SPECIALISED SCIENTIFIC COUNCIL ON FOREST SCIENCE

BULGARIAN ACADEMY OF SCIENCES

FOREST RESEARCH INSTITUTE

Tatiana Vassileva Stankova

POSSIBILITIES FOR DENSITY OPTIMIZATION OF SCOTS PIN E

AND AUSTRIAN BLACK PINE PLANTATIONS BY MATHEMATICAL

MODELS

EXTENDED SUMMARY

of a PhD thesis

Scientific specialty: Forest plantations, forest tree breeding and

seed production (code 04.04.01)

Scientific supervisor: Assoc. Prof. Dr. Masato Shibuya

Hokkaido University, Sapporo, Japan

Reviewers: Prof. DSc. Ivan Mihov

University of Forestry, Sofia, Bulgaria

Assoc. Prof. Dr. Milko Milev

University of Forestry, Sofia, Bulgaria

Sofia, 2006

The PhD thesis was debated and directed to a public defense procedure on a meeting of the Specialized Scientific Panel at the Forest Research Institute of Bulgarian Academy of Sciences, Sofia on 28 September 2006.

The thesis is written in Bulgarian language and consists of 168 pages, 129 pages of which are the main part and 39 pages are a complementary part. The main part includes text, 33 tables and 25 figures. The list of references comprises 148 titles, 74 of which are written on Cyrillic alphabet and 74 – on Latin alphabet. The complementary part includes Dictionary of the terms and 19 Appendices, 9 of which are in table form, while 7 are figures.

The PhD thesis public defense will take place on 12 February 2007 from 13

o’clock in Hall №4 of the University of Forestry – Sofia on a meeting of the Specialized Scientific Council on Forest Science at the Supreme Attestation Commission of the Republic of Bulgaria.

The thesis and the other documents are available for public access in room №331, floor 3 of the University of Forestry, Sofia, 10 “St. Kliment Ohridski” blv.

1. INTRODUCTION Two main scientific approaches, which are complimentary to one another,

have been generally applied to the problem for plantation density optimization to establish sustainable forest ecosystems for achievement of particular management goals. The first approach, which was the only approach used in Bulgaria, is from particularity to generalization. Allometric relationships between spacing and growth traits and among the growth characteristics themselves are established to determine the optimal planting density in order to satisfy particular management criteria by examining specifically designed experiments of different planting schemes through repetitive measurements of the major tree growth traits or tree characteristics related to stem quality. This approach, however, has derived only a partial solution to the density control of plantations because the observations have been restricted to relatively short periods of time in comparison with the life span of the tree species, the conclusions can be used only for the limited range of densities and growth conditions where the studies have been conducted and satisfy a limited number of quantitative and qualitative criteria.

The second approach is from generality to particularity: a broad spatial and temporal range of stand level data is incorporated into a complex mathematical model, which is designed to provide useful guidance to foresters in determining planting densities and prescribing thinning treatments. Stand Density Control Diagrams (SDCD) are such kind of models, which are developed initially in Japan and nowadays are approved and applied in the forestry practice of USA, Canada and other Asian countries as well. The SDCD are complex mathematical model for the spatial-temporal dynamics of natural or man-made forest stands under a broad range of growth conditions. The SDCD are applied in three directions: to evaluate stand growth parameters (mean breast height diameter, dominant height, density, yield) at any stand growth stage; to simulate various (alternative) thinning regimes and to estimate the total harvest and the corresponding profit; to determine the optimal initial density of forest plantations in accordance with the preferred management objective and thinning regime.

The main objective of the present investigation is to propose, to apply and to verify a new method for density control of the Scots pine (Pinus sylvestris L.) and Austrian black pine (Pinus nigra Arn.) plantations in Bulgaria, which can be used in density optimization according to various management objectives. The following tasks were assigned to accomplish the main objective:

1. Adaptation and modification of the SDCD methodology for application in Bulgaria by defining the mathematical models of the main elements of the SDCD.

2. Estimation and establishment of the SDCD models based on representative experimental data sets collected in Scots pine and Austrian black

pine plantations growing at broad range of densities, growth stages and site conditions.

3. Verification of the established SDCD models for Scots pine and Austrian black pine plantations.

4. Proposition of two exemplary ways for SDCD application. 2. SAMPLE PLOTS AND DATA COLLECTION Objects of the present investigation were Scots pine and Austrian black

pine plantations mainly in the mountainous part of south-western Bulgaria: the mountains Rila, Pirin, Sashtinska Sredna Gora, Kraishte, Golo Bardo, Lozenska, Viskyar, Lyulin, Vitosha and Plana, the western part of the Stara Planina mountain, the central and eastern Rhodopes and in the eastern part of the Stara Planina mountain. The field investigation took place on the territory of 16 Forest Estates and Vitosha Natural park (Figure 1) by temporary sample plots of rectangular or circular form and of different sizes depending on the density and the homogeneity of the stands and according to the SDCD methodology. Detailed description including information on the location, growth conditions and stand growth parameters of each sample plot was prepared (Figure 2). The information about the types of the forest sites was based on the Forest Inventory Plans, while the slope, the aspect and, in most of the cases, the altitude were measured during the plot establishment. In each plot, breast height diameters of all trees and heights of 20% of the trees to estimate the mean and the dominant height were measured. The values of the growth parameters mean breast height diameter, mean and dominant heights, density, basal area and yield were estimated. One hundred and thirty sample plots in Scots pine plantations on 21 types of forest sites, of altitudinal range from 480 to 1300 m a.s.l. and slopes from 0° to 37° were established. The Austrian black pine plantations were presented by 122 sample plots on 24 types of forest sites, at altitudes 275 to 1350m a.s.l. and slopes from 0° to 39°. The soil fertility of the growth sites ranged from poor (A) to rich (D) and the soil humidity – from dry (1) to humid (3). Beside the personally recorded data, additional data from 83 Forests Estates in Bulgaria which include 468 plots in P. sylvetsris plantations and 323 plots in P. nigra plantations, either published or granted by other researchers were included in the data set.

Figure 1. Number of the established temporary sample plots in Scots pine (ScP) and Austrian black pine (ABP) plantations by Forest

Estates

1 – denomination of the forest unit within the Forest Estate (number and letter); 2 – denomination of the type of the forest site according to the “Classification scheme of the types of forest sites of Bulgaria”. 1983. Ministry of forests and forest industry, Sofia; 3- relative site index in the range from 1 to 4, determined according to the age and the mean height; 4 - local name of the place (countryside); 5 – mean height class, determined according to the mean height and mean breast height diameter and applicable to assortment table utilization.

“Rila monastery” Forest Estate “Rila” Forestry sub -division Sample plot Date Work team Tree species Rila0503 25 July 2003 Plot dimens. Plot size (m2) R=10m 314.16

Tatiana Stankova, Hristo Stankov Scots pine

General description of the forest unit according to the Forest Inventory Plan from 2001 Reg.For.Div. Forest Estate Forest unit1 Type pf forest site2 Area (ha) Kyustendil Rila monastery 171 l МТY II B1,12,2 (133) 3,6 Age (years) Stocking rate Site index3 Altitude (m) 30 1 4 750 Slope (degrees) Relief Exposition Planting scheme 27 Slope – upper part NW Personally recorded data in 2003 Forest unit Name of the

4Altitude (m) Slope (degrees) Exposition

171 l Kukov rid 775 11 N - NW mean height class5 18 domin.height

dbh number BA (m2) volume (m3) mean height

(m) (m) 7 1 0.0038 0.027 14 16 8 8 0.0402 0.291 13.5 14.5 9 12 0.0763 0.586 16 15.5 10 12 0.0942 0.754 16.75 17 11 7 0.0665 0.546 15.25 17 12 10 0.1131 0.95 15 17.75 13 9 0.1195 1.026 16 17.5 14 17 0.2617 2.312 16 17 15 11 0.1944 1.738 15.5 17 16 12 0.2413 2.196 16 18.5 17 2 0.0454 0.42 18 6 0.1527 1.434 19 3 0.0851 0.816 20 1 0.0314 0.305 21 0 0 0 22 1 0.0380 0.381 QMD 13.3 mean 12.9 0.0140 0.123 15.4 16.8 total 112 1.5637 13.781

Figure 2. Exemplary description of a sample plot (Rila0503), established in a Scots pine plantation, “Rila monastery” Forestry Estate (July 2003).

R=10m N-NW

3. METHODS The main theoretical postulate employed in the SDCD is that the stand

growth stage is presented by their dominant height. Stand age, which is the usual growth stage parameter, does not reflect the site quality on which the stand growth is dependent. On the other hand, in comparison with the diameter growth, height growth is less influenced by the density. Dominant height class as a growth stage indicator reflects the age - site quality interaction, i.e. its particular values can be achieved at different ages in relation to the particular growth conditions. Defining the allometric relationship of this parameter to other stand characteristics, mainly mean height, would facilitate significantly its utilisation for practical purposes. The mean-dominant height relationship was estimated in the present investigation in order to utilize the available published data from sample plots in Scots pine and Austrian black pine plantations, which miss data for the dominant height.

3.1. Mean – dominant height relationship Linear functions and polynomials of 2-nd and 3-rd order differing in

combinations of terms and intercept (14 functions in total) were examined in expressing the mean-dominant height relationship in the present study. Their goodness of fit was estimated and compared through several statistical tests: F-test for significance of the regressions, t-tests for significance of the coefficients and the regression coefficient (R2); standard error of the model SY (Himmelblau, 1973; Steel and Torrie, 1981) and Akaike’s information criterion AIC (Inoue, 1999) and the final choice of the most adequate model was done through the symmetrical criterion of Williams-Clut (Himmelblau, 1973) for comparison of 2 functions which are proven to have comparable goodness of fit. The residual plots were examined and when violations of assumptions about the errors were suspected, the appropriate statistic - the K-numerical test of non-additivity and the h-test of heteroscedasticity (Anscombe & Tukey, 1963) - was calculated.

The dominant height values, of the published data that miss them, were determined based on the estimated mean-dominant height relationships.

3.2. Stand density Control Diagrams (SDCD) The main trends presented on the SDCD are the yield - density

relationships expressed both in space and in time. The SDCD are composed of 5 elements, which are defined, directly or indirectly, by principal stand growth parameters. These elements are:

Equivalent height curves Equivalent height curves describe the relationship between stand yield and

density at a given growth stage, which is presented by the dominant height class. The Equivalent height curves are expressed by the reciprocal equation of the C-D effect (Hagihara 1998, 1999, 2000):

BAty

+=

ρρ

(1)

BAtv

orBAt

v +=+

= ρρ

11 (2),

where y, ρ and v are yield, density and mean stem volume, respectively, and At and B are regression coefficients. The parameters At and B depend on the dominant height class, and in the present study they were estimated by previously developed three-stage procedure (Stankova and Shibuya, 2003). The plots were grouped according to their dominant height into height classes by 2 m. At the first step, At and B of the reciprocal equation were evaluated by dominant height classes through weighted least squares method. On the next step, the estimates of At and B from the first step were regressed on the dominant height class H by the non-linear regressions:

=At )ˆ-ˆ(1 2

21

1dd HCHC

T (3)

2-2

ˆ= bHaB (4),

where 22121 ,,,,, addCCT and 2b are regression coefficients. The predicted values of At and B from the second step were then

substituted in the reciprocal equation (Eq. 1), that produced the final estimates of yield.

Full density line Full density line is the upper boundary of the stand yield – density

relationship and connects the points of density – maximum yield combinations. It is a power function (Yoda et al., 1963):

αρ −= Kv

or αρ −= 1Ky (5),

where K and α are constants. Based on the formulae by Stankova and Shibuya (2003), the slope of the self-thinning line α and the reciprocal value of the asymptotic stand density ε were determined. They were used to fix the full density line, described by Eq. 5, where the value of ε was used to determine the asymptotic density ρε=1/ε and its corresponding yield yε for each growth stage (Eq. 1). The intercept K was estimated using the values of ρε, yε and α (Stankova and Shibuya, 2003).

Natural thinning curves Natural thinning curves describe the yield growth of stands of given initial

densities with time-lapse, considering the process of self-thinning. The curves describing the process of natural thinning were determined according to the formula by Shibuya (1995):

fKv −= −αρ (6)

or ρρ α fKy −= −1 (7), where parameter f is estimated for arbitrary initial densities (N0) using the formula:

α0N

Kf = (8)

The values of f in the present investigation were determined for 23 initial density values N0 (444÷40000/ha) and different initial survival rates were

considered ( 0*0 )95.075.0( NN ÷= ).

Equivalent mean diameter curves Equivalent mean diameter curves are trajectories on the SDCD, which

connect yield-density combinations of stands having the same mean diameter. They are determined from stand form height, basal area, stand stock (yield), dominant height and density. The stand form height (HF) is defined as a ratio of the stand stock to the basal area (Equation 9) and is related linearly to the dominant height (Equation 10). After successive substitution of Equations 9-12, the relationships for the Equivalent diameter curves are obtained, for values of the quadratic mean diameter from 2 to 32cm (by 2cm interval) for the mean diameter classes:

G

yHF = (9)

HbaHF 11 += (10)

40000

2dbhHFy

πρ= (11)

or ( ) ( )Hbadbhy ˆ40000 11

2 += πρ, (12)

where HF - stem form height (m); G - basal area (m2/ha); dbh – quadratic mean diameter (cm); H - dominant height (m);

−11,ba constants Yield index curves Yield index is estimated as a ratio of the yield per hectare of a given stand

to the yield of a stand on the Full density curve in the same dominant height class. On the double logarithmic scale, the Yield index curves are presented by lines parallel to the Full density curve, i.e. they are determined by an equation

αρ −= 1yy RR Ky (13),

where yRK is a constant and the Yield index obtains values from 0.1 to 0.9.

The goodness of fit of the regressions expressed by Eqs. 3, 4 and 10 was estimated through the coefficient of determination (R2), its significance (F-test) and the significance of the estimated regression coefficients (t-tests). Run test of residuals was performed and the residual plots were examined to check for data deficiencies (Draper & Smith, 1981).

3.3. Verification of the models of SDCD Two main approaches were employed for verification of the SDCD

models. They were applied to verify the Natural thinning curves and the Equivalent mean diameter curves. The Natural thinning curves were exposed to verification, because their evaluation was not a result of a direct approximation of repeated measurements in time from self-thinning stands, but the coefficient estimates of the Equivalent height curves and the Full density line were utilized in their determination. The Equivalent mean diameter curves were exposed to verification, because the experimentally measured values of dbh were not included directly in their estimation.

3.3.1. Verification by comparison between actual and predicted values A. Natural thinning curves Data on the initial planting schemes, known from the forest inventories

were used to verify the Natural thinning trajectories. Six possible percentages of survival (75-100%) during plantation establishment were also considered. The experimental data of the present density and stand stock were used to estimate the initial density according to the model of the Natural thinning curves, which was compared to the actual initial density. Data on the initial density together with the present stand stock were used to estimate the present density according to the Natural thinning curves and its value was compared to the actual present density.

The predicted densities were compared to the actual densities through: t-test for comparison of their means; Wilcoxon signed ranks test for comparison of their distributions and estimation of the relative errors and their distribution by percentiles (10, 25, 50, 75 and 90). Error distributions by percentiles for both initial and present density were analyzed in two ways. In the first case, the error percentiles were determined and compared by initial survival percentages. In the second case, to analyze the level of precision of the Natural thinning curves according to the growth stage of the experimental stands, the error distribution was determined by large-scale growth stages: 4-6m, 8-12m, 14-16m, 18-32m dominant height classes.

B. Equivalent mean diameter curves The experimentally determined values of the quadratic mean diameters

were not directly utilized in fixing the Equivalent mean diameter curves,

because they were constructed by mean diameter classes of particularly assigned values for dbh: 2-32cm, by 2cm interval (Eqs. 9-12). This fact allowed comparison of the experimentally determined values of the quadratic mean diameter with those predicted by the model of the Equivalent mean diameter curves (from Equation 12). Similarly, the precision of the Equivalent mean diameter curves could be estimated regarding the stand stock by using (in Equation 12) the experimentally determined values of the quadratic mean diameter as an input variable for the predicted yield. Error distribution for the quadratic mean diameter and yield was analyzed through estimation of the percentiles (10, 25, 50, 75 and 90) by dominant height classes.

3.3.2. Verification by comparison with the maximum possible densities determined by the crown diameter

The model by Zhelev (1971) for unit of canopy closure of a tree was used to evaluate the relative growth space of the average tree in the stand in order to relate it to the main growth parameters in the model of SDCD. According to Zhelev’s model, the growth space of a tree in a stand (m2) at full canopy closure 1.0 (10000/ number of trees per hectare) equals the crown projection (the surface of a circle of a crown diameter Dk). Thus, the experimental data for density ρact were used to evaluate the growth space per tree: 10000/ ρact(m

2) and its corresponding crown diameter Dk:

)(20000

cmDact

k πρ= (14).

Additionally, the relationships between crown diameters at full canopy closure 1.0 and breast height diameters by dominant height classes were established in order to determine the minimum possible growth space per tree. The relationship was presented by a straight-line function as suggested by studies on plantations of other tree species. Based on the estimated relationships the 95% confidence intervals, which include 95% of all possible values of Dk for each value of dbh, by dominant height classes, were estimated. The lower margin of the interval indicates the smallest values of Dk, i.e. the least possible growth space and its corresponding maximum density for the given dbh and dominant height class. Thus, the maximum possible densities, which would allow the minimum possible relative growth space per tree, were estimated by equivalent height classes and equivalent mean diameter classes. These marginal values were compared to those estimated for the crossing points of the equivalent mean diameter curves with the equivalent height curves and of the natural thinning curves with the equivalent height curves.

3.4. Examples of SDCD application 3.4.1. Defining of groups of initial densities according to the middle

points of the growth gradients in space and time The C-D index, that is the growth gradient of the C-D trajectory, is a

measure of space utilization by plants (Shinozaki and Kira, 1961). The increase of stand stock itself is a volume increment and consequently the stand stock

increase with density decrease at a given growth stage )(log

log

space

va

ρ∂∂−= can

be defined as volume increment in space. The points on the C-D curves where half of the potential yield increment for the particular growth stage is achieved

(2

1

)(log

log =∂

∂−=space

va

ρ) can be called middle points of the growth gradient

(volume increment) in space (Shinozaki and Kira, 1961). They are derived by Shinozaki and Kira (1961) and these are the so-called B-points of the C-D curves. The stand stock increase with density decrease of a particular stand in

the process of self-thinning ()(log

log

time

vb

ρ∂∂−= ), on the other hand, is a

measure of time utilization by plants to grow and can be defined as volume increment in time. By analogy with the B-points on the equivalent height curves, points on the natural thinning curves can be defined - middle points of the growth gradient (volume increment) in time Kf for the corresponding initial densities.

It can be assumed that at dominant height class 4m, which corresponds to mean heights 2.6 and 2.8m for Scots pine and Austrian black pine plantations, respectively, at ages 5-10 years, the plantations are finally established and have formed a forest stand. Consequently, the middle point of the growth gradient (volume increment) in space for 4m growth stage can be considered reference point to define the initial densities, which are too high and indicate ineffective space utilization. These are the planting schemes which initial density is higher than the density co-ordinate of the B-point for 4m dominant height class. The estimated Kf-points of the natural thinning trajectories allow the establishment of another boundary by taking into account the initial density at which the middle point of the growth gradient (volume increment) in time Kf exceeds the maximum attainable yield. Thus, the plantations established at this or lower initial density can be managed without thinnings, because they will not undergo significant yield increment losses until the rotation age. Consequently, the middle points of the growth gradient in time (Kf) for the particular initial densities and in space (B) for 4m dominant height class can be considered to classify the initial densities into 3 groups: initial densities which are not advisable for afforestation; initial densities which can be managed without thinnings to rotation age and initial densities which require at least one thinning during their rotation period.

3.4.2. Determination of optimal planting densities using the SDCD-s A. Optimal initial density for desired maximum yield A direct way to apply the SDCD for the plantation management is to

determine the optimal initial density to achieve the desired maximum yield by a self-thinning stand at the end of the rotation period. The desired maximum attainable yield (Y max) was set to have the maximum value of the stand stock, which was known from the experimental data set for the latest growth stage ( H =28m) in this study. The desired maximum attainable yield (Y max) is achieved at the latest growth stage by a stand of density ρ* and yield y*=Y max, which is the intersection point of the equivalent height curve for H =28 m on the maximum attainable yield (Y max).

The stand of estimated parameters ρ* and y* is characterized by the

natural-thinning curve:

**1** )( fKy ρρ α −= −⇒

*

*1** )(

ρρ α yK

f−=

− (15)

The stand relative initial density*inρ for ∗y is estimated from Eq. 15

for 0* →iny :

0)( **1** =−= − fKy ininin ρρ αα

ρ

1

**

=⇒

f

Kin (16)

B. Optimal initial density for desired large-size wood production The large-size wood was defined by the size of the mean diameter, which

in this study was set to obtain value of dbh=30 cm. It corresponds to the II-nd group (out of 5 groups) of timber assortments determined for the Scots pine (Krastanov et al., 1979) and Austrian black pine (Tsakov, 1984) in Bulgaria. The desired mean stem diameter is achieved by a self-thinning stand, which is located at the intersection point of the equivalent mean diameter curve of the desired mean dbh= 30 cm on the equivalent height curve of the latest growth stage (H =28 m). The final estimation of the initial planting density for desired mean diameter is done following Eqs. 15 and 16.

The dominant height – age relationship for Scots pine and for Austrian black pine plantations was additionally estimated to make the results of the present investigation comparable to the results by other investigators. The function by Richards (1959) was preferred to express the relationship in accordance with studies by other investigators (Beck, 1971; Payandeh, 1974)

mlAgekH −−−= 1

1

))exp(1( (17),

where k, l, and, m are coefficients. Data from 445 sample plots in Scots pine plantations and 313 sample plots in Austrian black plantations were used for estimation of the relationships.

4. RESULTS AND DISCUSSION 4.1. Mean – dominant height relationship Data from 154 sample plots were used to estimate the mean-dominant

height relationship for Scots pine (Pinus sylvestris L.) plantations. The data range is presented in Table 1 and the precision with this data set was 2.84% sample error for the mean height and 2.61% sample error for the dominant height. The regression coefficients R2, F-tests and t-tests allowed selection of 6 statistically significant models. Four out of the 6 chosen regressions had relatively small values of their standard error and coefficient AIC. The two most adequate functions – the straight-line model (y=ax+b) and the polynomial function y=ax3+cx+d were selected and tested further.

The residual plots showed tendencies to heteroscedasticity (curvilinear model) or violation of the assumption for additivity (straight-line model), that imposed the performance of analytical tests (Anscombe & Tukey, 1963). The results from the K-numerical test for non-additivity of the linear model showed that the assumption for additivity was not violated. The coefficient of heteroscedasticity (h) for the curvilinear model, on the other hand, proved to be significantly different from 0. The result from the application of the symmetrical criterion of Williams-Clut (Himmelblau, 1973) did not reveal superiority of one of the tested models to the other. Thus, the final tests for evaluation of the most adequate regression model to express the mean-dominant height relationship for Pinus sylvestris plantations confirmed that it is the linear function:

Hdom=0.996Hm+1.455 (18) A representative data set comprising 120 sample plots of height range

from 3.4 to 26.7m for mean height and from 4.4 to 28.3m for dominant height was designated to establish the mean-dominant height relationship for Austrian black pine (Pinus nigra Arn.) plantations. The precision achieved was estimated to be P=3.07% for the mean height and P=2.83% for the dominant height. Six of the 14 examined functions were proven to be statistically significant and the values of SY and AIC were estimated for them. The lowest values of these coefficients were obtained for the straight- linear function (y=ax+b) and the residual plot suggested that there were no violations of the assumptions about the errors. Thus, the mean-dominant height relationship for Austrian black pine plantations is adequately presented by the linear regression:

Hdom=0.991Hm+1.256 (19) A 1-st order linear relationship between mean and dominant height was

established for Scots pine and Austrian black pine in many studies. The linear form of the mean-dominant height relationship for Scots pine plantations was derived also by the present investigation, which covered the variety of sites,

densities and growth stages for the plantations. The comparison to similar studies on Scots pine natural stands in Bulgaria (Douhovnikov, 1972; Mihov, 1986; Shikov, 1974) and abroad (M.L.W.F., 1980) showed the higher degree of height differentiation in the natural stands than in the plantations. This can be seen from the differences between the heights of the average and the dominant trees, which are quantitatively characterized by the slope (a>1 for natural stands and а<1 for plantations) and the intercept (b (natural stands)>b (plantations)) of the lines defining the mean-dominant height relationship.

Straight-linear form of the mean-dominant height relationship was convincingly proven for the Austrian black pine plantations. In agreement with the study by Shikov (1974), the present survey estimated smaller slope (a=0.990) and intercept (b=1.256) of the line expressing mean-dominant height relationship for Pinus nigra plantations than the slope and the intercept of the mean-dominant height relationship of the P. sylvestris plantations (a=0.996; b=1.455). This fact suggests the tendency of higher degree of height structure homogeneity in the Austrian black pine plantations than that in the Scots pine man-made stands, because the difference between mean and dominant heights was smaller in P. nigra plantations than in P. sylvestris plantations.

Table 1. Descriptive statistics of the data used in estimation of the mean-dominant height relationship

Mean height (m) Tree species

Range(m) Mean(m) St. deviat.(m) Coef.Var.(%) Precis.error (%) Pinus sylvetsris 3.18÷26.50 14.46 5.10 35.24% 2.84

Pinus nigra 3.39÷26.69 14.00 4.70 33.59% 3.07

Dominant height (m) Tree species

Range(m) Mean(m) St. deviat.(m) Coef.Var.(%) Precis.error (%) Pinus sylvetsris 3.58÷27.00 15.86 5.14 32.40% 2.61

Pinus nigra 4.37÷28.31 15.12 4.70 31.05% 2.83

4.2. Stand Density Control Diagram Scots pine (Pinus sylvestris L.) Equivalent height curves were determined for dominant height classes

from 4 to 26 m over data set of 519 Scots pine sample plots, with precision of stratified sample error 2.04% for the yield. There were no sufficient representative data for the 4 m dominant height class, and it was excluded from the analyses for estimation of the parameters At and B. For all other height classes yield data were regressed on the density at the first step of the procedure with good degree of determination (R2= 0.329–0.771). Parameter B was approximated by the power function of the dominant height on the next step of the analyses with high degree of determination (R2= 0.980) and the regression was statistically significant (coef. F = 343.650, P<0.001). Parameter At was expressed by the 5-coefficient function of H (Eq. 3) with good precision -

4m

6m

8m

10m

12m

14m16m

18m20m

22m24m

26m

Y40000Y20000

Y12500Y10000

Y8333Y6667

Y5000

Y4444Y3333

Y2500Y2222

Y2000Y1667

Y1600Y1333

Y1111Y952

Y816Y714

Y625Y556

Y494Y444

2cm

4cm

6cm

8cm

10cm

12cm14cm

16cm

18cm

20cm

22cm

24cm

26cm

28cm

30cm

32cm

10

100

1000

100 1000 10000 100000density (1/ha)

yie

ld (m

3 /ha

)

Equivalent height curves Full density line Natural thinning curves

Equivalent mean diameter curves Yield index lines

Stand Density Control Diagram for Scots pine plantationsY0.9Y0.8Y0.6

Y0.5

Y0.4

Y0.3

Y0.7

Y0.2

Figure 3. Stand Density Control Diagram for Scots pine plantations

R2=0.940, coef. F = 51.352, P<0.01. The residual plots for parameters At and B on the independent variable (H ) were examined and no violations of the assumptions about the errors were detected which was confirmed also by the run tests of residuals. Self-thinning exponent (α) of 1.69 was estimated for Scots pine plantations, and the full density line was expressed by the power function:

69.0163267 −= ρy . Five hundred eighty six sample plots in total were used to fit the dominant height – stand form height relationship and the precision with this data set was evaluated to be 1.79% sample error for the dominant height and 1.38% sample error for the stem form height. The stand form height (HF) was approximated well by the linear function of dominant height (Eq. 10) - R2= 0.847, coef. F = 3231.396, P<0.001 and the residual plot on the independent parameter (H) confirmed its goodness of fit. The Stand Density Control Diagram for Scots pine plantations is shown on Figure 3.

Austrian black pine (Pinus nigra Arn.) Equivalent height curves were estimated for dominant height classes from

4 to 28 m using data from 359 sample plots of Austrian black pine. The precision of a stratified sample error of 2.33% for the yield was estimated, and the 4 and 28 m dominant height classes were excluded from estimation of parameters At and B because of insufficient data. The yield data from 6 to 26 m dominant height class were approximated by the reciprocal equation of density at the first step of the work procedure with good degree of determination (R2= 0.243–0.713). Parameter B was regressed by the power function of dominant height class with R2=0.905, and the goodness of fit of the regression was proven by the statistical tests (coef. F = 96.171, P<0.001). The five-coefficient regression for At (Eq. 3) showed good degree of determination of R2=0.882 and proven statistical significance (coef. F = 36.577, P<0.01). The full density line of Austrian black pine plantations was expressed by the

function: 75.0385843 −= ρy , and the self-thinning exponent obtained value of

α=1.75. Equivalent mean diameter curves were determined over data set of 427 sample plots used to estimate the dominant height – stand form height relationship, and the precision of sample error was 2.13% for dominant height and sample error 1.75% for the stem form height. The estimated linear regression of stand form height on dominant height (Eq. 10) was statistically significant (R2= 0.812, coef. F = 1841.056, P<0.0001) and the residual plot on the independent variable (H) confirmed its goodness of fit. The Stand Density Control Diagram for Austrian black pine plantations is shown on Figure 4.The dependencies of the growth parameters At and B of the reciprocal equation of C-D effect, derived in a previous investigation (Stankova and Shibuya, 2003), were applied to estimate the equivalent height curves in SDCD in this study. The parameter At was obtained by a regression consisting of the difference of two power functions, while parameter B was formulated by a power function of height. They were preferred to Ando’s empirical formulae (Ando, 1962),

4m

6m

8m

10m

12m

14m

16m18m

20m22m

24m26m28m

Y40000Y20000

Y12500Y10000

Y8333Y6667

Y5000Y4444

Y3333Y2500

Y2000Y1667

Y1600Y1333

Y1111Y952

Y816Y714

Y625Y556

Y494Y444

2cm4c

m

6cm8c

m

10cm

12cm

14cm

16cm

18cm

20cm

22cm

24cm

26cm

28cm

30cm

32cm

Y2222

y = 385843ρρρρ -0.75

10

100

1000

100 1000 10000 100000density (1/ha)

yie

ld (m

3 /ha

)

Equivalent height curves Full density line Natural thinning curves

Equivalent mean diameter curves Yield index lines

Stand Density Control Diagram for Austrian black pine plantations

Y0.9Y0.8Y0.7Y0.6Y0.5

Y0.4

Y0.3

Y0.2

Figure 4. Stand Density Control Diagram for Austrian black pine plantations

because they are theoretically derived on the basis of Hagihara’s new models (Hagihara, 1998, 1999, 2000) and thus they are applicable to both selfthinning and non-selfthinning stands.

In the present study, a different approach to determine the full density line was applied which avoids the disadvantages of the methods applied until now (Drew and Flewelling 1977, 1979; Solomon and Zhang, 2002; Shibuya et al., 2004). It is a new method which is based on derivation and presenting the slope of the self-thinning line α through the coefficients used in expressing the growth parameters At and B as functions of the dominant height class (Stankova and Shibuya, 2003). Furthermore, subjectivity in fixing the line intercept K was avoided by application of the estimated values of the reciprocal stand density (ε), rather than empirically determined uppermost points.

The value of the self-thinning exponent estimated for Scots pine plantations (α=1.69) was smaller than the one for Austrian black pine plantations (α=1.75) in the present results. This result indicates that the growth space is faster saturated by the plant biomass in the Scots pine than in the Austrian black pine plantations. The mathematical nature of the self-thinning constant (Shibuya et al., 2004) also assumes that achieving of a particular amount of yield increment requires larger decrease in stand density for the Scots pine plantations than for the Austrian black pine stands. According to other investigators (Begin et al., 2001; Westoby, 1984), the light tolerance of tree species is reflected in the value of the intercept of the full density line. They consider that the shade tolerant species attain larger amount of biomass per unit of spacing than the shade intolerant ones, and this is expressed by higher values of the intercept K. The results of the present investigation agreed with this statement, because the estimated value of the intercept for Austrian black pine plantations (lnK=12.86) was higher than that for Scots pine plantations (lnK=12.00).

The trajectory of natural thinning consists of early stand growth stage when the plants increase in size without density reduction, followed by a phase of biomass increase coupled with decrease in density due to self-thinning, which in the latest phase approaches asymptotically the full density line. The models proposed for expressing of the natural thinning trajectories usually include parameters, which cannot be always easily measured or determined (Aikman and Watkinson, 1980; Puettmann et al., 1992). The model by Shibuya (1995) was preferred in the present investigation, because it is proven with data from stands of different origin, species, growth stage and site conditions and describes well the main phases of the natural thinning trajectory. The model utilizes the already-determined values of the slope α and the intercept K of the full density line and estimates the natural thinning trajectory for any chosen initial density. Its main advantage is that it does not require repeated measurements from permanent sample plots, which is indispensable in other models. The initial density, as it is formulated here, is a relative initial density when the biomass

increases without density decrease (Shibuya, 1995). This means that the process of initial establishment of the plantation, with the respective losses of plants which are difficult to predict, has been accomplished. For this reason, the SDCD-s of the present study were constructed for 6 different survival percentages (of initial survival rate: 75-100%) assumed for each of the planting schemes and the appropriate one should be chosen for any particular case.

The Equivalent diameter curves, unlike the classical model (Stankova et al., 2002), were constructed over the quadratic mean diameter, rather than the arithmetic one. This was done for the sake of the practical application of the model. Similar approach is preferred by Sturtevant et al. (1998) in construction of SDCD for mixed Abies balsamea and Picea mariana stands, but in his study, alike the SDCD by Newton and Weetman (1994) for Picea mariana, the diameter is expressed as a function of density and mean volume, rather than through derivation from the stem form height and the basal area.

The Stand Density Control Diagram of the present study is closest in its elements and construction to those by Sturtevant et al. (1998) for mixed Picea mariana - Abies balsamea stands and those by Newton and Weetman (1993, 1994) for Picea mariana. In all cases, however, there is difference in at least one of the elements, mainly the natural thinning curves and the equivalent height diameter curves.

4.3. Verification of the SDCD models 4.3.1. Verification by comparison between actual and predicted values А. Natural thinning curves The usual approach for verification of the Natural thinning trajectories is

through comparison with experimental data from repeated measurements of sample plots of different initial densities. Such comparison allows evaluation of the ability of the proposed model to describe the process of natural thinning of the validation data set. Different methods, which also provide justified proof of the reliability of the proposed model, were applied in the present investigation, because of lack of validation data set of repeated measurements in time.

The statistical tests comparing the sets of actual and predicted initial densities, as well as the sets of actual and predicted present densities showed that their values were comparable and did not differ significantly for both species. The comparison also provided some information on the initial survival rate of the validation data sets, which was 80-95% for the Scots pine and 75-85% for the Austrian black pine.

Data set of 109 sample plots of 9 planting schemes presenting initial densities from 2500 to 20000/ha were used to verify the initial density for the Scots pine plantations. The comparison between predicted and actual initial densities through the t-test and the non-parametric test showed that the difference was not statistically significant for 4 out of 6 percentages of initial survival rates and the mean error percentage for the high percentages of initial

survival (85-100%) did not differ significantly from 0. The actual and the predicted values of the present density were compared for data set of 111 sample plots in Scots pine plantations. Statistically significant differences were found only for the highest (100%) and the lowest (75%) percentage of initial survival rate.

Data set of 67 sample plots covering 14 planting schemes of initial densities from 2500 to 20000/ha was used to verify the predicted values of the initial density for the Austrian black pine plantations. The actual initial densities did not differ significantly from the predicted ones for the initial survival percentages 75-80% and the mean error percentage for initial survival 75-85% did not differ significantly from 0. The comparison between the actual present densities and those predicted by the natural thinning curves for the Austrian black pine plantations was done over data set of 69 sample plots. The density estimates for the lowest initial survival percentage (75%) did not differ significantly from the actual ones.

Important conclusions on the precision of the models of the Natural thinning curves can be drawn from the error variation by large-scale growth stages. The results achieved for the predicted initial densities showed that the most accurate estimates of the initial density through the Natural thinning curves could be done in the earliest growth stage – 4-6m. The predicted values of the present density, on the other hand, showed great variation of the estimated errors at this stage, with tendency to density overestimation probably due to the low values of the initial survival rates and to the large differences among them.

The error percentages for the predicted initial densities and their variation increase after the initial growth stage, reaching highest values for the 14-16m dominant height class of the Scots pine and for the 8-12m dominant height class of the Austrian black pine. This fact can be explained by the processes of intensive self-thinning, which begin at different time and have different intensity for the plantations of different initial densities, which is in agreement with the model of the natural thinning curves. From the derived by Shibuya (1995) gradient of the mean size – density trajectory:

α

α

NK

fNd

vd

−−=

1log

log,

directly follows that the process of natural thinning begins earlier in the dense plantations, because the coefficient f obtains smaller value for the higher value

of the initial density (N0) and, consequently Nd

vd

log

log of the dense plantations

gets higher value than the sparse ones. On the opposite, the predicted and the actual values of the present density show highest comparability for the growth stage 8-12m for the Austrian black pine plantations and 14m for the Scots pine plantations. This finding is explained by the fact that the different initial density

and the different degree of natural thinning intensity at this growth period are considered in the model for the present density estimate. The process of intensive self-thinning takes place in Scots pine plantations 26-37 years old and in Austrian black pine plantations 16-30 years old, according to the dependences established between age and dominant height in the present investigation. The observed tendency is in agreement with the observed by Tsakov (1986) dynamics in the tree number of Scots and Austrian black pine plantations of initial density 7000-8000/ha. His results showed that there was well-expressed tendency to more intensive density reduction in the earlier ages for the Scots pine plantations (15-25 years) than for the Austrian black pine plantations (23-40 years).

An interesting tendency was observed for both tree species in the error percentage estimated in the late growth stages (18-32m). The estimated errors for the predicted initial densities were of narrow range and obtained positive values indicating underestimation of the initial density. The predicted values of the present density in the growth stage 18-32m, on the other hand, have negative error values, which indicates overestimation of the actual present density. An unambiguous explanation of these tendencies is the assumption that at this growth stage the plantations have already undergone thinnings, which have brought the deviations from the naturally determined process of self-thinning.

B. Equivalent mean diameter curves The error estimates for the quadratic mean diameter by the Equivalent

mean diameter curves showed very high degree of agreement between actual and predicted values of this growth parameter. Higher precision was achieved for the Scots pine plantations, with error range ±20% and mean error value -2.53% (4.32% mean absolute error). The error range for the quadratic mean diameter of the Austrian black pine plantations was ±40%, with mean error value -4.02% (9.28% mean absolute error) with slight tendency to parameter overestimation. Only the predictions for the quadratic mean diameters of 4m-dominant height class for both species showed unsatisfactory precision (mean error values -37-38%) with tendency to parameter overestimation.

A good level of accuracy, but inferior to the diameter estimate, was recorded for the yield estimated through the Equivalent mean diameter curves by dominant height classes. The error estimates for the yield of the Scots pine plantations were in the range of ±50%, while the error range for the stand stock of the Austrian black pine plantations was ±60%. The mean error values were -4.02 and 7.06%, and the mean absolute errors were 3.01 and 8.15% for Scots pine and Austrian black pine, respectively. A sleight tendency to yield underestimation through the Equivalent mean diameter curves was observed for the Austrian black pine plantations.

4.3.2. Verification by comparison with the maximum possible densities determined by the crown diameter

The mean crown diameters estimated by dominant height classes (Eq. 14) were approximated by linear function on the mean breast height diameters to determine the marginal values of the minimum possible crown diameters and their corresponding maximum possible densities. Straight-line function of the form y=ax+b or y=ax was preferred according to the estimates of the coefficient of determination (R2) and the significance of the regression (F-test) and its coefficients (t-tests). The regression estimates were used to determine the margins of the 95% confidence interval by equivalent dominant height classes and equivalent mean diameter classes. The lower margin of the confidence interval indicates the minimum growth space and its correspondent maximum density within the particular dominant height class.

To prove being reliable and evidential regarding the Natural thinning curves, the SDCD model should satisfy the requirement that the density values of the intersection points of the equivalent height curves and the natural thinning curves should not exceed the maximum possible densities determined by the minimum growth space. The comparison between the density values estimated for the natural thinning curves by dominant height classes and the maximum possible densities showed unequivocally that in none of the cases the density predicted by the SDCD model violates the requirement of the minimum growth space required for the stand development. Comparison between the density values predicted through the equivalent mean diameter curves by equivalent height classes and the maximum possible densities was performed for verification of the Equivalent mean diameter curves. The requirement for the minimum necessary growth space for the normal stand development was violated by neither of the density values estimated through the SDCD model by equivalent mean diameter curves and equivalent height classes.

4.4. Examples of SDCD application 4.4.1. Defining of groups of initial densities according to the middle

points of the growth gradients in space and time The middle points of the growth gradient in time for the Scots pine

plantations were estimated for the initial planting schemes from 0,5×0,5m to 2,5×2,0m. For the Austrian black pine plantations, the same estimates were performed for the initial planting schemes from 0,5×0,5m to 2,0×1,5m. Such estimates were not conducted for the natural thinning trajectories of initial densities sparser than the ranges above, because their middle points of the growth gradient in time were attained at yield values higher than the empirically determined maximum (910m3/ha for Scots pine and 1020m3/ha for Austrian black pine). The densities of the middle points of the growth gradient in space were estimated for 4m dominant height class. Their values are

ρB=8285/ha for Scots pine and ρB=12071/ha for Austrian black pine plantations, respectively.

Although the SDCD allow modeling of numerous regimes of establishment and management of pine plantations, initial referential information is available from the estimated values of the middle points of the growth gradients in space and time. As shown, the middle point of the growth gradient in space B (ρB, yB) at 4m dominant height class can be used as a reference point for defining the initial densities, which are too dense and indicate ineffective space utilization for growth. These are the densities, which are higher than the densities estimated for the B-point of the 4-m dominant height class: 8285/ha for the Scots pine and 12071/ha for the Austrian black pine. Thus, the initial densities of the Scots pine plantations which are over 12 500/ha can be considered too high for optimal use of the growth space regardless of the initial survival rate. For higher values of the initial survival rate (85-100%) planting schemes of 1,5×0,8m and 1×1m are also too much limiting the yield growth (Table 2). For the Austrian black pine plantations, density of 20000 trees per hectare is too high regardless of the initial survival rate, while in the case of the 100% initial survival rate the planting scheme 0.8×1m is too dense as well (Table 3). The above conclusions are confirmed by a survey on afforestations against erosion with Scots pine and Austrian black pine of high initial densities (10-12000/ha) (Iliev et al, 1996). The study by Iliev et al. (1996) showed significant decrease in the height increment (after the age of 25 years), in the diameter increment (after the age of 10 years) and in the volume increment (after the age of 20 years) in comparison to those predicted by the Growth and Yield tables currently in use. The initial densities of the plantations, which can be managed without thinnings during the rotation period, were derived through the Kf-points of the natural thinning trajectories. For the Scots pine plantations of initial densities lower or equal to that corresponding to the planting scheme 2×2m (3×1.5m for initial survival rate 85-90% and 2×2.5m for initial survival rate 95-100%) the middle point of the growth gradient in time is attained for stand stock higher than the empirically determined maximum of 910 m3/ha (Table 2).

For the Austrian black pine plantations values of the stand stock of the Kf-points (yKf) larger than the empirically determined maximum - 1020m3/ha are attained for initial densities <3333/ha for 85-100% initial survival rate and <4444/ha for 75-80% initial survival rate (Table 3). This observation allows the conclusion that the pine plantations established at lower densities can be managed without thinnings during the rotation period without significant losses in the volume increment. This conclusion is confirmed by the study of Kostadinov et al. (1996), according to which a possible alternative to the early thinnings in the Austrian black pine plantations in the Strandja mountain region are initial densities of less than 3000/ha.

For the group of initial densities of intermediate values (the lower boundary of which is the density of the B-point and the upper boundary is set by the Kf-point of the largest stand stock which is smaller than the empirical maximum) the need of thinnings can be suggested, because the middle point of growth gradient in time is reached for value of the stand stock smaller than the empirically determined maximum yield. Observations on Austrian black pine plantations managed through thinnings (Kostadinov, 1980) showed that their density should be of average 6000/ha (1.5-1.8 × 1-0.9m), which is within the range recommended in the present investigation: 3333 - 12500 /ha (Table 3) and partially confirms the need of thinnings for optimal utilization of the growth space.

The middle point of the growth gradient in time Kf estimated for the Austrian black pine plantations of the initial density (7000 - 8000/ha) of the Growth and yield Tables (Tsakov, 1983) is attained at dominant height 14-18m, corresponding to age 20-25 years. This is the age when the maximum of the mean yield and biomass increment for the good sites (Tsakov, 1984a, 1985) and the maximum of the height increment for the intermediate sites (indices II – III) (Tsakov, 1981) are achieved. The middle point of the growth gradient in time of Table 2. Groups of initial densities of the Scots pine plantations according to the middle points of the growth gradients in time (Kf) and space (B)

Initial density (1/ha) Planting scheme No*=No No*=0.95No No*=0.9No No*=0.85No No*=0.8No No*=0.75No 0,5××××0,5 40000 38000 36000 34000 32000 30000 0,5××××1 20000 19000 18000 17000 16000 15000 0,8××××1 12500 11875 11250 10625 10000 9375 1××××1 10000 9500 9000 8500 8000 7500

1,5××××0,8 8333 7917 7500 7083 6667 6250 1××××1,5 6667 6333 6000 5667 5333 5000 2 ×××× 1 5000 4750 4500 4250 4000 3750

1,5××××1,5 4444 4222 4000 3778 3556 3333 1,5××××2 / 3333 3167 3000 2833 2667 2500

2××××2 2500 2375 2250 2125 2000 1875 3×1,5 2222 2111 2000 1889 1778 1667 2,5××××2 2000 1900 1800 1700 1600 1500 3××××2 1667 1583 1500 1417 1333 1250

2,5××××2,5 1600 1520 1440 1360 1280 1200 3××××2,5 1333 1267 1200 1133 1067 1000 3××××3 1111 1056 1000 944 889 833

3××××3,5 952 905 857 810 762 714 3,5××××3,5 816 776 735 694 653 612 4××××3,5 714 679 643 607 571 536 4××××4 625 594 563 531 500 469

4××××4,5 556 528 500 472 444 417 4,5××××4,5 494 469 444 420 395 370 5××××4,5 444 422 400 378 356 333

- not advisable for afforestation; - management with thinnings - management without thinnings

the Scots pine plantations of density 7000-8000 trees per hectare, which corresponds to the initial density value of the Growth and yield tables (Krastanov et al., 1983), is attained at dominant height classes 14-16m when the plantations are 26-37 years of age. On the other hand, the maximum of the height and volume increment of the Scots pine plantations is achieved at relatively early age, about 15 years, and the maximum of the mean stem volume increment is reached at 25-40 years, depending on the site index (Krastanov et al., 1979; 1980). The comparison revealed that the periods of the maximum mean increment coincide with the middle points of the growth gradient in space (Kf), estimated for the initial densities of the Growth and yield Tables.

The biological peculiarities of the studied species should be considered when drawing conclusions and giving recommendations for the time of the thinnings in the young Scots pine and Austrian black pine plantations in relation to the middle points of the growth gradient in time (Kf). According to Assmann (1970), the Scots pine, as a light demanding species, not only has early maximum of the height increment, but also at middle and advanced age, when the diameter increment increases and the stem biomass is accumulated, has limited ability of crown and root growth at release. The significantly higher Table 3. Groups of initial densities of the Austrian black pine plantations according to the middle points of the growth gradients in time (Kf) and space (B)

Initial density (1/ha) Planting scheme No*=No No*=0.95No No*=0.9No No*=0.85No No*=0.8No No*=0.75No 0,5××××0,5 40000 38000 36000 34000 32000 30000 0,5××××1 20000 19000 18000 17000 16000 15000 0,8××××1 12500 11875 11250 10625 10000 9375 1××××1 10000 9500 9000 8500 8000 7500

1,5××××0,8 8333 7917 7500 7083 6667 6250 1××××1,5 6667 6333 6000 5667 5333 5000 2 ×××× 1 5000 4750 4500 4250 4000 3750

1,5××××1,5 4444 4222 4000 3778 3556 3333 1,5××××2 / 3333 3167 3000 2833 2667 2500

2××××2 2500 2375 2250 2125 2000 1875 3×1,5 2222 2111 2000 1889 1778 1667 2,5××××2 2000 1900 1800 1700 1600 1500 3××××2 1667 1583 1500 1417 1333 1250

2,5××××2,5 1600 1520 1440 1360 1280 1200 3××××2,5 1333 1267 1200 1133 1067 1000 3××××3 1111 1056 1000 944 889 833

3××××3,5 952 905 857 810 762 714 3,5××××3,5 816 776 735 694 653 612 4××××3,5 714 679 643 607 571 536 4××××4 625 594 563 531 500 469

4××××4,5 556 528 500 472 444 417 4,5××××4,5 494 469 444 420 395 370 5××××4,5 444 422 400 378 356 333

- not advisable for afforestation; - management with thinnings - management without thinnings

plasticity of the young Scots pine plantations is confirmed also by the explanation of Roubtsov (1969), who emphasized the fast development of the leaves and the crowns of the young individuals, which favors the amount of increment. On the other hand, the trees of large growth space, which develop vigorous crowns while young, would have fast reaction when freed and would make better use of the released resources, so that no significant increment loss would be allowed as compared to the unthinned stands (Mäkinen and Isomäki, 2004). The need of early release and increase of the growth space is even stronger for the dense plantations, which have earlier culmination of the mean and the current increment (Roubtsov, 1969).

Thinning experiments of different intensities in young Austrian black pine plantations (14-year-old) in the Strandja mountain region (Kostadinov, 1990) imposed similar conclusions for this species as well. According to the author, high intensity thinnings (48% of the trees) are possible, if they are performed up to 15 years of age, when the stands are more flexible and because of their limited aboveground biomass – more resistant to the unfavorable climatic conditions. Intensive thinning at higher age, when the trees are of small diameter and underdeveloped root system because of the high density, is risky and can lead to stand disruption (Kostadinov, 1990).

The above considerations and the results of the present investigation lead to the conclusion that, if a thinning is required, it has to be done in the period around the middle point of the growth gradient in time (Kf). According to the ages established for the merchantable wood production from Austrian black pine plantations (Tsakov, 1984b), a thinning at the time of the middle point of the growth gradient in time (Kf) – 20-25 years would provide maximum harvest of small-size-wood of V-VI assortment class (diameter of the thinner end 3-11cm) and some amount of intermediate-size-wood (III-V assortment class) of diameter of the thinner end 8-17cm. At the time of the middle point of the growth gradient in time (Kf) for the Scots pine plantations – 26-37 years, the age for merchantable wood production of the assortments of the IV group (diameter of the thinner end 8-17cm) will be attained for all site indices (except for the IV-th) and maximum harvest of small-size-wood (diameter of the thinner end 3-11cm) will be provided (Krastanov et al., 1979).

4.4.2. Determination of optimal planting densities using the SDCD-s The optimal initial densities for maximum yield and large-size timber

production in the process of natural thinning were estimated. Initial density of 5776/ha is required for the Scots pine plantations to achieve the empirically determined maximum yield of 910m3/ha through natural thinning (Figure 5). The maximum yield for the Austrian black pine plantations obtained from the experimental data for H =28m amounts to 1020m3/ha and is achieved through initial density of 2546/ha (Figure 6). The initial density for establishment of Scots pine plantations to obtain large size timber production (dbh = 30cm) at H =28m, when stand stock of 644.2 m3/ha will be attained in the process of

natural thinning is 958/ha and is shown on Figure 5. The Austrian black pine plantations for large size timber production through natural thinning will reach total yield 948.8m3/ha being established at initial density of 1502/ha (Figure 6).

A way for naturally sustainable management of the manmade forests is to design them for achieving a particular silvicultural goal driven by the natural processes, without human interference through thinnings. Achievement of maximum attainable final yield through natural thinning, though relatively slow process, is still a possible management goal at long rotation period. The estimated values of the optimal initial density for the desired maximum yield showed that at the end of the rotation period ( m28=H ) the Scots pine plantations will be older than 90 years, while the Austrian black pine plantations will be older than 100 years, of mean heights 26.7 and 27 m, respectively. Survival percentage of the Scots pine plantations will be 27.0%, while the Austrian black pine plantations will have 57.2% survival, by the end of the rotations. The estimated values of the quadratic mean diameter (dbh=24 cm and 26 cm for Scots pine and Austrian black pine, respectively) at these phases indicate that the pine stands will be appropriate for merchantable wood production by the rotation age. The optimal initial densities for the maximum yield derived by the present study generally agreed with those recommended by Zahariev et al. (1983) for intensively managed Austrian black pine plantations in Bulgaria, but preference was given to the rarer planting schemes of the above mentioned study (initial planting schemes 2×1.5, 2×2, 2.5×1, 2.5×1.5m). However, the Austrian black pine plantations of such spacings, though very productive by the time of harvesting (1020m3/ha), are not expected to provide high quality timber wood (Bachvarov, 1978). The initial planting schemes derived for the maximum yield production from Scots pine plantations (910m3/ha) are relatively dense (initial planting schemes of the range 0.8×1.5, 1×1.5, 2×0.8m) and are not appropriate for intensive plantations (Zahariev et al., 1983). Nevertheless, the advantage of such dense plantations is that the natural thinning process starts earlier in the dense stands (also shown in this study). This process facilitates formation of easily decomposable litter, speeding up the nutrient cycle, the penetration of the precipitation water into the soil and the plant resistance to drought (Roubtsov, 1969).

The initial densities recommended for Scots pine plantations by the present investigation agree with the results of Atanasov (1964) for optimal initial densities regarding the time of canopy closure and with the optimal initial density of 5500/ha derived by Krastanov et al. (1980) in accordance with the postulate for the optimal stocking rate. The initial densities recommended by the present study for Austrian black pine plantations agree with those recommended by Lyapova and Palashev (1980) for the region of Standja mountain. The optimal density for the maximum yield for Scots pine plantations determined by the present study, on the other hand, disagreed with the larger spacing (4 m2 per

Scots pine plantations

28m

958

5775

30cm

873m3/ha

Initial density 2500

Initial density 3500

10

100

1000

100 1000 10000density (1/ha)

yiel

d (m

3 /ha

)

28m height class Full density line

Optimal initial density for large size timber production Optimal initial density for maximum final yiled

30cm mean diameter class

910m3/ha

y = 163267ρρρρ -0.69833m3/ha

Figure 5. Optimal initial densities for maximum yield and large size timber production through natural thinning for Scots pine plantations and initial density range recommended by Ordinance №17 (2000).

Austrian black pineplantations

28m

1502

1020m3/ha

2546

30cm

1050m3/ha

Initial density 2500 Initial density 3500

y = 385843ρρρρ -0.75

10

100

1000

10000

100 1000 10000density (1/ha)

yiel

d (m

3 /ha

)

28m height class Full density line

Optimal initial density for large size timber production Optimal initial density for maximum final yiled

30cm mean diameter class

1019m3/ha

Figure 6. Optimal initial densities for maximum yield and large size timber production through natural thinning for Austrian black pine plantations and initial density range recommended by Ordinance №17 (2000).

plant) recommended for the region of Standja mountain (Lyapova and Palashev, 1980). According to the present results, initial density of not less than 5500 trees per hectare is required for plantations of Pinus sylvestris with no thinning treatment to obtain maximum yield at rotation age.

A comparison between the derived by the present investigation optimal initial densities and the initial density range of 2500-3500/ha recommended for afforestation with Scots pine and Austrian black pine by Ordinance №17 (2000) is shown on Figures 5 and 6. It can be seen that, plantations of Austrian black pine established at initial density within the proposed density range will provide maximum final yield at long rotation period, if managed as self-thinning stands. The results of Table 3, on the other hand, indicate that in the case of initial survival rate below 85%, such a management regime will not cause significant increment loss. For the Scots pine plantations, on the other hand, was estimated significantly higher value of the optimal initial density (5775/ha) than those recommended by Ordinance №17 (2000). It will provide from 35 to 75m3/ha more yield by the end of the long-term rotation period through natural thinning. The high mortality rate, however, and the yield variation according to the density changes revealed that the profitable management of even smaller densities than those recommended for afforestation (2500-3500/ha) requires thinnings (Table 2). The derived values of the optimal initial densities confirmed that process of natural thinning is much more intensive in the Scots pine plantations than in the Austrian black pine plantations and the accumulation of the volume increment is coupled with very strong competition for growth space in the Scots pine plantations. The biological peculiarities of the species is reflected also in the result that, at the same age the Scots pine plantations are taller (difference of 1 dominant height class), while the Austrian black pine plantations are of larger mean diameter and stand stock. The tendency of the estimated optimal initial densities, which are higher for the Scots pine plantations than for Austrian black pine plantations, generally agrees with the finding by Shikov (1974) based on the concept of the optimal stocking rate for maximum increment, that the optimal initial densities are 5000 and 4000/ha for Scots pine and Austrian black pine plantations, respectively.

The results of the present study revealed that the production of large-size wood by self-thinning plantations can be achieved only by sparse planting schemes: 958/ha for the Scots pine and 1502/ha for the Austrian black pine (Figures 5 and 6). The survival by the rotation time will be around 76 % for the plantations of Pinus sylvestris, established at plantation schemes 3×3.5, 4×2.5, 4×2, 3×3, 3.5×2.5, 4.5×2, 5×2m. The plantations of Pinus nigra planted at spacing 3×2, 2×2.5, 4.5×1.5, 3.5×1.5m will have mortality of around 29 % by the time of mean stand diameter of 30 cm.

In the forestry practice of Bulgaria, the management objective of large-size merchantable wood production is usually achieved by high initial density plantations, followed by thinnings (Zahariev et al. 1983). The main reasons for

this approach are the strong competition by the intensively growing weeds or by the shrubs or other tree species on rich sites. Good quality stem wood production is also a problem for Austrian black pine and for the coarse-branched forms of Scots pine. The regular weeding until canopy closure and pruning, or using selected fine branched forms for both species are a possible solution of this problem. In relation to growing high-quality timber Zahariev et al. (1983) found the tendency of some provenances of the Austrian black pine to form thinner, shorter and less branches at the lower whorls, which implies that the selection of fine-branch provenances for application in the case of the sparse densities might be successful. The expenses for the intensive cultivation will be offset by the decreased number of planted seedlings, the insignificant losses of trees until rotation age and the omitted thinnings. The present results generally agree with the recommendation by Kostov et al. (1978) that the most intensified silviculture of pine plantations in Bulgaria should be done with initial spacing of more than 4m2, followed by intensive cultivation.

C O N C L USI O NS 1. The goodness of fit of 14 most probable functions for estimation of the

mean-dominant height relationship for Scots pine and Austrian black pine plantations was examined. The straight-line function was proven as the most adequate model for both species and the dependencies were expressed by the equations: Hdomin=0.996Hav+1.455 for Scots pine plantations and Hdomin=0.991Hav+1.256 – for Austrian black pine plantations. The derived relationships are applicable for estimation of dominant height through the mean height in the range from 3.2 to 26.5m for the Scots pine plantations and from 3.4 to 27.7m for Austrian black pine plantations, but extrapolations beyond these ranges are not recommended.

2. Models of Stand Density Control Diagrams (SDCD) for Scots pine and for Austrian black pine plantations in graphical and functional forms were estimated. They consist of 5 main elements: Equivalent height curves; Natural thinning curves; Yield index lines; Full density line; Equivalent mean diameter curves, which are defined and expressed by principal stand growth parameters. In the models of SDCD:

- The Equivalent height curves characterize the spatial dynamics of the yield of the pine plantations by growth stages, represented by the dominant height class: from 4 to 26m dominant height class for the Scots pine plantations and from 4 to 28m dominant height class for the Austrian black pine plantations.

- The Full density lines set the upper boundaries of the density – maximum yield combinations, with values of the self-thinning exponents: αααα=1.69 and αααα=1.75 for Scots pine and Austrian black pine, respectively.

- The process of stand self-thinning in time is modeled by the Natural thinning curves for 23 initial densities (444-40000/ha) and 6 possible

percentages (100, 95, 90, 85, 80 and 75%) of the initial survival rate for each of them are considered.

- The spatial-temporal dynamics of pine plantations of the same mean diameter is modeled by the Equivalent mean diameter curves, evaluated for values of the quadratic mean diameter from 2 to 32cm.

3. Two main approaches were applied for verification of the SDCD models: by comparison between experimental data and the parameter values estimated by the models and by comparison between the densities estimated through the SDCD and the maximum possible (marginal) values of density. These two approaches were applied to verify the Natural thinning curves and the Equivalent mean diameter curves.

4. The verification of the Natural thinning curves showed that: - The sets of actual and predicted initial densities for the different initial

survival rates were comparable and did not differ significantly for both species. The same conclusion holds for the sets of actual and predicted present densities.

- Most precise estimate of the initial density through the natural thinning curves is possible when the stands are in early growth stage (4-6m). The predicted and the actual values of the present density show highest comparability after the initial growth stage (8-12m for the Austrian black pine plantations and 14m for the Scots pine plantations), when the processes of intensive self-thinning have started (26-37 years for Scots pine plantations and 16-30 years for Austrian black pine plantations).

- The density values estimated for the natural thinning curves by dominant height classes exceeded in none of the cases the maximum possible densities.

5. The verification of the Equivalent mean diameter curves showed that: - The estimation of the quadratic mean diameter by the Equivalent mean

diameter curves showed very high degree of agreement between actual and predicted values of this growth parameter. Higher precision was achieved for the Scots pine plantations where the mean error value was -2.53%, while for the Austrian black pine plantations it was -4.02%. A good level of accuracy was recorded for the yield estimated through the Equivalent mean diameter curves by dominant height classes of mean error values -4.02 and 7.06% for Scots pine and Austrian black pine plantations, respectively.

- The density values predicted through the equivalent mean diameter curves by equivalent height classes do not exceed the maximum possible densities estimated through the crown diameters for both species.

6. A method for practically oriented classification of the initial densities into groups through estimation of the middle points of growth gradient in time Kf (ρρρρf,yf) for the particular initial densities and in space for 4m growth stage B4 (ρρρρB,yB) was proposed. Three groups of initial densities were determined: initial densities, which are not advisable for afforestation; initial densities that can be managed without thinnings to rotation age and initial densities, which require at least one thinning during their rotation period.

7. A method of direct application of the SDCD to estimate the optimal initial densities of self-thinning pine plantations to obtain maximum yield and large size wood production at long-term rotation period was shown. The particular estimates at growth stage 28m dominant height class are: relative initial density of 5775/ha is required for achievement of final yield of 910m3/ha by the Scots pine plantations and relative initial density of 2545/ha is determined for attainment of 1020m3/ha maximum final yield by the Austrian black pine plantations. For large size wood production (of mean dbh=30cm) by a self-thinning stand at the rotation age (28m dominant height class) initial density of 958/ha for the Scots pine plantations and initial density of 1502/ha for the Austrian black pine plantations are required.

R E C O MM E N DA TI O NS 1. Initial densities higher than 8333/ha are not advisable for establishment

of Scots pine plantations, while densities over 10000/ha are not advisable for establishment of Austrian black pine plantations.

2. Pine plantations grown to long term rotation age can be managed in 2 principal ways: a.) by self-thinning - for Scots pine plantations of initial density less than 2200/ha and for Austrian black pine plantations of initial density less than 3300/ha; b.) by a thinning activity performed around the middle point of the growth gradient in time (Kf), estimated for the particular initial density.

3. The management objective: achievement of the empirically determined maximum final yield (910m3/ha) at long term rotation period (28m dominant height corresponding to 93-118 years of age) from the Scots pine plantations can be attained in the process of self- thinning for initial densities 5700-7700/ha, but such management regime is not sufficiently profitable. If a self-thinning management regime is to be chosen (of initial density <2200/ha), the final yield by the rotation age will be about 90% from the empirically determined maximum.

4. The management objective: achievement of the empirically determined maximum final yield (1020m3/ha) at long term rotation period (28m dominant height corresponding to >108 years of age) from the Austrian black pine plantations can be attained in the process of self-thinning for initial densities 2500-3400/ha. Such management regime would be profitable, if the lower margin of the above range is chosen, but a thinning activity can be considered in the cases of higher initial density values.

5. The management objective: large size merchantable wood production (mean dbh=30cm) at long-term rotation period can be attained in the process of self-thinning by Scots pine plantations of initial densities 1000-1300/ha and Austrian black pine plantations of initial densities 1500-2000/ha.

INFORMATION ABOUT THE THESIS CONTRIBUTIONS - Mean - dominant height relationships for Scots pine and Austrian black

pine plantations in the range from 3 to 28m are established. - Models of Stand Density Control Diagrams for Scots pine and for

Austrian black pine plantations in their graphical and functional forms are estimated and verified. They characterize the spatial - temporal dynamics of the main stand growth parameters (density, yield, dominant height, mean diameter) of the Scots pine and the Austrian black pine plantations for growth stages from 4 to 28m dominant height class (5 – 120 years), of natural thinning trajectories for 23 initial densities.

- A method was derived for practically oriented classification of the initial densities of the Scots pine and the Austrian black pine plantations in the range from 400 to 40000/ha into 3 groups according to the recommended management regime: not advisable for afforestation; for management without thinnings to rotation age and for management with at least one thinning during their rotation period.

- The optimal initial densities of self-thinning pine plantations to obtain maximum yield and large size wood production at long term rotation period were derived

LIST OF THE PUBLICATIONS BASED ON THE THESIS - Stankova, T., M. Shibuya, A. Hagihara. 2002. A method for density

control of forest plantations. Forest Science (Sofia) 2, 27-38. - Stankova, T. 2005. A density control model for Austrian black pine

plantations in Bulgaria. Forest Science (Sofia) 3, 29-50. (In Bulgarian) - Stankova, T., H. Stankov, M. Shibuya. 2006. Mean-dominant height

relationships for Scots pine and Austrian black pine plantations in Bulgaria. Ecological engineering and environmental protection 2, 59-66.

ACKNOWLEDGEMENTS I wish to express my sincere gratitude to my scientific supervisor Dr.

Masato Shibuya from Hokkaido University, Japan for his exceptionally relevant and competent suggestions and guidance during my work on the PhD thesis and to Dr. Akio Hagihara from the University of Ryukyu, Japan for his valuable advices. The field work was done in fast and efficient manner with the professional and competent help of Dr. Roumen Petrin, Hristo Stankov, Velichko Kolev, Ekaterina Andonova and Dr. Tsvetan Zlatanov. I owe also special gratitude to Dr. Roumen Petrin, because of his irreplaceable contribution for formulating the terminology and presenting the work methodology in Bulgarian and to Hristo Stankov for editing the stile and the grammar of the thesis and the articles in English.

Deepest gratitude is owed also to Dr. Ivan Ts. Marinov, Pavel Panov, Alexander Alashtinov and Dr. Hristo Tsakov, which helped me by presenting their personally recorded data of sample plots in Scots pine and Austrian black pine plantations. Very valuable for the representativeness of the data set for the models estimation were the data that I was able to use from the theses and the research reports in the library of the Forest Research Institute of BAS for which I am grateful.

I would like to express also gratitude to the colleagues working in the Forest Estates, where the field investigation took place for their co-operation.

I wish to thank also to the Department of Forest Genetics, Physiology and Plantations, Dr. Milko Milev, Dr. Hristo Tsakov and Dr. Ivan Mihov for their critical remarks, advices and recommendations, which helped me to improve the quality of my thesis.

The research work was carried out with the financial and educational support of the Bulgarian-Swiss Forestry Program for which I express my deepest gratitude. I want to thank also to the Bulgarian Ministry of Education and Science, which financed the investigation of the Scots pine plantations in Rila mountain and supported the short-term visit of Dr. Masato Shibuya and Dr. Akio Hagihara in Bulgaria during the autumn of 2001.