Stand density and basal area prediction of unthinned irrigated plantations of Eucalyptus camaldulensis in the hot desert of India

Bioresource Technology 98 (2007) 1106–1114

Stand density and basal area prediction of unthinned irrigated plantations of Eucalyptus camaldulensis in the hot desert of India V.P. Tewari

*

Arid Forest Research Institute, P.O. Krishi Mandi, New Pali Road, Jodhpur 342 005, India Received 20 July 2004; received in revised form 30 March 2006; accepted 31 March 2006 Available online 21 June 2006

Abstract Growth modelling is an essential prerequisite for evaluating the consequences of a particular management action on the future development of a forest ecosystem. Mathematical growth models are not available for many tree species in India. The objectives of this study were to estimate potential stand density and model the actual tree density and basal area development in pure even-aged stands of Eucalyptus camaldulensis. Relationships between quadratic mean diameter and stems ha1 were developed, and parameter values of this relationship were used to establish the limiting density line. Two different models were compared to describe the natural decrease of stem number. The model including site index as one of the variables performed slightly better than the model without site index. Seven different stand level models also were compared for predicting basal area in the stands. The models tested in this paper belong to the path invariant algebraic difference form of a nonlinear model. They can be used to predict future basal area as a function of stand variables like initial basal area, age or dominant height, and stems ha1 and are crucial for evaluating different silvicultural treatment options. The performance of the models for basal area was evaluated using different quantitative criteria. Among the seven models tested, the two models proposed by Pienaar and Shiver and Forss et al. had the best performance. The equations proposed to predict future basal area and stem number are related and, therefore, simultaneous regression technique has also been used to investigate the differences between parameter coefficients obtained by fitting the equations separately and jointly.  2006 Elsevier Ltd. All rights reserved. Keywords: E. camaldulensis; Potential density; Path invariant basal area prediction model; Simultaneous regression technique, India

1. Introduction The Indira Gandhi Canal Project (IGNP) was constructed to improve agricultural growth and the living conditions of the people in the drought prone arid parts of the Rajasthan State in India. The State Forest Department has conducted massive afforestation activities in the area by planting various tree species including Eucalyptus camaldulensis to combat desertification. Plantations have varying stand densities and age groups. E. camaldulensis is an important tree species adapted to a wide variety of soils and climate. This species is used extensively for poles and

*

Tel.: +91 291 2722588; fax: +91 291 2722764. E-mail address: [email protected]

0960-8524/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2006.03.027

posts, pulp and papermaking, firewood and even as timber for furniture making. Its bark is used for tanning leather, and oil from leaves is used for medicinal and other purposes. Growth models for many tree species in India are not available. Information on stem number development for E. camaldulensis is unavailable but crucial for evaluating different silvicultural treatment options. Moreover, basal area and trees ha1 can be used to define the type and weight of a thinning (Gadow and Hui, 1999; Staupendahl and Puumalainen, 1999). Estimating the potential density of forest stands, in terms of the surviving trees ha1, is a central element of growth modelling. It is also one of the most difficult problems to solve, mainly because suitable data from untreated, densely stocked stands are rarely available. Furthermore,

V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114

the natural decline in trees ha1 in an unthinned forest is usually characterized by intermittent brief spells of high mortality, followed by long periods of low mortality (Gadow and Hui, 1999). Populations of trees growing at high densities are subject to density-dependent mortality or self-thinning. For a given mean tree size, there is a limit to the number of trees per hectare that may co-exist in an even-aged stand. The relationship between the mean tree size (increasing over time) and the number of live trees per unit area (declining over time) may be described by means of a limiting density line. The stand basal area is an important density measure, which simultaneously takes into account the mean tree size and the number of trees per unit area. Basal area is used to analyse the relationship between stand density and tree growth (Assmann, 1970). Moreover, in combination with the number of trees, basal area can be used to define the type and intensity of a thinning (Gadow and Hui, 1999; Staupendahl, 1999). Models of stand basal area growth have been developed using a differential equation or the path invariant algebraic difference form of a nonlinear equation. The latter approach, proposed by Clutter et al. (1983), is especially effective due to its path invariant nature (Gadow and Hui, 1999). Gadow and Hui (1993) modelled the natural decline of stem number in unthinned Cunninghamia lanceolata stands in central China. Equations also were generated to predict the natural decline of stem number in stands of Acacia mangium stands in Indonesia (Forss et al., 1996). Hasenauer et al. (1997) modelled basal area development in thinned and unthinned Pinus taeda plantations, while Eid (2001) presented models for prediction of basal area, mean diameter, and number of trees for forest stands in southeastern Norway. Various models were successfully used for predicting basal area in Picea abies (Gurjanov et al., 2000) and these were used to predict basal area in evenaged Azadirachta indica stands in Gujarat State of India (Tewari and Gadow, 2005). Models were given for predicting basal area of Pinus sylvestris branches (Ma¨kinen and Ma¨kela¨, 2003). Zhang et al. (2004) gave individual-tree basal area growth models for Pinus backsiana and Picea mariana in northern Ontario. Forest growth and yield models usually consist of a number of equations to describe the stand development over time. It is not unusual in forestry literature to treat the same variable as dependent in one equation and independent in another. If a variable is used as both an endogenous (dependent) variable on the left-hand side of one equation and on the right-hand side of another equation, this renders the system of equations simultaneous (Goldberger, 1964). A system of equations can also be simultaneous if they share a common error structure (non-zero covariance), even if there are no endogenous variables on the right-hand side (Zellner and Theil, 1962). Depending on variable interrelationships and model structure, simultaneous estimation of parameters of the models may be nec-

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essary in order to provide estimates that are consistent and efficient. Ignoring the simultaneous nature of a system of growth equations may result in inconsistent parameter estimates as well as cumulative loss in both efficiency and accuracy of predictions (Hasenauer et al., 1998). In the current forestry literature, simultaneous estimation is the standard and accepted approach in growth modelling papers where multiple equations are fit to build a growth and yield system. The aim of the present paper is to estimate potential density and model the natural decline of stem number and change in basal area in even-aged plantations of E. camaldulensis. Since in the present study we have two equations (basal area and stem number) that are related, the simultaneous regression technique has also been used to compare the two sets of parameter coefficients obtained by fitting the equations separately and simultaneously. 2. Methods 2.1. Data and field procedure The area is characterized by large variation in diurnal and seasonal temperatures. Summer temperature often exceeds 46–48 C, especially during May and June. During December and January, the night temperature occasionally reaches 0 C. The mean monthly maximum temperature varies between 39.5 C and 42.5 C, while mean monthly minimum temperature varies between 14 C and 16 C. Sandy soils in the desert often reach 62 C during May and June and they remain higher than air temperature at least by 10 C. The diurnal range of surface soil temperature in the dune areas varies between 25 C and 40 C during summer and monsoon periods (Tewari et al., 2002). The mean annual rainfall in the area varies from 120 mm to 300 mm. The majority of the rainfall is received during the southwest monsoon season (July–September). The number of rainy days varies from 8 days yr1 to 17 days yr1 in the area. Wind speeds as high as 130 kph have been experienced during the summer months. Dust storms are also common in the region. The terrain of the area is very undulating and is frequently subjected to moving sand dunes. The area consists of dry undulating planes of hard sand and gravely soil, or rolling planes of loose sand. The soil is rich in K but poor in N and organic matter. The soils have very low productivity due to their sandy texture, and low concentrations of N and organic matter. Many soils have semi-consolidated lime concretionary or gypsum strata at varying depths of 36 cm to more than 100 cm. The soils are coarse textured with low water retention capacity (Shankaranarayana and Gupta, 1991). For conducting growth and yield studies on E. camaldulensis, 35 permanent sample plots (PSP) were established at various locations throughout the IGNP area, covering the available age groups, stand densities, and sites using stratified multistage sampling (Philip, 1994). The plots, representative of the growing conditions in the stand, ranged

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V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114

from 220 m2 to 1003 m2 and contained about 32–187 trees. Mortality observed in some plots was attributed to a hard calcareous pan, insects and diseases, and density dependent mortality. The study began in 1995 and annual measurements were made in each plot for four consecutive years. Twenty plots (nos. 1–6, 11, 13–19 and 21–26) were installed in the first year of the study while 15 plots (nos. 7–10, 12, 20, 27–35) were installed during the second year of the study, thus they have four and three annual measurements, respectively. Plot data included age (t), dominant height (H), number of trees ha1 (N), basal area ha1 (G), and quadratic mean diameter (Dg). Age of the even-aged stands was ascertained from the plantation records of the Forest Department. The quadratic mean diameter was derived from basal area ha1 and the number of stems ha1. The entire range of each plot was considered in generating the summary statistics (Table 1). 2.2. Potential density The relationship between quadratic mean diameter (Dg), dominant stand height (H), and the number of stems per unit area (N) can be described using the following equation (Goulding, 1972): Dg ¼

1 a0 H a1 N þ b0 H b1

ð1Þ

The basal area ha1 is equal to:

a1 a1 b0 1 b 1  ð2b0 Þb1 Dg1G max a0

ð2Þ

b0 ðb1 a1 Þ H a0

ð3Þ

By substituting N in Eq. (1), the quadratic mean diameter at maximum basal area was: 1 2b0 H b1

ð4Þ

Table 1 Summary statistics for the 35 plots of E. camaldulensis from western India

ð5Þ

2.3. Stem number In the practice of forest management the limiting line is hardly ever reached (Gadow and Bredenkamp, 1992) because trees often die from suppression before reaching the limiting density. At the limiting density, the physiological point of no return is reached in the balance between photosynthesis and respiration, giving the 3/2-power law (Yoda et al., 1963). The results from spacing trials (Gadow and Hui, 1999) show that mortality processes are effective well before the maximum basal area is attained. Clutter and Jones (1980) used an ordinary differential equation for modelling the rate of change in the number of stems ha1 (N) as a function of stand age: 1 dN ¼ a  N b  tc N dt

ð6Þ

where N is the number of surviving trees ha1 in the stand, t is the stand age (years) and a, b, c are the empirical parameters. It is convenient, after integrating, to use the following algebraic difference form: 1

The first derivative of this equation with respect to N was set to zero, to obtain stems ha1 at maximum basal area (Sterba, 1975):

DgG max ¼

N G max ¼

N 2 ¼ ½N a1 þ bðtc1  tc2 Þa

p pN G ¼ D2g  N ¼ a 1 4 4½a0 H N þ b0 H b1 2

N G max ¼

Solving Eq. (4) for H and substituting the expression in Eq. (3), NG max (the limiting line) was (Sterba, 1987):

ð7Þ

where N1, N2 are the stems ha1 corresponding to stand ages t1 and t2, and a, b, c are the empirical parameters. Pienaar et al. (1990) modified Eq. (7), by including site index as an independent variable, and proposed the following model:   1  c  h t 2 id h t 1 id a N 2 ¼ N a1 þ b þ  ð8Þ SI 10 10 where N1, N2 are the stems ha1 corresponding to stand ages t1 and t2, SI is the site index (height of the dominant trees in the stand at the reference age) and a, b, c, d are the empirical parameters. Eq. (8) is an improved version of Eq. (7) where another independent variable (site index) has been used to include the effect of site variability in the modelling and analysis of the data.

Attribute

Mean

Standard deviation

Minimum

Maximum

2.4. Basal area prediction models

Age (years) Dominant height (m) Stems ha1 Quadratic mean diameter (cm) Basal area (m2 ha1) Site indexa (m)

12.18 17.83 1636 12.91

0.49 4.98 608.12 5.96

3.20 8.16 439 4.74

31.40 31.13 3257 35.88

19.27 15.31

0.92 3.51

3.45 8.48

58.70 20.55

In the analysis of basal area growth, the path invariant algebraic difference form of several growth functions has been applied. After screening the literature, seven such equations were selected. Pienaar and Shiver (1986) developed a projection function to predict future basal area as a function of age, height, and stem number:

a

Reference age for the site index was taken as 10 years.

V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114

 lnðBA2 Þ ¼ lnðBA1 Þ þ a 

1 1  A2 A1



þ b  ðln N 2  ln N 1 Þ þ c  ðln H 2  ln H 1 Þ   ln H 2 ln H 1  þd A2 A1

2.5. Model evaluation

ð9Þ

where BA1 and BA2 are the basal area at age A1 and A2, H1 and H2 are the top height at age A1 and A2, N1 and N2 are the number of stems at age A1 and A2, and a, b, c and d are the model parameters. Forss et al. (1996) modified Eq. (9) as follows:   1 1 lnðBA2 Þ ¼ lnðBA1 Þ þ a   þ b  ðln N 2  ln N 1 Þ A2 A1 þ c  ðln H 2  ln H 1 Þ

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The quantitative evaluation of models is a very important part of growth modelling. Indices of model precision (Table 4) are the root mean square error (RMSE), the model efficiency (MEF), and the variance ratio (VR). The root mean square error is based on the residual sum of squares, which gives more weight to larger discrepancies. The model efficiency index is analogous to R2 and provides a relative measure of performance. The variance ratio is the ratio of estimated to observed variance. The root mean square errors may be expressed as relative values, which is more revealing when components with different measurement units are compared.

ð10Þ

If there is no or low mortality we can approximate that there will be no change in number of stems ha1 at age A1 and age A2 and N1 = N2. In this case Eq. (10) can be simplified to yield the following equation:   1 1 lnðBA2 Þ ¼ ln BA1 þ a   þ b  ðln H 2  ln H 1 Þ A2 A1 ð11Þ Hui and Gadow (1993) developed the following equation for projecting a known basal area for stands of Cunninghamia lanceolata of varying density:  c H2 1aH b2 aH b1 1 BA2 ¼ BA1  N 2  N1  ð12Þ H1 Applying the condition when N1 = N2, this equation will be simplified as:  c H2 BA2 ¼ BA1  ð13Þ H1 Schumacher (1939) proposed following an age dependent basal area model, which was later on used by other workers (e.g., Schumacher and Coile, 1960; Clutter, 1963; Sullivan and Clutter, 1972):   A1 lnðBA2 Þ ¼ a þ ðln BA1  aÞ  ð14Þ A2 Souter (1986) presented another model based on Schumacher model, which can be given as:     A1 A1 lnðBA2 Þ ¼  ln BA1 þ a  1  A2 A2     A1 þ b  ln N 2   ln N 1 ð15Þ A2 The parameters of Eqs. (9)–(15) were estimated with the statistical software package STATISTICA using nonlinear least squares (NLS) techniques. Eqs. (9)–(15) were fitted to the 125 annual measurements on the 35 plots. For fitting, we have used interval data of successive measurements and converted Eqs. (9)–(11) and (14),(15) by taking exponential of both the sides to make their statistics comparable with those of Eqs. (12) and (13).

3. Results and discussion Fig. 1 presents the development of stems ha1, dominant height, and basal area over stand age as well as stems ha1 and basal area versus dominant height for the 35 plots. There was no thinning in the plots and decrease in the stem number ha1 shown in Fig. 1(a) was the result of competition. 3.1. Potential density The data collected from the 35 plots were used to fit Eq. (1) to develop the relationship between quadratic mean diameter, dominant height, and number of stems ha1. The parameter estimates with standard errors, coefficient of determination (R2), and root mean squared errors (RMSE) are given in Table 2. These estimated parameter values were used to obtain the limiting line of maximum basal area using Eq. (5). The relationship between the quadratic mean diameter and the number of living trees per unit area along with the limiting line is shown in Fig. 2. The solid line in Fig. 2 represents the potential density in the plots, i.e., the maximum stems ha1 the plots can have with respect to the quadratic mean diameter at maximum basal area. For the diameter range of 10–20 cm, in some plots the observed number of stems ha1 exceeds the maximum limit shown by the limiting line. The data points above the limiting line represent trees that would die from density dependent mortality, as shown for some plots in Fig. 1(a). 3.2. Stem number The data were used to model the decrease in the number of trees ha1 by applying Eqs. (7) and (8). For the purpose, we used the interval data of successive measurements instead of considering all possible intervals, which means only differences between the measurements in the year 2 and year 1, and so on, were considered. Differences such as those between measurements in year 3 and year 1 were not considered.

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V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114 35

3000

30 Dominant height (m)

3500

Stems/ha

2500 2000 1500 1000 500

20 15 10 5 0

0 0

10

20

(a)

30

0

40

10

20

Age (years) 70

3500

60

3000

50

2500

40 30

30

40

Age (years)

(b)

Stems/ha

Basal area (m2/ha)

25

2000 1500

20

1000

10

500 0

0 0

10

30

20

(c)

0

40

20

30

40

Dominant height (m)

(d)

Age (years)

10

70

Basal area (m 2/ha)

60 50 40 30 20 10 0 0

10

(e)

20

30

40

Dominant height (m) 1

Fig. 1. Graphic representation of the data: (a) stems ha versus age; (b) dominant height versus age; (c) basal area versus age; (d) stems ha1 versus dominant height; and (e) basal area versus dominant height for the 35 plots of E. camaldulensis.

Table 2 Parameter estimates and statistics for the data sets obtained by fitting Eq. (1) to the data from the 35 plots of E. camaldulensis Parameters a0 a1 b0 b1

Values 6

6

8 · 10 (1.6 · 10 ) 0.3534 (0.0657) 9.2688 (0.9012) 1.8550 (0.2587)

R2

RMSE

0.899

1.9261

Standard errors for the coefficients are given in parenthesis.

The fit statistics indicated that Eq. (8) performed marginally better than Eq. (7) (Table 3). The standard errors of the regression coefficients indicated that coefficients of

the equations were significant. Both the equations had very high R2 for stem number development. To analyse the accuracy of the prediction by the two models, average bias was also calculated. The bias was 0.80 and 0.22 stems ha1, for Eqs. (7) and (8), respectively. Eq. (7) produced slightly larger bias than Eq. (8); Eq. (7) underestimated the prediction, while Eq. (8) slightly overestimated it. Thus, overall performance of Eq. (8) was slightly better, most likely because of an extra independent variable in Eq. (8) representing the quality of the site. One of the most common procedures for evaluating a model is to examine the residuals for all possible combinations of variables. The aim is to detect dependencies or pat-

V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114 6000

Nmax=35835.69*Dg-1.1905

Stems/ha

5000 4000 3000 2000 1000 0 0

5

10

15

20

25

30

35

40

Average tree diameter (cm)

Fig. 2. Relationship between stems ha1 (declining over time) and average tree diameter (increasing over time) for E. camaldulensis. The solid line is limiting line. The equation is derived from Eq. (5) using the parameter values given in Table 2.

Table 3 Parameter estimates and summary statistics resulted from fitting Eqs. (7) and (8) to the interval data of the 35 plots of E. camaldulensis Equations

a

b

c

Eq. (7)

0.0971 (0.0082) 0.5027 (0.1129)

0.0002 (0.00005) 3.0526 (0.5612)

1.9646 (0.6914) 21.3766 (4.1946)

Eq. (8)

d

2.4940 (0.6063)

R2

RMSE

0.990

59.2769

0.991

57.7998

Standard errors for the coefficients are given in parenthesis.

terns that indicate systematic discrepancies and to verify that assumptions of the model are valid. Observed values may be plotted over predicted values, or residuals over predicted values (Gadow and Hui, 1999). The residuals were randomly distributed and no systematic trend was observed in their distribution (Fig. 3a). Both the equations did well in predicting the stem number development with time (Fig. 3b). Gadow and Hui (1993) applied Eq. (7) on the data set from unthinned Cunninghamia lanceolata growth trials in central China to model the natural decline of stem number (R2 = 0.93). The average relative discrepancy between observed and expected values was 0.07%. The equation was unbiased, based on the results of the simultaneous Ftest. Forss et al. (1996) applied Eq. (8) to Acacia mangium stands in Indonesia to generate equation for predicting the natural decline of stem numbers in the stands. The error of prediction was 5.3%. Thus, in both the cases a good fit was observed. 3.3. Basal area prediction The fit statistics show that Eqs. (9) and (10) had high R2 and low mean sum of squared residuals (MSE), which indicates the precision of the model, compared to other models tested (Table 5). Thus these two equations performed better than the other equations. The superiority of any model cannot be established only on the basis of the fit statistics. Therefore, all the models were validated using quantitative evaluation based on the

1111

statistical criteria already discussed under ‘model evaluation’ to test their predictive abilities. Eqs. (9) and (10) had lower RMSE and hence higher precision than the other models (Table 6). The models are statistically sound in prediction if they give values for MEF and VR close to 0 and 1, respectively (Gadow and Hui, 1999). Here also, we see that only Eqs. (9) and (10) consistently met these conditions. Eqs. (14) and (15) are the poorest performers for these criteria. Overall, the statistical criteria used for model evaluation clearly reflected the superiority of Eqs. (9) and (10) for their predictive abilities over the other equations considered. These equations were successfully applied also for basal area prediction in Norway spruce (Gurjanov et al., 2000). Mean residual (bias) is also an important model evaluation tool. But, the sample size in the present study is too small (35 plots) to report bias trends; future studies can provide this verification. Eqs. (3), (5) and (6) are more suited for predicting basal area when no mortality or change in number of stems ha1 is observed in the plantations, i.e. N1 = N2. If there is mortality or appreciable change in stem number ha1 with time, Eqs. (1), (2), (4) and (7) may be considered. Even under the condition N1 = N2, these equations can be applied after simplification. There are some limitations to the modelling approach presented in the paper. The data were not obtained from thinned stands. Basal area growth is different in thinned versus unthinned plantations where natural mortality occurs due to overcrowding. In managed plantations, where a thinning regime is followed, little to no natural mortality occurs due to absence of competition. In thinned plantations, basal area is reduced by thinning, and increases until the next thinning as trees left in the plantation grow in size. In the present study, the observed decrease in the stem numbers in the unthinned plots was mainly due to natural mortality, and hence it cannot be ascertained how these equations would behave when applied to thinned plantations. The model may be less accurate when used to predict basal area when natural mortality is significant, e.g., in dense stands and over long projection intervals (Gadow and Hui, 1999). 3.4. Simultaneous and non-simultaneous regression The nonlinear regression technique (NLS) was used to pick the best model for stem number and best model for basal area. Then these two final models (Eqs. (8) and (10)) were fitted simultaneously using two-stage least squares (2SLS). Table 7 gives the estimated coefficients and standard errors between nonlinear and simultaneous regression techniques by predictor variable. In basal area model (Eq. (10)), ln(N) is used as an endogenous predictor variable on the right-hand side. Because of this stochastic predictor, simultaneous regression procedure leads to different estimates for the basal area model (Table 7). The NLS standard errors are slightly less compared to the 2SLS standard errors. The NLS and 2SLS

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V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114

50

50

0

0

-50

-50

-100 -150

-100 -150

-200

-200

-250

-250

-300 200

800

1400

(a)

2000

2600

3200

-300 200

3800

600

1000

Predicted Values

1400

1800

2200

2600

3000

2600

3000

3400

Predicted Values

3800

3800

3200

3200

2600

2600 Observed Values

Observed Values

Equation 6 (Clutter and Jones) 100

Residual Values

Residual Values

Equation 7 (Piennar et al.) 100

2000

1400

2000

1400

800

800

200

200 200

800

(b)

1400

2000

2600

3200

200

3800

600

1000

1400

1800

2200

3400

Predicted Values

Predicted Values

Fig. 3. (a) Plot of residuals versus predicted values, (b) plot of observed versus predicted values for stem number development in E. camaldulensis stands.

results are same for the stem number model because no endogenous variable is used as a predictor variable on the right-hand side.

Table 5 Estimated parameters and summary statistics obtained by fitting the basal area models to data from the 35 plots of E. camaldulensis Model no. 9

Table 4 Criteria for evaluating model performance (y = observed values; ^y ¼ predicted values; ðy  ^y Þ ¼ residuals; p = number of model parameters) Criterion Root mean square error Model efficiency

Variance ratio

Formula RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sX ðy i  ^y i Þ2

n1p X ðy i  ^y i Þ2 MEF ¼ X ðy i  y Þ2 X ð^y i  ^y i Þ2 VR ¼ X ðy i  y Þ2

Ideal value

10 11 12

0

a

b

c

d

R2

MSEa

3.0537 (0.5671) 3.0211 (0.5314) 2.5571 (0.6386) 1.3962 (0.4588)

0.5291 (0.1649) 0.5055 (0.0879) 0.5864 (0.1203) 0.3155 (0.1281)

0.6512 (0.1211) 0.6626 (0.1006)

8.5422 (4.9929)

0.993

0.7449

0.993

0.7366

0.990

1.0690

0.991

0.9785

0.989

1.2415

0.979

2.2775

0.980

2.2178

13 0

14 15

1

3.5577 (0.0746) 2.2677 (0.7195)

0.1795 (0.0996)

0.2058 (0.1107) 0.9178 (0.0910)

a MSE = mean squared errors; standard errors for the coefficients are given in parenthesis.

V.P. Tewari / Bioresource Technology 98 (2007) 1106–1114 Table 6 The estimated values for the statistical criteria considered for testing the predictive abilities of the basal area equations applied to the 35 plots of E. camaldulensis Equation no.

RMSE

MEF

VR

(9) (10) (11) (12) (13) (14) (15)

0.00876 0.00871 0.01049 0.00987 0.01131 0.01549 0.01503

0.00660 0.00660 0.00968 0.00858 0.01138 0.02087 0.02009

0.9849 0.9846 0.9704 0.9849 0.9946 0.8112 0.8082

Table 7 Coefficient estimates and standard errors for basal area and stem number models by nonlinear (NLS) and two-stage least squares simultaneous regression techniques (2SLS) Model

Variable

Nonlinear

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statistical criteria. Eq. (9) needs four coefficients to be estimated while Eq. (10) needs only three. The standard error indicated that the coefficient ‘d’ in Eq. (9) was insignificant (Table 5) therefore Eq. (10) may be preferred. When growth equations in a stand projection system are related, simultaneous regression techniques should be considered for estimating parameters. Ignoring simultaneous nature of the equations can result in estimates that may be biased and inconsistent. Acknowledgements The author wishes to thank research staff of the Forest Resource management & Economics Division for their assistance in the data collection. Thanks are also due to Director, AFRI and Head, FRM&E Division for their help and support during the course of this study.

Simultaneous

Estimates

Standard error

Estimates

Standard error

References Assmann, E., 1970. The Principles of Forest Yield Study. Pergamon Press, New York, 506 p. Clutter, J.L., 1963. Compatible growth and yield models for loblolly pine. For. Sci. 9, 354–371. Clutter, J.L., Jones, E.P., 1980. Prediction of growth after thinning in old field slash pine plantations. USDA For. Serv. Res. Paper SE-217. Clutter, J.L., Fortson, J.C., Pienaar, L.V., Brister, G.H., Bailey, R.L., 1983. Timber Management—A Quantitative Approach. John Wiley & Sons, Chichester, 411 p. Eid, T., 2001. Models for prediction of basal area mean diameter and number of trees for forest stands in south-eastern Norway. Scand. J. For. Res. 16, 467–479. Forss, E., Gadow, K.v., Saborowski, J., 1996. Growth models for unthinned Acacia mangium plantations in South Kalimantan, Indonesia. J. Trop. For. Sci. 8 (4), 449–462. Gadow, K.v., Bredenkamp, B.V., 1992. Forest Management. Academica, Pretoria, 152 p. Gadow, K.v., Hui, G.Y., 1993. Zur Stammzahlentwicklung und potentielle Bestandesdichte bei Cunninghamia lanceolata. Centralblatt fu¨r des gesamte Forstwesen 110, 41–48. Gadow, K.v., Hui, G.Y., 1999. Modelling Forest Development. Kluwer Academic Publishers, Dordrecht, 213 p. Goldberger, A.S., 1964. Econometric Theory. John Wiley & Sons, New York. Goulding, C.J., 1972. Simulation technique for a stochastic model of growth of Douglas-fir. Ph.D. Thesis, University of British Columbia, Vancouver. 185 p. Gurjanov, M., Orios, S.S., Schro¨der, J., 2000. Grundfla¨chenmodelle fu¨r gleichaltrige Fichtenreinbesta¨nde. Centralblatt fu¨r des gesamte Forstwesen 117, 187–198. Hasenauer, H., Burkhart, H.E., Amateis, R.L., 1997. Basal area development in thinned and unthinned loblolly pine plantations. Can. J. For. Res. 27, 265–271. Hasenauer, H., Monserud, R.A., Gregoire, T.G., 1998. Using simultaneous regression techniques with individual-tree growth models. For. Sci. 44 (1), 87–95. Hui, G.Y., Gadow, K.v., 1993. Zur Modellierung der Bestandesdrungfla¨chenentwicklung-dargestellt am Beispiel der Baumart bei Cunninghamia lanceolata. Allgemeine Forst-und Jagd-Zeitung 164, 144–149. Ma¨kinen, H., Ma¨kela¨, A., 2003. Predicting basal area of Scots pine branches. For. Ecol. Manage. 179, 351–362. Philip, M.S., 1994. Measuring Trees and Forests, second ed. CAB International, Wallingford, 310 p.

Basal area

a b c

3.0211 0.5055 0.6626

0.5314 0.0879 0.1006

2.4773 0.3036 0.6361

0.5413 0.1406 0.1157

Stem number

a b c d

0.5027 3.0526 21.3766 2.4940

0.1129 0.5612 4.1946 0.6063

0.5027 3.0526 21.3766 2.4940

0.1129 0.5612 4.1946 0.6063

4. Conclusions Eq. (2) was used to fit the data collected from the plots to develop the relationship between average tree diameter and surviving stem numbers ha1 for the pure even-aged stands of E. camaldulensis. The estimated parameters were used to construct the limiting line that described the maximum number of trees expected in the stand with respect to the quadratic mean diameter at maximum basal area. This relationship will help in deciding the maximum number of trees ha1 at a given basal area to be retained in the stand, which is crucial for evaluating different silvicultural treatments. Two different models reported in the literature (Clutter and Jones, 1980; Pienaar et al., 1990) were also fitted to the data for modelling the natural decline of stem number, and both the models performed well. The model represented by Eq. (8) performed slightly better due to inclusion of site index as an independent variable. This model could also be used to generate survival curves for E. camaldulensis plantations for different site indices. The model predicted the mortality of the unthinned plantations at a given age and could be helpful in deciding appropriate thinning regimes to avoid unnecessary mortality and loss of production. Seven different equations were used to predict basal area in the stands. The equations proposed by Pienaar and Shiver (1986) and Forss et al. (1996) performed best based on

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Sterba, H., 1975. Assmanns Theorie der Grundfla¨chenhaltung und die ‘‘Competition-Density-Rule’’ der Japaner Kira, Ando und Tadaki. Centralblatt fu¨r des gesamte Forstwesen 92, 46–62. Sterba, H., 1987. Estimating potential density from thinning experiments and inventory data. For. Sci. 33, 1022–1034. Sullivan, A.D., Clutter, J.L., 1972. A simultaneous growth and yield model for loblolly pine. For. Sci. 18, 76–86. Tewari, V.P., Gadow, K.v., 2005. Basal area growth of even-aged Azadirachta indica stands in the Gujarat State of India. J. Trop. For. Sci. 17 (3), 386–398. Tewari, V.P., Verma, A., Kumar, V.S.K., 2002. Growth and yield functions for irrigated plantations of Eucalyptus camaldulensis in hot desert of India. Bioresour. Technol. 85 (2), 137–146. Yoda, K., Kira, T., Ogawa, H., Hozumi, K., 1963. Self-thinning in overcrowded pure stands under cultivated and natural conditions. J. Biol. Osaka City Univ. 14, 107–217. Zellner, A., Theil, H., 1962. Three-stage least squares: simultaneous estimation of simultaneous equations. Econometrica 30, 54–78. Zhang, L., Peng, C., Dang, Q., 2004. Individual-tree basal area growth models for jack pine and black spruce in northern Ontario. Forest. Chron. 80 (3), 366–374.