SITE QUALITY CURVES FOR AFRICAN MAHOGANY PLANTATIONS IN BRAZIL

Ribeiro, Andressa; Ferraz Filho, Antonio Carlos; Tomé, Margarida; Scolforo, José Roberto Soares

doi:10.1590/01047760201622042185

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Articles • CERNE 22 (4) • Oct-Dec 2016 • https://doi.org/10.1590/01047760201622042185 copy

SITE QUALITY CURVES FOR AFRICAN MAHOGANY PLANTATIONS IN BRAZIL

CURVAS DE CLASSIFICAÇÃO DE SÍTIO PARA PLANTIOS DE MOGNO AFRICANO NO BRASIL

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Site quality estimation is an important tool in forest management since it is useful for modeling growth and yield for even-aged stands. Data from African mahogany (Khaya ivorensis A. Chev.) Brazilian plantations were used to develop a model to predict dominant height growth, comparing dynamic base-age invariant site index models with the guide curve method (static models). For the evaluation of the candidate models qualitative and quantitative criteria were used. We also verified the stability of the candidate models, preferring a model providing fewer site class changes when predicting site index from different ages. The Lundqvist-Korf function fitted with the guide curve method proved to be effective and accurate for site classification and dominant height predictions of African mahogany stands. The range of observed site index, at a reference age of 15, was between 17 and 33 meters.

Keywords:
Forest management; Nonlinear equations; Dominant height; Site index

Authorship

Andressa Ribeiro ^**andressa.florestal@gmail.com

Federal University of Piaui - Bom Jesus, Piauí, Brasil Federal University of PiauiBrazilBom Jesus, Piauí, Brazil Federal University of Piaui - Bom Jesus, Piauí, Brasil

Antonio Carlos Ferraz Filho

Federal University of Lavras - Lavras, Minas Gerais , Brasil Federal University of LavrasBrazilLavras, Minas Gerais, Brazil Federal University of Lavras - Lavras, Minas Gerais , Brasil

Margarida Tomé

University of Lisbon - Lisbon, PortugalUniversity of LisbonPortugalLisbon, Portugal University of Lisbon - Lisbon, Portugal

José Roberto Soares Scolforo

Federal University of Lavras - Lavras, Minas Gerais , Brasil Federal University of LavrasBrazilLavras, Minas Gerais, Brazil Federal University of Lavras - Lavras, Minas Gerais , Brasil

*andressa.florestal@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Federal University of Piaui - Bom Jesus, Piauí, Brasil Federal University of PiauiBrazilBom Jesus, Piauí, Brazil Federal University of Piaui - Bom Jesus, Piauí, Brasil

Federal University of Lavras - Lavras, Minas Gerais , Brasil Federal University of LavrasBrazilLavras, Minas Gerais, Brazil Federal University of Lavras - Lavras, Minas Gerais , Brasil

University of Lisbon - Lisbon, PortugalUniversity of LisbonPortugalLisbon, Portugal University of Lisbon - Lisbon, Portugal

Figures | Tables | Formulas

Figures (6)
Tables (5)
Formulas (13)

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FIGURE 1
Observed dominant height development of Khaya ivorensis A. Chev. stands in Brazil

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FIGURE 2
Standardized residuals plotted over the fi tted values for the best equations to estimate dominant height.

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FIGURE 3
Comparison of height curves produced by the best models selected for site classifi cation of African mahogany plantations in Brazil

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FIGURE 4
Height curves for equation Lk and MD with fixed asymptote parameter (A=45 and A=40, respectively).

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FIGURE 5
Autocorrelation and Q-Q plot for the selected equation Lundqvist-Korf (a), Richards (b) and LG (c).

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FIGURE 6
Mean annual increment in diameter of plantation grown Khaya ivorensis A. Chev. in Brazil considering different site index classes obtained by the Lundqvist-Korf integral form model.

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Table 1
Characteristics of the sample plots of African mahogany plantations used in the study.

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Table 2
Candidate models for dominant height estimative in function of age for Khaya ivorensis A. Chev. stands in Brazil.

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Table 3
Goodness-of-fit statistics and parameter estimations of candidate functions, where ns indicates a non-significate parameter at 95% of probability.

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Table 5
Classification stability of the best models selected for site classification.

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Table 6
Dominant height estimative limits in meters by age and site index classes for Khaya ivorensis A. Chev. in Brazil.

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(1)

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(2)

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(3)

FIGURE 1 Observed dominant height development of Khaya ivorensis A. Chev. stands in Brazil

FIGURE 2 Standardized residuals plotted over the fi tted values for the best equations to estimate dominant height.

FIGURE 3 Comparison of height curves produced by the best models selected for site classifi cation of African mahogany plantations in Brazil

FIGURE 4 Height curves for equation Lk and MD with fixed asymptote parameter (A=45 and A=40, respectively).

FIGURE 5 Autocorrelation and Q-Q plot for the selected equation Lundqvist-Korf (a), Richards (b) and LG (c).

FIGURE 6 Mean annual increment in diameter of plantation grown Khaya ivorensis A. Chev. in Brazil considering different site index classes obtained by the Lundqvist-Korf integral form model.

Table 1 Characteristics of the sample plots of African mahogany plantations used in the study.

Region	Variable	Minimum	Mean	Maximum	SD
Southeast	t	1.1	3.7	7.2	1.6
(n=125)	hdom	1.7	10.9	23.0	4.9
	nm	2	4	6	2
Midwest	t	4.9	5.7	6.7	0.7
(n=20)	hdom	11.4	16.5	20.3	2.3
	nm	2	2	2	0
North	t	14.0	19.2	39.0	9.9
(n=5)	hdom	23.7	29.1	38.7	4.7
	nm	2	2	2	0

Where: n = number of plots; t = age (years); hdom = dominant height (m); nm = number of measurements; SD = standard deviation.

Table 2 Candidate models for dominant height estimative in function of age for Khaya ivorensis A. Chev. stands in Brazil.

Model	Base function (integral form)	Parameter related to site	Dynamic function
Lk	Lundqvist-Korf	k	$h d o m_{2} = A {(\frac{h d o m_{1}}{A})}^{{(t_{1} / t_{2})}^{d}}$
LA	$h d o m = A e^{- k / t^{d}}$	A	$h d o m_{2} = h d o m_{1} e^{- k ((\frac{1}{t_{1}^{d}}) - (\frac{1}{t_{2}^{d}}))}$
LG		A,k	$h d o m_{2} = e^{A - (k / t_{2}) + [\ln (h d o m) - A + (k / t_{1})] . [c - (1 / t_{2})] . [c - (1 / t_{1})]}$
Rk	Richards		$h d o m_{2} = A {1 -^{t_{2} / t_{1}}}^{1 / (1 - m)}$
RA	$h d o m = A {(1 - e^{- k t})}^{1 / (1 - m)}$	k	$h d o m_{2} = h d o m_{1} {(\frac{1 - e^{- k t_{2}}}{1 - e^{- k t_{1}}})}^{1 / (1 - m)}$
Rm		A	$h d o m_{2} = A^{1 - (ln (1 - e^{- k t_{2}}) / ln (1 - e^{- k t_{1}})) . h d o m_{1}^{ln ((1 - e^{- k t_{2}}) / ln (1 - e^{- k t_{1}})}}$
MD	Hossfeld IV/ McDill-Amateis $h d o m = A \frac{t^{k}}{A . c + t^{k}}$	m	$h d o m_{2} = \frac{A}{1 - (1 - (A / h d o m_{1})) . {(t_{1} / t_{2})}^{k}}$

Table 3 Goodness-of-fit statistics and parameter estimations of candidate functions, where ns indicates a non-significate parameter at 95% of probability.

Model	RMSE	RE	ē	Parameter	Estimate	SE	t-value
Guide curve method
Lundqvist-Korf	1.50	12.9	-0.008	A	57.9873	3.9614	14.64
				k	3.2358	0.0508	63.71
				d	0.5393	0.0266	20.27
Richards	1.58	13.6	-0.040	A	34.2267	0.9611	35.61
				k	0.1311	0.0080	16.32
				m	0.1276	0.0265	4.81
McDill-Amateis	1.54	13.3	-0.034	A	39.5919	1.4591	27.14
				k	1.2604	0.0332	37.97
				c	0.3195	0.0114	28.10
Difference equation method
Lk	0.98	7.71	0.020	A	35.6852	2.2150	16.11
Lk	0.98	7.71	0.020	c	0.7301	0.0345	21.17
LA	1.13	8.89	0.057	k	2.8727	0.0756	38.02
LA	1.13	8.89	0.057	c	0.6776	0.0377	17.99
LG	0.94	7.36	0.014	A	3.3246	0.0166	200.66
				k	3.2222	0.0716	45.04
					1.0879	0.0134	81.36
Rk	Did not converge
RA	1.49	11.71	-0.203	k	0.0588	0.0694	0.847^ns
RA	1.49	11.71	-0.203	m	-0.0209	0.0330	-0.634^ns
Rm	1.04	8.13	0.019	A	24.8564	0.7210	34.47
Rm	1.04	8.13	0.019	k	0.24732	0.0149	16.53
MD	0.97	7.57	0.032	A	23.2717	0.5912	39.36
MD	0.97	7.57	0.032	k	1.7581	0.0398	44.16

Table 5 Classification stability of the best models selected for site classification.

	Stability of the site classification
Number of changes (weight attribute)	Lundqvist-Korf	Richards	LG
0 (x0)	50 (0)	42 (0)	43 (0)
1 (x1)	41 (41)	44 (44)	37 (37)
2 (x2)	40 (80)	33 (66)	34 (68)
3 (x3)	15 (45)	22 (66)	26 (78)
4 (x4)	4 (16)	9 (36)	9 (36)
5 (x5)	0 (0)	0 (0)	1 (5)
Total	150 (182)	150 (212)	150 (224)

Table 6 Dominant height estimative limits in meters by age and site index classes for Khaya ivorensis A. Chev. in Brazil.

Age (years)	Site classes
Age (years)	V (17)	IV (21)	III (25)	II (29)	I (33)
1	1.6 - 2.0	2.0 - 2.5	2.5 - 2.9	2.9 - 3.3	3.3 - 3.8
5	7.7 - 9.8	9.8 - 11.8	11.8 - 13.9	13.9 - 15.9	15.9 - 18.0
10	12.4 - 15.8	15.8 - 19.1	19.1 - 22.4	22.4 - 25.7	25.7 - 29.0
15	15.0 - 19.0	19.0 - 23.0	23.0 - 27.0	27.0 - 31.0	31.0 - 35.0
20	16.4 - 20.7	20.7 - 25.1	25.1 - 29.4	29.4 - 33.8	33.8 - 38.2
25	17.1 - 21.6	21.6 - 26.2	26.2 - 30.7	30.7 - 35.3	35.3 - 39.8
30	17.4 - 22.1	22.1 - 26.7	26.7 - 31.4	31.4 - 36.0	36.0 - 40.7
35	17.6 - 22.3	22.3 - 27.0	27.0 - 31.7	31.7 - 36.4	36.4 - 41.1

h d o m_{2} = A {(\frac{h d o m_{1}}{A})}^{{(t_{1} / t_{2})}^{d}}

h d o m = A e^{- k / t^{d}}

h d o m_{2} = h d o m_{1} e^{- k ((\frac{1}{t_{1}^{d}}) - (\frac{1}{t_{2}^{d}}))}

h d o m_{2} = e^{A - (k / t_{2}) + [\ln (h d o m) - A + (k / t_{1})] . [c - (1 / t_{2})] . [c - (1 / t_{1})]}

h d o m_{2} = A {1 -^{t_{2} / t_{1}}}^{1 / (1 - m)}

h d o m = A {(1 - e^{- k t})}^{1 / (1 - m)}

h d o m_{2} = h d o m_{1} {(\frac{1 - e^{- k t_{2}}}{1 - e^{- k t_{1}}})}^{1 / (1 - m)}

h d o m_{2} = A^{1 - (ln (1 - e^{- k t_{2}}) / ln (1 - e^{- k t_{1}})) . h d o m_{1}^{ln ((1 - e^{- k t_{2}}) / ln (1 - e^{- k t_{1}})}}

h d o m = A \frac{t^{k}}{A . c + t^{k}}

h d o m_{2} = \frac{A}{1 - (1 - (A / h d o m_{1})) . {(t_{1} / t_{2})}^{k}}

(1)

R M S E = \sqrt{\frac{\sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}}{n - p}}

(2)

R E (%) = \frac{\sqrt{\sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2} / n - p}}{\bar{y}} .100

(3)

\bar{e} = \frac{1}{n} \sum_{i = 1}^{n} (y_{i} - {\hat{y}}_{i})

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UFLA - Universidade Federal de Lavras Universidade Federal de Lavras - Departamento de Ciências Florestais - Cx. P. 3037, 37200-000 Lavras - MG Brasil, Tel.: (55 35) 3829-1706, Fax: (55 35) 3829-1411 - Lavras - MG - Brazil
E-mail: cerne@dcf.ufla.br

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[1] *andressa.florestal@gmail.com