35

Silva Balcanica, 14(1)/2013

APPLICABILITY OF STAND DENSITY MANAGEMENT DIAGRAMS TO SCOTS PINE PROVENANCE TEST

Tatiana StankovaForest Research Institute – Sofia Bulgarian Academy of Sciences

Hristo StankovBulgarian Software Technologies Ltd. – Sofia

Abstract

The main objectives of the present investigation are to examine the goodness-of-fit of the regional-scale and the national-scale models of Stand Density Man-agement Diagrams (SDMD) established for Scots pine plantations in Bulgaria with data from provenance test plantation, to study the provenance variation of the main growth parameters and to analyze the obtained results in terms of SDMD model ap-plicability to genetically diverse monospecific plantations.

The prediction precisions of the main stand variables quadratic mean diame-ter, density, total volume and dominant height were evaluated and the results consis-tently revealed the superiority of the regional SDMD model to the national one. The provenance influence on the variation of diameter and height was proved statistically significant and accounted for 3 to 18% of the observed differences.

The provenances most remote in latitude from the test site exhibited con-sistently largest deviation from their predicted by the national-scale model values which implies influence of site-provenance interaction on the model application pre-cision. No significant correlations were found between the degree of precision of the regional-scale model regarding the stand growth performance and the provenance geographic origin which reveals predominant environmental influence on the preci-sion of the SDMD model.

Key words: Scots pine plantations, stand density management diagram, prov-enance variation, stand-level models

INTRODUCTION

Stand Density Management (or Control) Diagrams (SDMD or SDCD) are stand-level distance-independent models which graphically illustrate the relation-ships between yield, density and mortality throughout all stages of stand develop-ment. They are applied to evaluate stand growth parameters at any time of the stand development, to simulate alternative thinning regimes and to determine the optimal initial density of forest plantations in accordance with the preferred management ob-

36

jective and regime. SDMD can be subdivided into (1) static, which lack a net density change sub-model which accounts for ingress and mortality and (2) dynamic, which include a net density change sub-model (Newton, 2008). The SDMD have been built at different scales (national and regional types) and model differentiation by site indices have been derived and implemented (Newton and Weetman, 1994). SDMD models, however, do not take into consideration the amount of genetic variation of the experimental data sets used in the model elaboration and the respective limits of model application to genetically diverse plant material.

A dynamic type of SDMD for Scots pine (Pinus sylvetrsis L.) plantations in Bulgaria was first developed for the region of Rila Mountain (Stankova, 2004; 2008), which was followed by a national-scale model elaboration (Stankova, Shibuya, 2007). The main objectives of the present investigation are to examine the goodness-of-fit of the regional and the national models of SDMD for Scots pine plantations with data from provenance test plantation established in Rila, to study the variation of the main growth parameters of its provenances and to analyze the obtained results in terms of model applicability to genetically diverse monospecific Scots pine plantations.

MATERIALS AND METHODS

Provenance test plantationSeeds from 17 natural provenances of Pinus sylvestris L. situated in South-

western Bulgaria at altitudes from 850 m to 1600 m a. s. l. were collected for the establishment of the experimental plantation (Fig. 1). For the purposes of the present study the latitudes and longitudes of the particular provenances were also defined as relative to each other. The test site was chosen in the northern part of mountain Rila at altitude of 1220 m (42.25 N, 23.49 E) on land previously occupied by natural mixed Norway spruce-Scots pine stand. It is characterized with slight northern as-pect (5°) and deep, rich and wet Cambisols. The provenance test was established in 1973 in a randomized complete block design with 4 replications and 36 trees per plot at 2×2 m planting scheme. In 1986 the test plantation was subjected to systematic thinning by removal of 50% of the trees in each plot in a checkerboard manner.

Data collection and analysesData collection took place in the summer of 2007. In each plot, breast height

diameters of all trees and density were measured and the basal area was calculated. The heights of 20% of all trees per provenance – those of quadratic mean and of dominant diameters – were measured to estimate the mean and the dominant heights, respectively. Total stem volume was estimated using the volume tables for Scots pine plantations by Krastanov et al. (1983).

Prediction of the main stand variables by provenances through regional and national SDMD models. The main stand variables – quadratic mean diameter,

37

Scale 1:1 500 000

Provenance number Provenance name Altitude

(m a. s. l.) Location (mountain) Latitude Longitude

1 Shiroka Laka (69) 1200 Rhodopes S E2 Velingrad 1480 Rhodopes N W3 Snejana 1230 Rhodopes N W4 Yakoruda 1450 Rila N W5 Dospat 1350 Rhodopes S W6 Beslet 1500 Rhodopes S W7 Velingrad 850 Rhodopes N W8 Hvoina 1600 Rhodopes N E9 Teshel 1200 Rhodopes S E10 Dospat 1550 Rhodopes S W11 Momchilovtsi 1300 Rhodopes S E12 Devin 1350 Rhodopes S E13 Velingrad 1100 Rhodopes N W14 Velingrad 1250 Rhodopes N W15 Shiroka Laka (68) 1200 Rhodopes S E16 Eleshnitsa 1300 Rhodopes N W17 Slaveino 1600 Rhodopes S E

Fig. 1. Location of the provenances of Scots pine (Pinus sylvestris L.) represented in the experimental plantation

38

density, total volume and dominant height were predicted by implementation of the Equivalent mean diameter curves sub-model of the SDMD as recommended in the studies by Stankova, Petrin (2008a, 2008b) and using the following formulae:

(1)

(2)

(3)

( ) (4),

where a1, b1 are constants (Stankova et al., 2002) and d1.3,ρ, y and H are qua-dratic mean diameter (cm), density (1/ha), total volume (m3/ha) and dominant height (m), respectively. The abbreviations G, HF and Ĥ stand for basal area, stand form height and dominant height class (height classes by 2 m) and the abbreviations exp and pred in subscript denote the experimental and the predicted values, respectively. The constants a1, b1 are estimated via linear regression of stand form height on domi-nant height and obtain different values according to the type of the model (Stankova, 2004 for the regional model; Stankova, Shibuya, 2007 for the national model).

The adequacy of each model (regional and national) was examined for each of the predicted stand variables by estimation of the mean absolute and relative er-rors Em, their 95% confidence, prediction and tolerance intervals (Reynolds, 1984) as well as by t-test for Em equals zero preceded by Kolmogorov-Smirnov test for normality of the errors:

(5)

(6)95% Confidence Interval (CI): Em ± St0.975/n

1/2 (7)95% prediction interval (PI): Em ± St0.975(1+1/n)1/2 (8)95% tolerance interval (TI): Em ± Sg(1-γ, n, 1-α) for 1-γ=1-α=0.95 (9),

39

where E is the error, Varexp stands for the experimental value of the tested pa-rameter, Varpred is its corresponding predicted value, n is the number of experimental-predicted value pairs (n=17 in the present study), S is the standard deviation of the errors, t0.975 is the 0.975 quintile of the t distribution with n -1 degrees of freedom, and the function g(1-γ, n, 1-α) is the tolerance factor tabulated for specified values of n, α and γ (Crow et al., 1960) and provides that the estimated interval will contain at least (1-γ)100 percent of the future error distribution with probability (1-α).

The absolute values of the relative errors by provenances were analyzed to test for presence of correlation with the provenance altitude, latitude and longitude by estimation of Spearman’s correlation coefficient and its significance.

Thinning simulation. Thinning from below with intensity of no more than 40% is assumed in the SDMD implementation for thinning simulation (Stankova et al., 2002). Despite this fact, an attempt to model the 50% intensity cutting performed in 1986 was done in the present study. Three different approaches were examined for the thinning simulation. They are distinguished by their input variables and the parameters of the remaining after the thinning stand as related to the assumptions set prior to the simulation.

Simulation method 1 (Fig. 2A)The experimental values of dominant height class Ĥ and stand density ρ before

the thinning are used as input variables. The assumption that the dominant height class is kept unchanged during the thinning is imposed and the trajectory of stand

growth after the cutting is defined through its specific coefficient as:

, At=f(Ĥ), B=f(Ĥ) (10),

where K and α are the intercept and the slope of the Full density line of the SDMD; At and B are the coefficients of the Equivalent height curves and functions of the dominant height class: At=f(Ĥ), B=f(Ĥ) (Stankova, Shibuya, 2003). The coef-ficients K,α, At and B are model-specific and obtain different values according to the particular SDMD.

Simulation method 2 (Fig. 2B)The experimental values of quadratic mean diameter class DBH (mean diame-

ter classes by 2 cm) and stand density before the thinning are used as input variables in the thinning simulation. The assumption that the quadratic mean diameter class is kept unchanged during the thinning is imposed and the trajectory of stand growth after the cutting is defined as:

40

(11),

where Hafter thinning is the dominant stand height (H) after the simulated thinning and is determined by the equation:

(12).

Simulation method 3 (Fig. 2C)The input experimental values for the implementation of the third method are the

dominant height class Ĥ and the quadratic mean diameter d1.3 of the stand before the cut-

ting. The assumption that the mean stem volume

is kept unchanged during the cutting is imposed and the natural thinning trajectory after cutting is defined as:

(13).

Fig. 2. Modelling systemating thinning (50% thinning intensity) by 3 different simulation methods

41

In all three methods the estimation of the predicted values of stand density ρpred and total volume ypred at the present time (i.e. 20 years after the thinning) expressed by the dominant height class Ĥexp is done as the intersection between the respective Equivalent height curves and Natural thinning trajectories:

, At=f(Ĥexp ), B=f(Ĥexp ) (14).

The evaluation of the predicted values of stand density ρpred and total volume ypred at the present time Ĥexp is followed by quadratic mean diameter estimation:

(15).

The precision of predictions for each growth variable, SDMD model and sim-ulation method was evaluated by absolute and relative mean bias estimates (Em) and their respective confidence intervals.

Provenance variation in height and diameter Provenance variation in diameter at breast height, mean and dominant heights

was examined by Analysis of Variance and Variance Component Analysis. They were preceded by Shapiro-Wilk test for normality of the distributions, skewness es-timates and Levene’s test of equality of error variances. They detected deviation from normality for 2, 1 and 3 subsamples of diameter, mean and dominant height, respectively, and 4 significantly skewed diameter distributions. No violation of the assumption for equality of error variances was found for heights, while such viola-tion was present for diameter data. Regarding the inequality of the error variances, it has been postulated (Sokal, Rohlf, 1998) that the consequences of even moderate heterogeneity of variances are not too serious for the overall test of significance, except for single degree-of-freedom comparisons (not present here) and the test is even insensitive to heterogeneity when the sample sizes are equal (e.g. little varia-tion in the size of the diameter sub-samples was present). The consequences of non-normality of errors are also not very serious, since means will follow the normal dis-tribution more closely than the distribution of the variates themselves and only very skewed distributions would have marked effect on the significance level of the F-test and on the efficiency of the design (Sokal, Rohlf, 1998). Considering the fact that minor failures in the assumptions do not greatly disturb the conclusions from stan-dard analyses when the principal assumptions seem reasonably well satisfied in the

42

data (Snedecor, Cochran 1989) and that Analysis of Variance is robust regarding the assumptions for normality of the sample distribution and for equality of error vari-ances, and is still applicable even when they are not fully met (Sokal, Rohlf 1998, Morgan et al., 2004), ANOVA was performed to study the variation in height and di-ameter, regarding the provenance as a random effect factor. It was followed by Bon-ferroni’s multiple comparison test to distinguish the statistically significant groups of means by variables since it was recommended as the most flexible of the available techniques, because it imposes no restrictions on sample sizes for the different treat-ments, nor is it required that the sample means be statistically independent (Douglas et al., 1981). Hierarchical clustering based on the three studied growth parameters was applied using the furthest neighbor clustering method and the squired Euclid-ean distance measure to differentiate the provenances in regard with their combined growth performance. The influence of provenance altitude, longitude and latitude on the absolute error rates of the studied growth variables was examined by correlation analysis. Due to lack of information about the exact geographic co-ordinates of the seed lots, categorical values were assigned to the latitude (southern – 1, northern – 2) and latitude (western – 1, eastern – 2) and Spearman’s correlation analyses appli-cable to categorical variables, was implemented.

RESULTS

Model examinationThe main growth parameters examined were predicted with good precision by

the Equivalent mean diameter curves sub-model of both types of SDMD considering the absolute error range. The experimental values of stand density varied from 1024 to 1250 ha-1 and more than 10% deviation from the experimental value was record-ed for only one provenance (Velingrad 1250 m) as estimated by the regional-scale model. Quadratic mean diameters by provenances had values between 22 and 26 cm and the predicted by both models values deviated from the experimental ones by no more than 6% (Fig. 3). Total volume by provenances ranged from 417.51 to 546.65 m3/ha and the values predicted by the SDMD models differed with 0.11 – 11.39% for the national-scale and with 0.22 – 7.61% for the regional-scale model. The dominant height varied between the provenances from 17.3 to 19.6m and its predictions by the national-scale model exceeded the experimental values by more than 10% in 2 cases (Velingrad 1480 m; Slaveino 600 m), while the predictions by the regional-scale model – in 1 case (Velingrad 1250 m) (Fig. 3).

The results of the error examination consistently revealed the superiority of the regional SDMD model to the national one for all studied growth parameters (Ta-ble 1). The national-scale model showed variable over-evaluation for stand density, mean diameter and dominant height and under-evaluation of the total volume. The normality of the error distributions in all cases allowed implementation of t-tests for Em equals zero and the results rejected the null hypothesis for the mean relative and

43

Fig. 3. Heights and diameters at breast height of the provenances compared by Bonferroni multiple range test and classification dendrogram of the provenances by the growth variables. Provenance means with the same letter are not significantly different at P<0.05. The solid line indicates the values pre-dicted by the regional scale model, while the dotted line those predicted by the national scale model.

absolute errors estimated by the national-scale model for all studied growth variables (Table 1). The mean errors estimated through the regional-scale model, on the other hand, did not differ significantly from zero except for the dominant height. The ex-pected error for a single future observation would fall with 95% probability within the limits: (-68; 100) ha-1 for stand density, (-45.87; 31.46) m3/ha for total volume, (-0.76; 1.11) cm for mean DBH and (-1.11; 1.93) m for dominant height, if predicted by the regional-scale model. The tolerance intervals estimated for the relative errors by the same model revealed that 95% of the future observations will fall with 95% probability within the error range: -8.23 to 11.07% for stand density, -11.94 to 8.82% for total volume, -4.19 to 5.64% for mean DBH and -8.99 to 13.64% for dominant height.

The correlation analyses between the absolute error values and the seed lot geographic variables showed tendencies for both types of models. Positive correla-tion was found between the absolute errors estimated for the national scale model for all studied stand growth variables and the remoteness in latitude of the provenance origin from the test site (r=0.51, P<0.039 for total volume, density and quadratic mean diameter and r=0.55, P<0.021 for dominant height). The most southern prov-enances showed highest deviation from the predicted by the national model values. No significant correlation between provenance growth performance and the geo-

44

Tabl

e 1.

Abs

olut

e an

d re

lativ

e er

ror e

stim

ates

for t

he m

ain

stan

d va

riabl

es b

y th

e tw

o ty

pes o

f SD

MD

Stan

d va

riab

leSD

MD

m

odel

Uni

tsM

ean

erro

r E

m

Nor

mal

-ity

of

erro

rs*

Test

for

Em

= 0

95%

CI f

or E

m95

% P

I for

Em

95%

TI f

or E

mC

oef.

tSi

gnifi

c.

leve

l

Den

sity

regi

onal

1/ha

160.

869n

s1.

720.

106

-4

36-6

810

0-9

412

6%

1.42

0.89

7ns

1.73

0.10

2-0

.32

3.16

-5.9

58.

79-8

.23

11.0

7

natio

nal

1/ha

-57

0.93

8ns

-5.5

54.

36×1

0-5-7

9-3

5-1

5036

-179

164

%-4

.92

0.91

1ns

-5.5

64.

33×1

0-5-6

.80

-3.0

4-1

2.88

3.04

-15.

355.

51

Tota

l vo

lum

e

regi

onal

(m3 /h

a)-7

.20

0.95

3ns

-1.6

80.

113

-16.

321.

91-4

5.87

31.4

6-5

7.86

43.4

5%

-1.5

60.

938n

s-1

.77

0.09

6-3

.43

0.31

-9.4

86.

37-1

1.94

8.82

natio

nal

(m3 /h

a)22

.21

0.65

1ns

5.23

8.20

×10-5

13.2

131

.21

-15.

9760

.39

-27.

8167

.52

%4.

580.

947n

s5.

455.

37×1

0-52.

806.

36-2

.98

12.1

3-5

.32

14.4

8

Qua

-dr

atic

m

ean

diam

eter

regi

onal

(cm

)0.

180.

939n

s1.

710.

107

-0.0

40.

40-0

.76

1.11

-1.0

51.

40%

0.73

0.90

6ns

1.74

0.10

1-0

.16

1.61

-3.0

24.

48-4

.19

5.64

natio

nal

(cm

)-0

.57

0.80

7ns

-5.3

76.

26×1

0-5-0

.80

-0.3

5-1

.53

0.38

-1.8

21.

69%

-2.4

20.

917n

s-5

.54

4.52

×10-5

-3.3

4-1

.49

-6.3

41.

51-7

.56

2.73

Dom

i-na

nt

heig

ht

regi

onal

m0.

410.

582n

s2.

420.

028

0.05

0.77

-1.1

11.

93-1

.59

2.41

%2.

240.

582n

s2.

380.

030

0.25

4.24

-6.2

410

.73

-8.8

713

.36

natio

nal

m-1

.13

0.56

3ns

-6.8

24.

10×1

0-6-1

.49

-0.7

8-2

.63

0.36

-3.0

92.

64%

-6.2

70.

492n

s-6

.71

5×10

-6-8

.25

-4.2

9-1

4.67

2.14

-17.

284.

74

* K

olm

ogor

ov–S

mirn

ov Z

-sta

tistic

; ns –

P>0

.05.

45

graphical parameters of their origin was found for the regional scale model, except for the significant negative correlation between dominant height and latitude (r=-0.71, P<0.001).

Neither of the examined simulation methods succeeded to model satisfacto-rily the systematic cutting of 50% intensity. The predicted values for stand density, total volume and quadratic mean diameter underestimated the experimental ones in all instances (Table 2, Fig. 2). Simulation methods 1 and 2 produced similar results regarding the examined parameters and SDMD models, while the third simulation method had larger errors for density and total volume and smaller errors for qua-dratic mean diameter than the other two methods.

Provenance variationThe provenance influence on the variation of diameters, mean and dominant

heights was proved statistically significant (F=3.22, P< 0.001 for diameter; F=2.49, P< 0.01 for mean height and F=1.82, P<0.05 for dominant height). It accounted for 3.23% of the variation in diameter and 17.97 and 11.5% of the variation in mean and dominant height, respectively. Provenance 13 (Velingrad, 1100 m) showed su-periority in both height and diameter, was the only provenance of 20m dominant height class and formed an individual cluster group (Fig. 3). Provenances 8 (Hvoina, 1600 m) and 17 (Slaveino, 1600 m) were substantially inferior in their growth and diverged most strongly in a separate cluster group from the rest of the provenances. Provenances 1, 2, 3, 14 and 16 were distinguished in another cluster as having thick, but relatively short stems (Fig. 3). The correlation and regression analyses did not show statistically significant influence of the provenance origin latitude, longitude and altitude on their growth performance in the experimental plantation.

DISCUSSION

The national scale SDMD was built over experimental data from sample plots established in the mountainous part of South-Western Bulgaria on 21 types of forest sites, classified following the official nomenclature accepted in Bulgaria, at altitudes from 480 to 1300 m, while the data collection for the regional scale SDMD model took place on 7 forest site types at altitudes from 650 to 1200 m in Rila. The forest site range of the experimental data from Rila was a subset of this of the national-scale model and neither of them contained the type of the test plantation forest site. Despite this fact, the SDMD model for Scots pine plantations in Rila showed signifi-cant goodness-of-fit and predicted the main growth parameters of the experimental plantation with high confidence. The relatively poor fit concerning the dominant height prediction can be ascribed to the particular site conditions, which are charac-terized by wet, fertile soil favorable for growing of highly productive mixed Norway spruce – Scots pine stands, but are not specific to the natural range of the pure Scots pine stands (Penev et al., 1982). The dominant height is usually not calculated in

46

Tabl

e 2.

Abs

olut

e an

d re

lativ

e er

ror e

stim

ates

for t

he 3

thin

ning

sim

ulat

ion

met

hods

by

the

two

type

s of S

DM

D

Stan

d va

riab

leSD

MD

m

odel

Uni

ts

Sim

ulat

ion

met

hod

1Si

mul

atio

n m

etho

d 2

Sim

ulat

ion

met

hod

3

Mea

n er

ror

Em

95%

Con

fiden

ce

inte

rval

for

Em

Mea

n er

ror

Em

95%

Con

fiden

ce

inte

rval

for

Em

Mea

n er

ror

Em

95%

Con

fiden

ce

inte

rval

for

Em

Den

sity

regi

onal

1/ha

9842

154

102

4615

829

419

039

8%

8.09

3.53

12.6

58.

413.

8612

.96

25.0

816

.31

33.8

6

natio

nal

1/ha

175

123

227

177

125

229

370

244

495

%14

.79

10.7

418

.84

14.9

110

.85

18.9

731

.46

21.2

141

.72

Tota

l vol

ume

regi

onal

m3 /h

a19

2.05

170.

1721

3.93

192.

3917

0.46

214.

3221

2.73

190.

6523

4.80

%39

.61

36.7

442

.48

39.6

836

.80

42.5

644

.05

40.7

747

.33

natio

nal

m3 /h

a18

9.69

167.

1221

2.26

189.

6916

7.12

212.

2647

.90

199.

9127

2.56

%39

.13

36.0

042

.27

39.1

336

.00

42.2

724

1.48

41.7

854

.01

Qua

drat

ic

mea

n di

amet

er

regi

onal

cm4.

243.

674.

804.

213.

664.

772.

701.

623.

78%

17.9

615

.86

20.0

517

.84

15.7

519

.93

11.2

96.

5616

.01

natio

nal

cm2.

802.

273.

322.

782.

263.

312.

011.

402.

61%

11.8

09.

7513

.81

11.7

59.

7213

.78

8.48

5.94

11.0

3

47

the SDMD application, but it is one of the measured input variables used for other variables estimation, because it is broadly implemented as a site index measure de-pending more on the site conditions than on the other stand parameters. As a model constructed for the particular growth conditions of Rila the regional scale model had higher precision compared to the national scale model which is an average stand-level model approximated over much broader range of data. The precision of the national scale SDMD model can be further improved by differentiating the model by site indices as suggested by other investigators (Newton, 1998; Newton, Weetman, 1993; 1994) and by preceding validation studies for the SDMD model for Scots pine plantations in Bulgaria (Stankova,Petrin, 2008a; 2008b).

Although the provenance was proven as a significant source of variation in tree height and diameter, it accounted for less than 4% of the variation in diameter and 12-18% of the variation in heights. The mass selection is the lowest level in the forest tree improvement program, the selection intensity is limited by the great variation in natural stands, due to non genetic influence and the relatively small among-provenance differentiation in the growth traits in the provenance tests can be expected. Although trees originating from different provenances are expected to have different site indices when planted at similar sites, as inferred in the study by Tang et al. (2001), only the most superior in its growth provenance 13 was classified in a different height class (20 m vs. 18 m) in the present investigation. The manifes-tation of phenotypic variation in growth was further obscured by the environmental conditions combining excess of soil moisture, but also plenty of nutrients and requir-ing significant adaptation ‘efforts’ on the first place. This inference is supported also by the result that no distinct pattern of variation with the seed lot altitude alteration was found, although an altitudinal effect survey was planned through this particular provenance test. Nonetheless, in agreement with a previous survey (Kostov et al., 1986) and conclusions by other investigators (Dobrinov, Kalinkov, 1972; Dobrinov et al., 1982; Shutyaev, Giertych, 1997), the results from the provenance variation study confirmed the general tendency of superior growth of the provenances from the central part of the species natural range in regard with the altitude and the latitude and the inferiority of the marginal ones (Fig. 1, 3). The results for the significantly superior and inferior provenances in the present investigation also agreed with their ranking recorded in 1984 before the cutting (Kostov et al., 1986).

More information on the applicability of the SDMD models to genetically diverse monospecific Scots pine plantations was provided by the results from the correlation analysis. The most remote in latitude from the test site provenances exhibited consistently largest deviation from their predicted by the national scale model values which implies influence of Site×Provenance interaction on the model application precision. Better precision of the national scale model when applied to plantations established in the range of the provenance natural distribution will be expected. No significant correlations were distinguished, between the degree of pre-cision of the regional scale model regarding the stand growth performance and the

48

provenance origin variables which reveals predominant environmental influence on the precision of the SDMD model. It is further supported by the lack of significant influence of the geographical parameters on the overall provenance growth perfor-mance and ranking. The large error values of the dominant height predictions for the less remote in latitude provenances can be explained by the facts that the dominant height prediction precision did not prove sufficiently reliable even for the regional scale model and at the same time the less remote latitudinally provenances coincided with the superior and the inferior in their height growth performance provenances producing highest absolute errors (Fig. 1, 3). This outcome confirms the necessity to treat the dominant height as a measured input variable, which is most dependent on the specific growth conditions, thus being appropriate site index indicator, than as predicted by the models variable.

Two conditions are assumed in modeling thinnings through the SDMD – on the intensity (less than 40%) and on the method (from below) of the thinning – and they were both violated by the systematic cutting conducted. The intensity exceeded the marginal value by 10% and, more importantly, the cutting did not have selec-tive, but systematic nature, which explains the anticipated failure to model success-fully this cutting. The assumption for thinning from below means that the dominant height class is being kept constant during cutting, the stand remains on the same Equivalent height curve, but gets reduced density and total volume, as was the case in Simulation method 1. Such cutting simulation inevitably results in increase of the mean stand diameter of the remaining stand which is intrinsic to the thinnings from below (Fig. 2A). A different approach was proposed in the Simulation method 2 of the present investigation assuming that the systematic cutting did not change the value of the quadratic mean diameter. This approach, however, manifested anal-ogous disadvantage as Simulation method 1 by reduction in the dominant height through the modeled cutting, which is specific for the thinnings from above (Fig. 2B). The development of Simulation method 3 attempted to avoid the disadvan-tages of the other 2 methods considering the nature of the systematic cutting which does not give preferences to the removed trees and thus, should keep the average tree volume unchanged. Simulation method 3, however, did not produce improve-ment in the predictions (Table 2). Although the experimental values of the dominant height and quadratic mean diameter are experimental variables easy to measure, Simulation method 3 involves estimation of stand density, which was found to be the least precisely predicted through the SDMD stand variable (Stankova, Petrin, 2008a; 2008b). Simulation method 3, which was firstly proposed in a preceding investiga-tion, showed inferiority to Simulation method 1 in modeling thinnings from below, but still achieved satisfactory precision in the total volume prediction (Stankova, Petrin, 2008b). Simulation method 1 applied to national scale SDMD proved reli-able for modeling thinnings from below of intensity 0-37%, revealing best goodness of fit for the thinning intensity range 15-30% (Stankova, Petrin, 2008a). Although the present study showed that the SDMD implementation for management prescrip-

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tions should be done with caution and severe violations of its assumptions are not acceptable, experiments need to be undertaken to locate the scope for its application. These margins can be still broadened by fixing one of the simulation assumptions and extending the limits of the other to a reasonable degree.

Acknowledgements: This study is dedicated to Prof. Kosta Kostov who was in charge of, and to our colleague Dr. Konstantin Genov who was involved in the establishment of the experimental plan-tation in Rila Mountain. The authors are grateful to Prof. A. Alexandrov for presenting the past record documentation of the provenance test.

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E-mails: tatianastankova@yahoo.com, hstankov@yahoo.com