Modeling Dominant Height Growth in Planted Pinus pinea Stands in Northwest of Tunisia

Table 2

Base models and GADA formulations considered.

Base equation	Parameter related to site	Solution for 𝑋 with initial values (𝑡0, 𝑌0)	Dynamic equation	Model
Log-logistic (log-transformed): 𝑎𝑌=^11+𝑎2𝑡^−𝑎3	𝑎1=𝑏1𝑎+𝑋2=𝑏2/𝑋	𝑋0=12(𝑌0−𝑏1±(𝑌0−𝑏1)^2+4𝑏2𝑌0𝑡^−𝑏30)	𝑏𝑌=^1+𝑋01+𝑏2/𝑋0𝑡^−𝑏3	(M1)
	𝑎1=𝑏1𝑎+𝑋2=𝑏2𝑋	𝑋0=𝑌0−𝑏11−𝑏2𝑌0𝑡^−𝑏30	𝑏𝑌=^1+𝑋01+𝑏2𝑋0𝑡^−𝑏3	(M2)
	Bertalanffy-Richards: 𝑌=𝑎1(1−exp(−𝑎2𝑡))^𝑎3	𝑎1𝑎=exp(𝑋)3=𝑏2+𝑏3/𝑋	𝑋0=12(ln𝑌0−𝑏2𝐹0±(𝑏2𝐹0−ln𝑌0)^2−4𝑏3𝐹0); with 𝐹0=ln(1−exp(−𝑏1𝑡0))	𝑌=𝑌01−exp(−𝑏1𝑡)1−exp(−𝑏1𝑡0)^(𝑏2+𝑏3/𝑋0)	(M3)
𝑎1𝑎=exp(𝑋)3=𝑏3/𝑋		𝑋0=12(ln𝑌0±(ln𝑌0)^2−4𝑏3𝐹0); with 𝐹0=ln(1−exp(−𝑏2𝑡0))	𝑌=exp(𝑋0)(1−exp(−𝑏2𝑡))^𝑏3/𝑋0	(M4)
𝑎1𝑎=exp(𝑋)3=𝑏3+1/𝑋		𝑋0=12(ln𝑌0−𝑏3𝐹0±(ln𝑌0−𝑏3𝐹0)^2−4𝐹0); with 𝐹0=ln(1−exp(−𝑏2𝑡0))	𝑌=exp(𝑋0)(1−exp(−𝑏2𝑡))^𝑏3+1/𝑋0	(M5)
Lundqvist-Korf: 𝑌=𝑎1exp(−𝑎2𝑡^−𝑎3)		𝑎1𝑎=exp(𝑋)2=𝑏2/𝑋	𝑋0=12(ln𝑌0±(−ln𝑌0)^2+4𝑏2𝑡^−𝑏30)	𝑌=exp(𝑋0)exp(−(𝑏2/𝑋0)𝑡^−𝑏3)	(M6)