G.J.B.B., VOL.3 (2) 2014: 203-210
ISSN 2278 – 9103
PREDICTIVE MODELS BETWEEN DIAMETER, HEIGHT, CROWN
DIAMETER AND AGE OF PINUS BRUTIA TEN. IN ZAWITA AND
ATRUSH DISTRICTS
Mohammed Hadaet Obeyed
School of Forestry, Faculty of Agriculture and Forestry, University of Duhok, Kurdistan Region-Iraq
ABSTRACT
The study was carried out in Natural stand in Zawita and Atrush districts. The paper presents the analysis of some
characteristics of tree, following elements were analyzed: diameter at breast height, tree height, crown diameter and age of
tree at breast height were measured for 200 trees of Pinus brutia Ten. in Duhok province northern Iraq. We discuss the
approaches of modeling tree in order to establish the relationships between tree height with diameter at breast height,
crown diameter, age of tree at breast height with diameter at breast height, and age of tree at breast height with crown
diameter, regression analysis were applied. One linear and seven non-linear functions were selected for each of these
relationships to select the best fit model in each one of these relationships. Comparison of the models was carried out by
studying the adjusted coefficient of determination (R2), Standard error of estimated (SE. of Est) and the mean square error
(MSE). The results of the study indicated that the tree height with diameter at breast height, age at breast height with
diameter at breast height and crown diameter with diameter at breast height can be described by cubic function, except the
relationship between ages at breast height with crown diameter can be described by quadratic function.
KEY WORDS: Age of tree, Crown diameter, Dimensional relationship, Stem diameter, Tree measurements.
measurements of height are not available for modeling
purposes. Missing (H) may be predicted using a suitable
height-diameter model. (Temesgen and Gadow, 2004).
The crown of tree is the center of physiological activity,
particularly gas exchange, which drives growth and
development. The ability to predict (CD) from (D)
provides an efficient method of obtaining an estimate of
(CD). Estimates of (CD) can also be used to calculate
stand canopy closure, which is important for assessing
wildlife habitat suitability, fire risk, and competition for
regeneration (Crookston and Stage, 1999). Tree (CD) is
well correlated with tree (D) (Lockhart et al., 2005;
Hemery et al., 2005). Conifers have smaller (CD) than
deciduous trees, but the location of the tree is also
important, such that trees in southern Duhok have greater
(CD) than those in the north. Meanwhile, trees on poor
sites or in open growth stands have larger (CD) than those
on nutrient-rich sites or in denser stands. Total (H), and
(CD) could be estimated by means of stem (D), which is
easy to measure for the studies in ground-based forest
inventory and stand structure determination (Turan, 2009).
Foresters determine (A) by counting the growth rings of a
severed tree stump or by taking a core sample using an
increment borer. An increment borer is a specialized tool
used to extract a section of wood tissue from a living tree
with relatively minor injury to the tree. It is most often
used by foresters, researchers, and scientists to determine
the age of a tree. This enables the user to count the rings in
the core sample to determine (A) or the growth rate of the
tree. In this study, the process of measuring (D, H, CD and
A) variables of Pinus brutia Ten. grown naturally in
Zawita and Atrush are applied for the first time in these
two regions, to see the strength of relationship between
INTRODUCTION
The tree diameter at breast height (D) is one of the most
common and important characteristics used in forest
inventory. This variable has numerous beneficial
attributes: - It is easy to measure (Zhang et al., 2004),
volume of tree can be estimated and have strong
correlations with other tree characteristics such as tree
height (H), crown diameter (CD) and age of tree at breast
height (A). The measurement of (H, CD and A) variables
are more difficult and time consuming than that of (D)
variable. Therefore, regression analysis is one of the tools
usually employed to predict relationship between two or
more variables via models (equations).The distribution of
trees by diameter class allows foresters to understand
volume tables, stand structure, stand dynamics, and future
forest yield. Individual-tree diameter growth models are
among the most basic and essential components of forest
growth models (Sanchez et al., 2006). Stem diameter at
breast height is an important tree characteristics and an
accurate prediction of tree dimensions. It has become
prominent as analysis techniques, models, and other
statistical tools to allow for the rapid evaluation of
extensive volumes of data (Turan, 2009).
Tree height is a fundamental geometrical variable for
trees. Unfortunately, most measures are based on visual
inspection, and they are almost always considerably
biased. Generally most of methods for measuring tree
height are more difficult, cumbersome and timeconsuming than measuring diameter or girth especially in
dense stands. On the other hand, Tree diameter can easily
be measured at low cost, but tree height data are relatively
more difficult and costly to collect. Therefore, H-D
models can be used to predict height where actual
203
Models between diameter, height, crown diameter and age of Pinus brutia Ten
these variables with each other. Thus, the development of
a relationship between (D, H, CD and A) are considered
crucial in forest inventories as well as for estimating
timber volume and site index and are also important
variables in growth and yield modeling using an easily
measured predictor variable such as (D).
The aim of the present study: 1- develop regression
prediction models between tree height with diameter at
breast height, crown diameter with diameter at breast
height, age of tree at breast height with diameter at breast
height, and age of tree at breast height with crown
diameter for natural pure Calabrian pine in Zawita and
Atrush districts in Duhok province. 2- Select the best fit
model for each one of these relationships without
incurring unaffordable costs and time.
MATERIALS & METHODS
Study Area
Pinus brutia Ten. covers extensive areas in the Eastern
Mediterranean region: mainly Turkey, Greece, Cyprus, W.
Syria, Lebanon and Italy; scantly N. Iraq, W. Caucasus
and Crimea (Gezer, 1986; Fady et al., 2003). This species
is occurring naturally only in two districts in northern Iraq,
in Zawita and Atrush districts situated in Duhok province.
It lies at the very northern tip of Iraq, bordered by Turkey
As shown in Figure 1 .The study area for these two
districts are summarized in table (1).
FIGURE 1: Location of the study Area.
Characteristics
Coordinates
Altitude
Area
Ecoregion
Located
TABLE 1: Characteristics of location in Zawita and Atrush districts.
Zawita
Atrush
Latitude:
36° 89' 97" N
Latitude: 36°83'74" N
Longitude: 43° 14' 66" E
Longitude: 43°34'04" E
883 -1175 m above sea level.
741- 875 m above sea level.
287 ha.
317 ha.
Zagros Mountains Forest Steppe.
Zagros Mountains Forest.
about 13 km northeast of Duhok province
about 65 km east of Duhok province
health, and without visible evidence of major injury,
normal trees of the stand void with disease or insect attack
and free from natural injuries, such as broken tops due to
wind, storm, fire. The tree is open grown and relatively
free from competition of other trees generally at least 12 m
from neighboring trees (Forked or top damaged trees were
excluded). The following variables of the selected trees
were measured: diameter at breast height (D), tree height
(H), crown diameter (CD), and age at breast height (A).
Measurements and Data Collection
The data used in the study were obtained from the natural
pure Calabrian pine in Zawita and Atrush districts. The
age of trees ranged from (16) years to (66) years. A total
of 200 Calabrian pine individuals were measured (one
hundred tree for each district) from July to November
2012. Summary statistics, including mean, minimum,
maximum, and standard deviation of each of the individual
tree data sets are shown in Table (2). The tree was in good
204
G.J.B.B., VOL.3 (2) 2014: 203-210
ISSN 2278 – 9103
TABLE 2: A Summary Statistics of Field Data of Pinus brutia Ten. in Duhok province.
Standard
Variable
Minimum Mean
Maximum Range
deviation
D
11.40
30.35
59.70
48.30
11.47
H
4.50
13.69
23.60
19.10
4.27
CD
3.40
8.34
18.40
15.00
3.48
A
16.00
31.64
66.00
50.00
10.73
The diameter at breast height (D, cm) over bark of all of
the trees were found by taking the mean of the two
measurements that were made in the direction
perpendicular to each other by a caliper, to the nearest
0.01 millimeter, All trees selected had (D) larger than 11.4
cm. Total tree heights (H, m) were measured, using a Haga
altimeter, to the nearest 0.01 centimeter. Two crown
diameters (CD, m) were measured per tree; one being the
horizontal diameter of the axis of the crown which passes
through the centre of the plot and the second being
perpendicular to the first. The arithmetic mean crown
diameter calculated from these two field measurements to
the nearest 0.01 centimeter. Ages of trees at breast height
(A, year) were determined using increment borers. The
tool consists of a hilt, a borer bit, and core extractor. Since
trees were cored at the D (diameter at breast height, 1.30
m above ground), it refer to the age at this level. The
distance from solid wood to the estimated tree centre was
predicted based on the annual ring widths closest to the
pith. Extract a tree core by boring into the center of a tree
with the appropriate sized increment borer. Slip the
extractor fully through the core tube, break the core by
turning the increment borer counterclockwise one-half
turn and remove extractor with core. You will then be able
to see a core from the bark to the pith. You can count the
age of the tree by counting each annual ring increment as
one year. Note that one year includes both summer wood
and spring wood.
Statistical Analysis
In order to estimate the parameters of all models and
validate the models, Minitab ver. 16 and Statigraphics
plus: 5.0 programs were used. The data of a total of N =
200 trees were included in the analysis; thus, the
relationships between (H-D, CD-D, A-D and A-CD) were
determined. For each relationship between any two
variables, eight models were used represents (linear,
Quadratic, Cubic, power, Compound, Growth, Reciprocal
and Logarithmic) are summarized in Table 3. One of these
models is linear and others are non-linear. All parameters
were found to be significant at the 5% level. To select the
best fit model, eight candidate models were evaluated on
the basis of the adjusted coefficient of determination (R2
adj), standard errors of estimate (SE. of est.) and mean
square error (MSE). Model resulting in the largest R2 adj,
least S.E. of Est. and MSE was selected as the best model.
The F statistic and the significance F were then computed
and the results tabulated for the best model in each of the
relationships are mentioned above. Another important step
in evaluating the models was to perform a graphical
analysis for the best fit model to assess the appearance of
the fitted curves overlaid on the data set.
RESULTS & DISCUSSION
This study presents relationships between tree height with
diameter at breast height (H-D), crown diameter with
diameter at breast height (CD -D), age of tree at breast
height with diameter at breast height (A-D), and age of
tree at breast height with crown diameter (A-CD) for
natural pure Calabrian pine in Zawita and Atrush districts
in Duhok province. For all relationships, the diameter at
breast height was taken as the independent variable except
relationship between (A-CD) where CD of tree as
independent variable, while the (H, CD, and A) are taken
as the dependent variable. Several models for fitting data
were performed well and produced very similar results. To
select the best fit model for each of the relationships
above, the following data analysis were used:
205
Models between diameter, height, crown diameter and age of Pinus brutia Ten
Calama and Montero, 2004; Dieguez et al., 2005; Sharma
and Parton, 2007). According to the table 4 for prediction
(H) depending on (D) for Pinus brutia Ten., eight
candidate models was tested to select the best fit model
depending on The R2 adj, SE. of Est. and MSE. Models (5,
6, 7, 8) was dropped from analysis, because have
comparatively lower values of The R2 adj. and higher
values of S.E of est. and MSE than that of other models in
the set. The remaining models (1, 2, 3 and 4) nearly have
the same precision for estimating height (very close to one
another. The R2 adj ranging from (0.8639) in model (4) to
(0.8708) in model (3). SE. of Est. ranging from (1.5760)
in models (1 and 4) to (1.5358) in model (3). MSE for
model (3) have the value (2.35853) lower than other
models.
Tree Height with Diameter at Breast Height
Relationship (H-D)
Tree height is an important variable which is used for
preparing standard volume table (Mohammed, 2009) and
form class volume table (Muzahim and Mohammed,
2007), also used for estimating site quality and for
describing stand structure. As a tree increases in height,
it’s metabolic and growth requirements would increase
too, competition for light is important, especially in groups
of trees. Measuring tree heights is costly however, and
foresters usually welcome an opportunity to estimate this
variable with an acceptable accuracy. Missing heights may
be estimated using a height-diameter function. The trend
in this study was also in concert with models
formulation proposed by several findings on the
relationship of height and diameter (Canadas, 2000;
TABLE 4: Model statistics and parameter estimates from tree height prediction for Pinus brutiaTen. in Duhok province
S.E.
No.
B0
B1
B2
B3
R2 adj.
MSE
of Est.
1
3.18388
0.346345
0.8646
1.5760
2.48367
2
2.21999
0.411195
0.0009546
0.8644
1.5734
2.47558
3
8.72572
-0.261084
0.019908
-0.0001972
0.8708
1.5358
2.35853
4
1.00146
0.769932
0.8639
1.5760
2.48383
5
6.83411
1.02217
0.8330
1.7461
3.04871
6
1.91292
0.0221591
0.8331
1.7455
3.04671
7
31.9403
-709.738
5262.16
0.8406
1.7062
2.91119
3.04339
8
-20.5335
10.2428
0.8333
1.7445
Model (3) gave the best performance for estimating (H)
according to the values of the statistics. Consequently,
cubic model was selected. There was a strong positive
non-linear relationship between H and D (Figure 2.a). The
observed height versus the predicted heights is also drawn
for testing data (Figure 2.b), it show that the model (3) fits
the data well. The cubic model established between these
two variables was statistically significant (F = 448.189; P
< 0.001) as shown in table (5).
TABLE 5: The result of Analysis of Variance for cubic model to estimate H for Pinus brutia Ten.
Source
Regression
Error
Total
DF
3
196
199
SS
3171.20
462.27
3633.48
MS
1057.07
2.36
F-Test
448.189
P-value
0.001
FIGURE 2: a- The relationship between H and D b- Observed vs. predicted H for selected model
2003, Avsar, 2004; Pommerening and Stoyan, 2006)
Measurement of crown width is not common in forest
inventories, yet this value has wide applicability in
forestry. Consequently, quantification of crown width
attributes is an important component of many forest
Crown Diameter with Diameter at Breast Height
Relationship (CD-D)
Generally, the CD- DBH regressions were highly
significant and showed a strong relationship between the
two variables. This corroborates results reported by earlier
researchers (Bragg, 2001; Pretzsch et al., 2002; Foli et al.,
206
G.J.B.B., VOL.3 (2) 2014: 203-210
ISSN 2278 – 9103
growth and yield models. According to the table 6 for
prediction (CD) depending on (D) for Pinus brutia Ten.,
eight candidate models was tested to select the best fit
model depending on The R2 adj, SE. of Est. and MSE.
Models (7, 8) were dropped from analysis, because have
comparatively lower values of The R2 adj. and higher
values of S.E of est. and MSE than that of other models in
the set. The remaining models (1, 2, 3, 4, 5, and 6) slightly
have the same precision for estimating (CD). The R2 adj
ranging from (0.8408) in model (6) to (0.8542) in model
(3). SE. of Est. ranging from (1.3886) in model (6) to
(1.3288) in model 3. MSE for model (3) have the value
(1.7656) lower than other models.
TABLE 6: Model statistics and parameter estimates from crown diameter prediction for Pinus brutia Ten. in Duhok
province.
S.E.
No.
B0
B1
B2
B3
R2 adj.
MSE
of Est.
1
-0.114067
0.278711
0.8440
1.3781
1.89919
2
2.04312
0.133578
0.00213631
0.8511
1.3432
1.8041
3
5.98491
-0.273752
0.0147768
-0.0001195
0.8542
1.3288
1.7656
4
0.239257
1.03901
0.8442
1.3739
1.88771
5
3.28046
1.02938
0.8408
1.3889
1.92894
6
1.17999
0.0291634
0.8408
1.3886
1.92833
7
24.3777
-652.466
5282.92
0.8061
1.5324
2.34823
8
-18.468
8.02355
0.7704
1.6677
2.78134
Model (3) gave the best performance according to the
values of the statistics. Consequently, cubic model was
selected. There was a strong positive non-linear
relationship between CD and D (Figure 3.a). The observed
CD versus the predicted CD is also drawn for testing data
(Figure 3.b), it show that the model (3) fits the data well.
The cubic model established between these two variables
was statistically significant (F = 389.729; P < 0.001) as
shown in table (7).
TABLE 7: The result of Analysis of Variance for cubic model to estimate CD for Pinus brutiaTen.
Source
DF
SS
MS
F-Test
P-value
Regression
3
2064.43
688.144
Error
196
346.08
1.766
389.729 0.001
Total
199
2410.51
FIGURE 3: a- The relationship between CD and D
b- Observed vs. predicted CD for selected model
diameter has been examined and reported by earlier
researchers (Rayner, 1992; Faunt, 1992; Rose, 1993;
Burrows et al., 1995; Stoneman et al., 1997; Whitford,
2002).
According to the table 8 for prediction (A) depending on
(D) for Pinus brutia Ten., eight candidate models was
tested to select the best fit model depending on The R2 adj,
SE. of Est. and MSE. Models (5, 6, 7, 8) was dropped
Age of Tree at Breast Height with Diameter at Breast
Height Relationship (A-D)
Method of measuring the (A) of the tree at (D) is very
difficult when compared with the measurement of the
diameter, height, and Crown width. It also can be very
expensive and take large time as well as it needs to
muscular effort to extract a sample from the tree and then
calculate (A). The relationship between tree age and tree
207
Models between diameter, height, crown diameter and age of Pinus brutia Ten
height. The R2 adj ranging from (0.9201) in model (4) to
(0.9340) in model (3). SE. of Est. ranging from (3.0222)
in model (4) to (2.7564) in model (3). MSE for model (3)
have the value (7.59777) lower than other models.
from analysis, because have comparatively lower values of
The R2 adj. and higher values of S.E of est. and MSE than
that of other models in the set. The remaining models (1,
2, 3 and 4) slightly have the same precision for estimating
TABLE 8: Model statistics and parameter estimates from age at D prediction for Pinus brutia Ten. in Duhok province.
S.E.
No.
B0
B1
B2
B3
R2 adj.
MSE
of Est.
1
4.3452
0.899273
0.92528
2.9391
8.63839
2
8.89324
0.593285
0.00450404
0.92857
2.8665
8.21672
3
23.5792
-0.924306
0.0515988
-0.0004452
0.9340
2.7564
7.59777
4
1.59284
0.877403
0.9201
3.0222
9.13366
5
14.2054
1.02535
0.9160
3.1084
9.66201
6
2.64826
0.0251774
0.9160
3.1077
9.65776
7
81.9625
-2022.27
15993.8
0.8844
3.6471
13.3016
8
-55.4918
26.073
0.8572
4.0524
16.4219
Model (3) gave the best performance according to the
values of the statistics. Consequently, cubic model was
selected. There was a strong positive non-linear
relationship between A and D (Figure 4.a). The observed
(A) versus the predicted (A) is also drawn for testing data
(Figure 4.b), it show that the model (3) fits the data well.
The cubic model established between these two variables
was statistically significant (F = 938.925; P < 0.001) as
shown in table (9).
TABLE 9: The result of Analysis of Variance for cubic model to estimate CD for Pinus brutiaTen.
Source
Regression
Error
Total
DF
3
196
199
SS
21401.2
1489.2
22890.4
MS
7133.73
7.60
FIGURE 4: a- The relationship between A and D
F-Test
938.925
P-value
0.001
b- Observed vs. predicted A for selected model.
prediction (A) depending on (CD) for Pinus brutiaTen.,
eight candidate models was tested to select the best fit
model depending on The R2 adj, SE. of Est. and MSE.
Models (7, 8) were dropped from analysis, because have
comparatively lower values of The R2 adj. and higher
values of S.E of est. and MSE than that of other models in
the set. The remaining models (1, 2, 3, 4, 5, and 6) slightly
have the same precision (very close to one another) for
estimating (A). The R2 adj ranging from (0.8392) in model
(5 and 6) to (0.8457) in model (2). SE. of Est. ranging
from (4.3006) in model (5) to (4.2136) in model (2). MSE
for model (2) have the value (17.7547) lower than other
models.
Age of Tree at Breast Height with Crown Diameter
Relationship (A-CD)
The process of extracting the sample from the tree is affect
on its growth as it leads to a hole in the trunk of the tree,
which is considered one of the disadvantages of logs
during the sales process which affects the price and worth
less. Based on this, it is preferable to use regression
models to measure the age of the trees by using linear or
non-linear models between (A) as independent variable
and (CD) as the dependent variable. There are many
studies investigating the relationship between A-CD
(Grissino, 1995; Lindholm, et al., 1999; Peng, 2000;
Vanclay, 2002; Trasobares, 2004; Macke and Mathew,
2006; Bueno, 2009). According to the table 10 for
208
G.J.B.B., VOL.3 (2) 2014: 203-210
ISSN 2278 – 9103
TABLE 10: Model statistics and parameter estimates from age at D prediction for Pinus brutia Ten. in Duhok province.
S.E.
No.
B0
B1
B2
B3
R2 adj.
MSE
of Est.
1
8.0015
2.83245
0.8448
4.2352
17.9367
2
11.3828
2.01898
0.0417055
0.8457
4.2136
17.7547
3
11.456
1.99224
0.0446287
-0.000097
0.8449
4.2244
17.8453
4
6.37695
0.761287
0.8379
4.3185
18.6493
5
15.7616
1.08203
0.8392
4.3006
18.4947
6
2.75652
0.078941
0.8392
4.3005
18.4945
7
78.9049
-530.344
1201.81
0.8131
4.6360
21.4929
8
-16.6593
23.6805
0.7934
4.8747
23.7627
Model (2) gave the best performance according to the
values of the statistics. Consequently, polynomial model
was selected. There was a strong positive non-linear
relationship between A and CD (Figure 5.a). The observed
(A) versus the predicted (A) is also drawn for testing data
(Figure 5.b), it show that the model (2) fits the data well.
The polynomial model established between these two
variables was statistically significant (F = 546.128; P <
0.001) as shown in table (11).
TABLE 11: The result of Analysis of Variance for polynomial model to estimate A for Pinus brutiaTen.
Source
DF
SS
MS
F-Test
P-value
Regression
2
19392.7
9696.34
Error
197
3497.7
17.75
546.128
0.001
Total
199
22890.4
FIGURE 5: a- The relationship between A and CD
CONCLUSION
At the end of the regression analysis, there was a strong
positive non-linear relationship between (H-D, CD-D, AD and A-CD).It was determined that there were
statistically significant (P < 0.001) and strong (R2 adj >
0.77) relationships between (H-D, CD-D, A-D and A-CD)
which are significant. The corresponding F-values from
analyses of variance are also significant (P < 0.001) in
Calabrian pines. The strongest relationship determined
was the A-D relationship (R2 adj = 0.9340) very close
relationship, followed by the H-D (R2 adj = 0.8708) then
CD-D (R2 adj = 0.8542) and A-CD (R2 adj = 0.8457)
respectively. The results of the study indicated that the
relationships between (H-D, CD-D and A-D) can be
described by the cubic model, while (A-CD) relationships
can be described by the second-degree polynomial model.
Finally the important characteristics variables of tree such
as heights, crown diameters and age of tree can be
estimated by means of diameter at breast height, of which
measurement is easy, in Calabrian pines of the research
area.
b- Observed vs. predicted A for selected model.
REFERENCES
Avsar, M.D. (2004) The relationship between diameter at breast
height, tree height and crown diameter in Calabrian pines (Pinus
brutia Ten.) of Baskonus Mountain, Kahramanmaras, Turkey. J.
Biol. Sci 4: 437-440.
Bragg, D.C. (2001) A local basal area adjustment for crown
width prediction. North. J. Applied For18: 22-28.
Bueno-López, S.W. (2009) Understanding growth and yield of
Pinus occidentalis Sw. in La Sierra, Dominican Republic. PhD
Dissertation, College of Environmental Science and Forestry,
State University of New York, Syracuse, NY, USA, pp. 266.
Burrows, N.D., Ward, B. and Robinson, A.D. (1995) Jarrah
forest fire history from stem analysis and anthropological
evidence. Aust. For 58: 7-16.
Calama, R. and Montero, G. (2004) Interregional nonlinear
height–diameter model with random coefficients for stone pine in
Spain. Can. J. For. Res 34:150-163.
209
Models between diameter, height, crown diameter and age of Pinus brutia Ten
Canadas, N. (2000) Pinus pinea L. en el Sistema Central
(VallesdelTiétar y del Alberche): desarrollo de unmodelo de
crecimiento y producción de piña. Ph.D. Thesis, E.T.S.I. de
Montes, Universidad Politécnica deMadrid.
O’brien, S.T., Hubbel, S.P., Spiro, P., Condit, R. and Foster, R.B.
(1995) Diameter, height, crown and age relationships in eight
neotropical tree species.Ecology76: 1926–1939.
Peng, C. (2000) Growth and yield models for uneven-aged stand:
Past, present and future. For. Ecol. Manage 132:259-279
Crookston, N.L. and stage, A.R. (1999) Percent canopy cover
and stand structure statistics from the Forest Vegetation
Simulator. US For. Ser. Gen. Tech. Rep. RMRS-GTR-24. 11 p.
Pommerening, A. and Stoyan, D. (2006) Edge-correction needs
in estimating indices of spatial forest structure. Can. J. For. Res
36: 1723–1739.
Dieguez-Aranda, U., Barrio, A.M., Castedo, D. F. and Alvarez,
G.J. (2005) Relacionaltura-diametrogeneralizada-paramasas de
Pinussylvestris L. procedentes de repoblación en el noroeste
deEspaña. Invest Agrar: Sist Recur For 14: 229-241.
Pretzsch H., Biber P., Dˇursky´ J. (2002) The single tree-based
stand simulator SILVA: construction, application and evaluation.
For. Ecol. Manage 162: 3–21.
Fady, B, Semerci, H. and vendramin, G. (2003) Euforgen
Technical guidelines for genetic conservation and use for aleppo
pine (Pinus halepensis) and brutia pine (Pinus brutia).
International Plant Genetic Resources Institute, Rome, Italy.
Rayner, M.E. (1992) Application of dendrochronology, stem
analysis and inventory data in the estimation of tree and stand
ages in karri forest. Western Australian Department of
Conservation and Land Management Technical Report No. 27.
Faunt, K. (1992) Formation, frequency and longevity of hollows
in jarrah: Interim report. Unpublished report. CALM W.A.
Rose, P.W. (1993) Production of habitat hollows by wheat belt
eucalypts. Rose and Bending Forest and Environmental
Consultants Final Report, Save the Bush Research Grant 1991/92
- Project R053
Foli, E.G., Alder, D., Miller, H.G. and Swaine, M.D. (2003)
Modelling growing space requirements for some tropical forest
tree species. For. Ecol. Manage 173:79-88.
Sanchez, C.A.L., Varela J.G., Dorado F.C., Alboreca A.R.,
Soalleiro R.R., Gonzalez J.G.Á. and Rodriguez F.S. (2003) A
height-diameter model for Pinus radiata D. Don in Galicia,
north-west Spain. Ann. For. Sci 60: 237-245.
Gezer, A. (1986) The sylviculture of Pinus brutia in Turkey.
Options Méditerranéennes Ciheam 86: 55–66.
Grissino-mayer, H. D. (1995) Tree-ring reconstructions of
climate and fire History at El malpais National monument, New
Mexico. Ph.D. dissertation, University of Arizona, Tucson; 407
pp.
Sharma, M. and Parton, J. (2007) Height–diameter equations for
boreal tree species in Ontario using a mixed-effects modeling
approach for Ecol. Manage, 249: 187–198.
Hemery, G.E., Savill, P.S. and Pryor, S.N. (2005) Applications
of the crown diameter stem diameter relationship for different
species of broadleaved trees. Forest Ecol. Manage 215: 285-294.
Stoneman, G.L., Rayner, M.E. and Bradshaw, F.J. (1997) Size
and age parameters of nest trees used by four species of parrot
and one species of cockatoo in south-west Australia: Critique.
Emu 97: 94-96.
Herath, H. (2007) Changes of crown parameters with the age
and growth of Eucalyptus grandis Hill ex. Meiden, University
of Sri Jayewardenepura, Nugegoda, Sri Lanka.
Temesgen, H. and Gadow, K.V. (2004) Generalized heightdiameter models an application for major tree species in
complex stands of interior British Columbia. Eur. J. For. Res
123: 45-51.
Lindholm, M., Eronen, M., Timonen, M. and Merilainen, J.
(1999) A ring-width chronology of Scots pine from northern
Lapland covering the last two millennia. Annales Botanici
Fennici 36:119-126.
Trasobares, A. and Pukkala, T. (2004) Using past growth to
improve individual-tree diameter growth models for uneven-aged
mixtures of Pinus sylvestris L. and Pinus nigra Arn. in Catalonia,
north-east Spain. Ann. For. Science.
Lockhart, B.R., Robert, C., Weih, J.R. and Keith, M.S. (2005)
Crown radius and diameter at breast height relationships for six
bottomland hardwood species. J. Arkansas Acad. Sci 59: 110115.
Turan, S. (2009) Diameter at breast height-crown diameter
prediction models for Picea orientalis. Afr. J. Agric Res 4:215219.
Macke, E.D. and Mathew, R.W. (2006) Forest Mensuration, a
handbook for practitioners. HMSO Edinburgh. ISBN 0-85538.
621-625
Vanclay, J.K. (2002) Growth modeling and yield prediction for
sustainable for est Management, The Malaysian Forester 66:5869.
Muzahim, S. and Mohammed, H. (2007) Preparing Form Class
Volume Table for Brutia Pine plantations. 1st Agric. Res. Con.
Kirkuk Univ., pp 91-100.
Whitford, K. R. (2002) Hollows in jarrah (Eucalyptus marginata)
and marri (Corymbia calophylla) trees: I. Hollow sizes trees
attributes and ages. For. Ecol. Manage 160: 201-214.
Mohammed, H. (2009) Using Girard Formula in Volume Table
Construction for Brutia Pine plantations in Duhok Province.2nd
Biol. Sci. Con. Duhok Univ., pp 44-48.
Zhang, L., Peng, C. and Dang, Q. (2004) Individual-tree basal
area growth models for jack pine and black spruce in northern
Ontario. Forestry Chronic 80: 366-374.
210