - 0.0140 \ln (D_{2} H) \ln (A) t_{C} + 0.0595 \ln (D_{2} H) \ln (A) t_{10} - 0.0304 \ln (D_{2} H) \ln (A) t_{15} - 0.0054 \ln (D_{2} H) \ln (A) t_{15 + P})$	0.989	12%
Aboveground Biomass, Dodonaea viscosa	D²HA×t	$A G B = \exp (- 2.3153 t_{C} - 2.4033 t_{10} - 1.7860 t_{15} - 3.1044 t_{15 + P} + 0.6153 \ln (D^{2} H A) t_{C} + 0.5891 \ln (D^{2} H A) t_{10} + 0.5150 \ln (D^{2} H A) t_{15} + 0.7999 \ln (D^{2} H A) t_{15 + P})$	0.987	20%
Belowground Biomass, Robinia pseudoacacia	D×t	$B G B = \exp (- 4.6027 t_{C} - 6.3219 t_{10} - 4.6041 t_{15} - 3.3184 t_{15 + P} + 2.9721 \ln (D) t_{C} + 3.4241 \ln (D) t_{10} + 2.6873 \ln (D) t_{15} + 2.1638 \ln (D) t_{15 + P})$	0.993	7%
Belowground Biomass, Betula nigra	D+H	$B G B = \exp (- 4.5366 + 1.3177 \ln (D) + 1.4844 \ln (H))$	0.947	41%
Biomass, Robinia pseudoacacia	D²H×t	$B = \exp (- 6.0392 t_{C} - 4.4716 t_{10} - 3.8000 t_{15} - 2.0512 t_{15 + P} + 1.4751 \ln (D^{2} H) t_{C} + 1.1757 \ln (D^{2} H) t_{10} + 1.0561 \ln (D^{2} H) t_{15} + 0.8392 \ln (D^{2} H) t_{15 + P})$	0.998	6%
Biomass, Betula nigra	D+H+t	$B = \exp (- 3.3913 t_{C} - 3.9491 t_{10} - 3.5645 t_{15} - 3.5502 t_{15 + P} + 1.4974 \ln (D) + 1.5470 \ln (H))$	0.986	17%
Foliage, Robinia pseudoacacia	D	$F B = \exp (- 5.9554 + 2.8514 \ln (D))$	0.832	70%
Foliage, Betula nigra	DHA	$F B = \exp (- 9.9883 + 3.0465 \ln (D) + 3.6711 \ln (H) - 1.3975 \ln (A))$	0.813	130%
Foliage, Gliricidia sepium	D	$F B = \exp (- 6.5919 + 3.3388 \ln (D))$	0.935	82%
Foliage, Casuarina equisetifolia	D ² HA	$F B = \exp (- 3.4694 + 0.4713 \ln (D^{2} H A))$	0.820	79%
Foliage, Psidium cattleianum	D ² HA	$F B = \exp (- 2.2891 + 0.3076 \ln (D^{2} H A))$	0.802	16%
Foliage, Acacia koa	D ² HA	$F B = \exp (- 3.3293 + 0.5255 \ln (D^{2} H A))$	0.942	40%
Foliage, Morella faya	D ² HA	$F B = \exp (- 2.5505 + 0.5395 \ln (D^{2} H A))$	0.964	35%
Foliage, Dodonaea viscosa	D ² HA	$F B = \exp (- 3.1353 + 0.4958 \ln (D^{2} H A))$	0.870	61%
Twigs, Robinia pseudoacacia	DHA	$T w B = \exp (- 4.1455 + 3.4179 \ln (D) - 2.7893 \ln (H) + 0.6997 \ln (A))$	0.951	32%
Twigs, Betula nigra	D ² HA	$T w B = \exp (- 3.3878 + 0.4684 \ln (D^{2} H A))$	0.942	40%
Twigs, Gliricidia sepium	D+H+A	$T w B = \exp (- 7.003 + 1.9611 \ln (D) - 0.7271 \ln (H) + 0.8040 \ln (A))$	0.950	70%
Twigs, Casuarina equisetifolia	D²H×A	$T w B = \exp (- 1.4277 - 0.2137 \ln (D^{2} H) + 0.0973 \ln (A) + 0.1686 \ln (D^{2} H) \ln (A))$	0.917	34%
Twigs, Psidium cattleianum	D ² HA	$T w B = \exp (- 2.8927 + 0.4290 \ln (D^{2} H A))$	0.990	4%
Twigs, Acacia koa	D ² HA	$T w B = \exp (- 5.0404 + 0.6076 \ln (D^{2} H A))$	0.935	51%
Twigs, Morella faya	D²H×A	$T w B = \exp (- 2.9210 + 0.4098 \ln (D^{2} H) + 1.4436 \ln (A) - 0.1092 \ln (D^{2} H) \ln (A))$	0.982	27%
Twigs, Dodonaea viscosa	D ² HA	$T w B = \exp (- 3.6262 + 0.5445 \ln (D^{2} H A))$	0.880	65%
Secondary stem, Robinia pseudoacacia	D	$S S B = \exp (- 5.7638 + 3.1684 \ln (D))$	0.947	46%
Secondary stem, Betula nigra	D	$S S B = \exp (- 6.6658 + 2.7654 \ln (D))$	0.777	96%
Secondary stem, Gliricidia sepium^†	N/A	N/A	N/A	N/A
Secondary stem, Casuarina equisetifolia	D+H+A	$S S B = \exp (- 4.6921 + 0.2979 \ln (D) + 1.1462 \ln (H) + 0.8321 \ln (A))$	0.980	24%
Secondary stem, Psidium cattleianum^†	N/A	N/A	N/A	N/A
Secondary stem, Acacia koa	D ² HA	$S S B = \exp (- 7.0019 + 1.0096 \ln (D^{2} H A))$	0.966	34%
Secondary stem, Morella faya^†	N/A	N/A	N/A	N/A
Secondary stem, Dodonaea viscosa^†	N/A	N/A	N/A	N/A
Main stem, Robinia pseudoacacia	D ² H	$M S B = \exp (- 4.3149 + 0.9592 \ln (D^{2} H))$	0.980	22%
Main stem, Betula nigra	D+H	$M S B = \exp (- 4.0102 + 0.4005 \ln (D) + 2.6984 \ln (H))$	0.983	23%
Main stem, Gliricidia sepium	D²H×A	$M S B = \exp (- 3.5876 + 0.4966 \ln (D^{2} H) + 0.6297 \ln (A) + 0.0607 \ln (D^{2} H) \ln (A))$	0.977	44%
Main stem, Casuarina equisetifolia	D ² HA	$M S B = \exp (- 3.3659 + 0.5172 \ln (D^{2} H A))$	0.938	42%
Main stem, Psidium cattleianum	D ² HA	$M S B = \exp (- 4.2078 + 0.7903 \ln (D^{2} H A))$	0.970	15%
Main stem, Acacia koa	D+H	$M S B = \exp (- 3.9788 + 0.8887 \ln (D) + 2.2316 \ln (H))$	0.993	12%
Main stem, Morella faya	D ² HA	$M S B = \exp (- 3.3604 + 0.6877 \ln (D^{2} H A))$	0.991	20%
Main stem, Dodonaea viscosa	D ² H	$M S B = \exp (- 4.3164 + 1.0762 \ln (D^{2} H))$	0.971	28%

^aD = Basal diameter in cm; H = height in m; A = canopy width times canopy length (m²); t = fertilization treatment, indicating different parameters for control (t_C) vs. +10 g N m⁻² y⁻¹ (t₁₀) vs. +15 g N m⁻² y⁻¹ (t₁₅) vs. +15 g N m⁻² y⁻¹ + 15 g P m⁻² y⁻¹ (t_15+P). By definition, the ΔAIC value of each of these models is 0 because each model is the best fit among its candidate set [64].

^bFor models where treatment has an effect, equations are listed with treatments as binary variables. For example, t_c is 1 for the control but 0 for all other treatments.

^cAGB = Aboveground biomass; BGB = Belowground biomass; B = Biomass; FB = Foliar biomass; TwB = Twig Biomass; SSB: Secondary stem biomass; MSB = Main stem biomass.

^†No secondary stems.