Describing the Structure and Relationship of Height and Diameter in an Old Unmanaged <i>Eucalyptus</i> spp. Plantation

Raul de Abreu Neto

Universidade Federal de Lavras, Departamento de Ciências Florestais, Lavras, MG, Brasil

Universidade Estadual do Centro-Oeste, Departamento de Engenharia Florestal, Irati, PR, Brasil

Marcel Carvalho Abreu

Universidade Federal Rural do Rio de Janeiro, Instituto de Florestas, Departamento de Ciências Ambientais, Seropédica, RJ, Brasil

Alvaro Augusto Vieira Soares

Universidade Federal de Uberlândia, Monte Carmelo, MG, Brasil

Marco Antonio Monte

Universidade Federal Rural do Rio de Janeiro, Instituto de Florestas, Departamento de Silvicultura, Seropédica, RJ, Brasil

Emanuel José Gomes de Araújo

Universidade Federal Rural do Rio de Janeiro, Instituto de Florestas, Departamento de Silvicultura, Seropédica, RJ, Brasil

Rafaella de Angeli Curto

Universidade Federal Rural do Rio de Janeiro, Instituto de Florestas, Departamento de Ciências Ambientais, Seropédica, RJ, Brasil

Natane Amaral Miranda

Universidade Federal Rural do Rio de Janeiro, Instituto de Florestas, Departamento de Silvicultura, Seropédica, RJ, Brasil

CORRESPONDENCE TORafaella de Angeli Curto Universidade Federal Rural do Rio de Janeiro, Instituto de Florestas, Departamento de Ciências Ambientais, Seropédica, RJ, Brasil e-mail: rafaellacurto@yahoo.com.br

Identification	Model	Category	Autor
1	$H = β_{0} + β_{1} \ln D B H + ε$	Linear	Henriksen (1950)
2	$H = β_{0} + β_{1} D B H + ε$	Linear
3	$H = β_{0} + β_{1} D B H + β_{2} D B H^{2} + ε$	Linear
4	$H = β_{0} + β_{1} \frac{1}{D B H} + ε$	Linear	Assman (1970)
5	$\frac{1}{H} = \frac{1}{D B H} \frac{1}{D B H^{2}} + ε$	Linear
6	$H = e^{(β_{0} + \frac{β_{1}}{D B H})} + ε$	Nonlinear	Curtis (1967)
7	$H = β_{0} D B {H^{β}}_{1} + ε$	Nonlinear	Unknown
8	$H = \frac{β_{0}}{[1 + e^{(\frac{β_{1} - D B H}{β_{2}})}]} + ε$	Nonlinear	Verhulst (1838)
9	$H = β_{0} {(1 - {e^{- β}}_{1}^{D B H})}^{β}_{2} + ε$	Nonlinear	Chapman and Richards Pienaar and Turnbull (1973)
10	$H = β_{0} (1 - β_{1} {e^{β}}_{2}^{D B H}) + ε$	Nonlinear	Mitscherlich (1909)

Code	PDF	Probability Density Function
NOR	Normal	$f_{x} (x) = \frac{1}{\sqrt{2 π θ_{2}^{2}}} \exp \{- \frac{1}{2} {[\frac{(x - θ_{1})}{θ_{2}}]}^{2}\}$
LN2	2-parameters Log-normal	$f_{x} (x) = \frac{1}{{Xσ}_{\ln (x)} \sqrt{2 π}} \exp \{- \frac{1}{2} {[\frac{\ln (x) - μ_{\ln (x)}}{σ_{\ln (x)}}]}^{2}\}$
LN3	3-parameters Log-normal	$f_{x} (x) = \frac{1}{(x - k) σ_{y} \sqrt{2 π}} \exp \{- \frac{1}{2} [\frac{\ln (x - k) - μ_{y}}{σ_{y}}]\}$
GAM	Gamma	$f_{x} (x) = \frac{{(\frac{x}{a})}^{β - 1} \exp (\frac{- x}{a})}{θΓ (β)}$
WEI	Weibull	$f_{x} (x) = \frac{β}{a} {(\frac{x}{a})}^{β - 1} \exp [- {(\frac{x}{α})}^{β}]$
W3	3-parameters Weibull	$f_{x} (x) = \frac{β}{α} \{{[\frac{(x - k)}{α}]}^{β - 1} \exp \{- {[\frac{(x - k)}{α}]}^{β}\}\}$
GEV	Generalized Extreme Value	$f_{x} (x) = \frac{1}{α} [1 - β {(\frac{x - k}{α})}^{1 / (β - 1)} \exp \{- {[1 - β (\frac{x - k}{α})]}^{1 / β}\}]$

Parameters of regression models				Normality	Homoscedasticity¹
Parameters of regression models				H₀: residuals are normally distributed	H₀: residuals have constant variance
Model	β₀	β₁	β₂	p-value	p-value
1	-32.7598	18.7517		0.3023	0.0599
2	13.9501	0.5127		0.0956	0.3410
3	5.7242	0.9850	-0.0054	0.1916	0.1494
4	48.7643	-486.9083		0.0822	0.1542
5	0.0149	0.4582	2.7983	0.1857	0.1690
6	4.0871	-18.9816		0.3419	-
7	4.3391	0.5689		0.1310	-
8	50.8360	23.066	17.8770	0.1954	-
9	59.2955	0.0216	0.8910	0.2234	-
10	56.8869	0.9804	0.0252	0.2308	-

Model	r	AIC	Syx	MAE	p-value
Only fixed effects	0.82	808.86	17.88	4.23
3 cm	0.82	804.64	17.43	4.28	>0.99
5 cm	0.82	807.08	17.48	4.31	>0.99
10 cm	0.82	807.08	17.40	4.31	>0.99

Brasil