Predicting crown width and length using nonlinear mixed-effects models: a test of competition measures using Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.)

Table 2 Crown width or length basic models considered in the present study

Function no	Function	Function form	Reference
[CR1]	\(\mathrm{CR}={\phi }_{1}+{\phi }_{2}\mathrm{DBH}\)	Linear	Sánchez-González et al. (2007), Sönmez (2009), Buba (2013)
[CR2]	\(\mathrm{CR}={\phi }_{1}+{\phi }_{2}\mathrm{DBH}+{\phi }_{3}{\mathrm{DBH}}^{2}\)	Quadratic	Sánchez-González et al. (2007), Sönmez (2009), Martin et al. (2012)
[CR3]	\(\mathrm{CR}={\phi }_{1}+{\phi }_{2}\mathrm{DBH}+{\phi }_{3}{\mathrm{DBH}}^{2}+{\phi }_{4}{\mathrm{DBH}}^{3}\)	Cubic	Sönmez (2009)
[CR4]	\(\mathrm{CR}={\phi }_{1}{\mathrm{DBH}}^{{\phi }_{2}}\)	Power	Sánchez-González et al. (2007), Sönmez (2009)
[CR5]	\(\mathrm{CR}={\phi }_{1}[1-\mathrm{exp}\left(-{\phi }_{2}\mathrm{DBH}\right)]\)	Monomolecular	Sánchez-González et al. (2007)
[CR6]	\(\mathrm{CR}={[\mathrm{DBH}/({\phi }_{1}+{\phi }_{2}\mathrm{DBH})]}^{2}\)	Hossfeld	Sánchez-González et al. (2007)
[CR7]	\(\mathrm{CR}={\phi }_{1}{({\phi }_{2})}^{\mathrm{DBH}}\)	Compound	Sönmez (2009)
[CR8]	\(\mathrm{CR}=\mathrm{exp}({\phi }_{1}+{\phi }_{2}\mathrm{DBH})\)	Growth	Sönmez (2009)
[CR9]	\(\mathrm{CR}={\phi }_{1}\mathrm{exp}({\phi }_{2}\mathrm{DBH})\)	Exponential	Sönmez (2009)
[CR10]	\(\mathrm{CR}={\phi }_{1}/[1+{\phi }_{2}\mathrm{exp}\left(-{\phi }_{3}\mathrm{DBH}\right)]\)	Logistic	Fu et al. (2013)

CR, crown width or length; DBH, diameter at breast height; \({\phi }_{1}\), \({\phi }_{2}\), and \({\phi }_{3}\): formal parameters

ISSN: 1297-966X