A COMPARATIVE ANALYSIS OF SLENDERNESS OF THE MAIN TREE SPECIES OF THE NIEPOLOMICE FOREST

Stanisław Orzeł
Department of Forest Mensuration, Agricultural University of Cracow, Poland

ABSTRACT

The effect of age of trees on their slenderness (s) and the relationship between slenderness and tree d.b.h. (d) and height (h) were determined on the basis of measurements of d.b.h. and height of 6070 the upper story trees growing in over 400 circular plots established in stands of age class II and older in the Niepołomice Forest District. The following eight tree species were investigated: Pinus sylvestris, Quercus robur, Carpinus betulus, Betula verrucosa, Alnus glutinosa, Fraxinus excelsior, Tilia cordata, and Larix decidua. From among these species F. excelsior was characterized by the highest mean slenderness (1.047), while P. sylvestris by the lowest one (0.773). High, usually over 0.800 in value, coefficients of correlation between slenderness and d.b.h. indicated a great usefulness of d.b.h. for elaboration of formulae determining slenderness of analyzed tree species. A logarithmic function (s = α · ln d + β) turned out to be the best in estimation of slenderness of P. sylvestris, L. decidua, A. glutinosa, and B. verrucosa, while in the case of Q. robur, C. betulus, and F. excelsior an involution function (s = α · d ^β ) was the best, and for T. cordata – an exponential function (s = α · e ^β·d ).

Key words: coefficient of slenderness, coefficient of correlation, empirical formulae, tree stability.

INTRODUCTION

Polish forestry suffers considerable losses due to action of abiotic factors, especially wind and snow. For example in winter 1999/2000 these losses amounted to as much as 2.5 million cubic meters of timber [12], while during the decade 1978 – 1988 over 31.3 million cubic meters were damaged [17].

Actions improving the stability of trees and stands could considerably limit these damages. It is, therefore, important to get to know slenderness of trees, considered to be a measure of their stability, especially of conifers. This feature of a longitudinal section of tree trunks, defined as a quotient of height and d.b.h., significantly decreases with increase of tree age [1, 2, 3, 4, 10, 15, 16]. In mountains its value greatly depends on elevation [3, 4, 6].

In earlier studies slenderness was usually one of the factors analyzed [1, 2, 3, 4], or it was investigated in respect of trees of a single species [6, 10, 16], or it concerned several species growing in different regions [15].

Forest site diversity, from the fresh mixed coniferous forest to the ash-alder swamp forest, observed in the Niepołomice Forest, which is situated in the fork of the Vistula and San rivers, favors the development of forest stands of rich species composition in all their layers. In the case of 64% of these stands Pinus sylvestris is the dominant species, in 19% Quercus robur, and in 11% Alnus glutinosa. Stands with predominance of other tree species such as Larix decidua, Picea abies, Abies alba, Fagus silvatica, Fraxinus excelsior, Carpinus betulus, Betula verrucosa, Populus spp., and Tilia cordata occupy about 6% of forest area [8]. This richness of tree species, frequently of different site requirements and growing in a relatively small area, creates a unique opportunity to study their slenderness. Slenderness is one of the characteristics of the longitudinal section of tree trunks.

The aims of this study were to estimate slenderness of tree species forming stands of the Niepołomice Forest, to determine its variation due to age, and to determine the relationship between slenderness and tree d.b.h. and height.

MATERIAL AND METHODS

The study material consisted of measurements of d.b.h. and height of trees growing in circular sample plots established in stands of age class II (20 – 40 years) and older in the Niepołomice Forest District. Plot centers were situated in nodes of the network of squares 500 x 500 m oriented according to cardinal directions. Plots were from 0.01 ha to 0.10 ha in area depending on stand age. A detailed description of plot establishment and measuring methods may be found in other publications [7, 8].

The measured trees, especially those occurring in stands composed of many species and growing on fertile sites, occupied different layers of stands. Slenderness was determined only for trees from the upper stand layer. It was assumed that in each plot this layer was made up of trees higher than 2/3 of the mean height of 5 highest trees measured in a given plot. Only those species were included in the analysis in the case of which at least 100 trees fulfilled these criteria. In total 6070 trees of the following species were included in the study: Pinus sylvestris, Quercus robur, Carpinus betulus, Betula verrucosa, Alnus gluitinosa, Fraxinus excelsior, Tilia cordata, and Larix decidua (Table 1). P. sylvestris was the most numerously represented species (3276 trees), while the sample of L. decidua was the least numerous one (123 trees). Age of trees according to the Forest Management Plan ranged from 22 to 192 years. Measured d.b.h. ranged from 7.0 to 92.3 cm, and height from 9.0 to 38.0 m.

For tree species listed in Table 1 the basic parameters of distribution of their slenderness as well as relationships between slenderness and tree d.b.h, height and age were determined. Statistical analyses were performed using programs included in the packet Statistica 6 [13].

RESULTS

Slenderness of analyzed tree species
F. excelsior turned out to be characterized by the highest mean slenderness (1.047), while P. sylvestris by the lowest one (0.773). Large differences between mean values for individual species (Table 2) resulted not only from their growth properties but also from differences in their age (Table 1). Slenderness of Q. robur was the most variable one (32.3%). Its coefficient of slenderness assumed values from the greatest range: from 0.276 to 2.040. At the same time these slenderness values were the extreme values for the entire study material.

Because of large differences in age the comparison of mean values of slenderness of respective tree species is only an approximation. This is due to the fact that slenderness of trees growing under given conditions decreases with increase of their age, as it has been pointed out by studies carried out hitherto. Therefore any comparisons are valid only for trees of similar age. Taking this into consideration the analyzed tree species were arranged in individual 20-year age classes according to decreasing mean value of slenderness:

age class II: F. excelsor, C. betulus, B. verrucosa, Q. robur, T. cordata, A. glutinisa, L. decidua, P. sylvestris;
age class III: F. excelsior, C. betulus, A. glutinosa, T. cordata, B. verrucisa, Q. robur, P. sylvestris, L. decidua;
age class IV: F. excelsior, C. betulus, T. cordata, B. verrucosa, A. glutinosa, P. sylvestris, Q . robur;
age class V: T. cordata, A. glutinosa, P. sylvestris, B. verrucosa, C. betulus, Q. robur;
age class VI: P. sylvestris, F. excelsior, Q. robur, B. verrucosa;
age class VI: P. sylvestris, Q. robur.

This comparison shows that in age classes II and III broadleaf tree species are more slender than conifers. In the case of most analyzed species 20-year age intervals were long enough to show a significant effect (at α = 0.05) of age of trees on their slenderness.

Pinus sylvestris is a relatively stable species. The coefficient of slenderness of over 90% of trees of this species was below 1.0. For 59% it was below 0.8, and only for 1.4% it was higher than 1.2 (Table 3). For the remaining species the percentage of trees with slenderness above 1.2 was higher, ranging from 5.7% (L. decidua) to 25.4% (F. excelsior). Nearly 59% of trees of F. excelsior were characterized by slenderness above 1.0.

Relationship between slenderness and tree d.b.h and height
About 71% of slenderness variation of the main tree species occurring in the Niepołomice Forest was possible to be explained by d.b.h. and height (Table 4). These two tree characteristics explained a considerably wider range of slenderness variation of P. sylvestris and L. decidua (88%) than it was the case with broadleaf species, especially F. excelsior (71.10%) and Q. robur (71.69%). Irrespective of the tree species, the association of slenderness with d.b.h. was considerably stronger than with height. In the case of both characteristics the coefficients of linear correlation were negative, and for association of slenderness with d.b.h. they ranged from -0.7800 (A. glutinosa) to -0.8614 (B. verrucosa), while for that with height from -0.1175 (P. sylvestris) to -0.5802 (Q. robur). The elimination of a mutual relationship between d.b.h and height affected not only the strength of association of slenderness with these two characteristics but also affected the direction of these changes in the case of height. For all species coefficients of partial correlations between slenderness and d.b.h. at excluded effect of height (r_s,d.h) were considerably higher than those of correlations between slenderness and height at excluded effect of d.b.h. (r_s,h.d). Differences were especially high in the case of broadleaf trees, particularly Q. robur (Table 4).

High values of the coefficient of correlation between slenderness and d.b.h., mostly above -0.800, indicated a high usefulness of this characteristic for model elaborations permitting to determine tree slenderness. A general form of the formula for individual species (Table 5) was chosen from among five functions analyzed (linear, multinominal of second order, logarithmic, power, and exponential). The highest value of the explained variance, being a hundredfold value of the coefficient of determination, was the criterium used in this selection.

The comparison between coefficients of determination given in Tables 3 and 4 revealed that with functions based only on d.b.h. it was possible in the case of Q. robur, B. verrucosa, C. betulus, F. excelsior, and T. cordata to explain a wider range of slenderness than with a linear model taking simultaneously into account d.b.h. and height.

The diagrams of the elaborated functions cross one another (Fig. 2) which means that the elementary diameter increase in analyzed tree species caused unequal decrease in their slenderness.

To facilitate the observation of the relationships between slenderness and d.b.h. the values of slenderness of analyzed tree species obtained by elaborated functions were expressed as the multiple of slenderness of P. sylvestris. In the entire d.b.h. range only F. excelsior had a greater slenderness than P. sylvestris (Fig. 3). The difference in slenderness of these two species was about 15% for d.b.h. of 7 cm and it decreased with increase of diameter, thus in the interval from 15 to 30 cm it was below 5%. Subsequently it was successively increasing.

DISCUSSION

The determination of tree slenderness and its relationships with various characteristics of trees, or the relationship between mean slenderness and characteristics of the stand was the main aim of studies of such authors as Orzeł and Socha [6], Rymer-Dudzińska [10, 11], Rymer-Dudzińska and Tomusiak [12], Wang et al. [15], and Zajšczkowski [16]. Zajaczkowski [16] analyzed in detail slenderness of Pinus sylvestris and made numerous recommendations concerning silvicultural conduct aiming at increased resistance of this species to snow damage. Studies on the relationship between slenderness and various dendrometric characteristics of trees revealed that slenderness is most strongly correlated with d.b.h. [6, 10, 15]. Founding of a significant relationship between slenderness and volume increment of trees was the basis for elaboration by Rymer-Dudzińska [10] of the equations for determining the volume increment in which d.b.h. and slenderness are the explanatory variables. With these equations, depending on stand age, it is possible to explain from 64% to over 95% of variation of P. sylvestris volume increment. This percentage increases with decrease of stand age [10].

Also in the case of analyzed tree species of the Niepołomice Forest over 70% of variation of their slenderness can be explained by d.b.h. This result may be considered as satisfactory when it is compared with results of similar studies carried out by Wang et al. [15]. These authors analyzed in detail slenderness of five species (Populus tremuloides, Populus balsamifera, Pinus contorta, Picea glauca, and Picea mariana), and they described the relationship between slenderness and d.b.h. by three functions. The exponential function turned out to be the best, for which the value R² ranged from 0.252 to 0.629, i.e. considerably less than in the case of formulae elaborated for the main tree species of the Niepołomice Forest.

Frequently slenderness was only one of many aspects of wider studies or analyses [also: 1, 2, 3, 4, 9, 14, 16]. The coefficient of slenderness most often served to explain the effect of abiotic factors on stability of trees. Abetz [2] showed that trees of lower slenderness were more resistant to water deficit. At a definite ratio between the crown bulk and the trunk bulk trees of lower slenderness were more stable and less susceptible to strong winds [9]. Trees with long crowns are more stable than those with short crowns. This was proved by negative values of the coefficient of correlation between the coefficient of slenderness and the length of the crown computed by Wang et al. [15], as well as by results of Gerecke [4] who showed that mean values of the coefficient of slenderness was 0.64 for trees of Abies alba with their crowns making over 35% of tree height and 0.83 when crowns were shorter than 24% of tree height.

Slenderness of trees was not only considered to be a measure of their stability. The value of the coefficient of slenderness was a deciding factor for acceptance of trees for the analysis conducted by Thren [14] concerning the increment of P. sylvestris. In his study he took into consideration only trees of a “normal” slenderness, i.e. those for which the coefficient of slenderness was from 0.8 to 1.2. According to data in Table 3 the criterion of a “normal slenderness” assumed by Thren is fulfilled by only about 40% of P. sylvestris trees growing in the Niepołomice Forest.

The significant differences in respect of mean values of slenderness of the investigated tree species in respective 20-year age classes fully confirmed a known effect of age on tree slenderness. According to Wang et al [15] the coefficient of correlation between slenderness and age of trees was always negative ranging from -0.018 (Picea mariana) to -0.534 (Populus tremuloides). Much stronger relationship exists between the mean value of the coefficient of slenderness and age of the stand. Rymer-Dudzińska [11] on the basis of ample study material proved that the correlation between slenderness and stand age (-0.844) was stronger than correlations between slenderness and other characteristics of P. sylvestris stands.

CONCLUSIONS

1. Age of trees is a factor determining their slenderness. Generally, increase in age by one 20-year age class causes a statistically significant decrease of their slenderness.

2. In the Niepołomice Forest the analyzed broadleaf tree species in age classes II and III were more slender than trees of Pinus sylvestris and Larix decidua.

3. Irrespective of the species of a tree, its slenderness is considerably more correlated with its d.b.h than with its height. In the case of P. sylvestris and L .decidua both these characteristics explain a considerably wider range of variation of slenderness than is the case with broadleaf tree species.

4. In the case of Quercus robur, Betula verrucosa, Carpinus betulus, Fraxinus excelsior, and Tilia cordata a wider range of variation of slenderness may be explained using the elaborated functions based on d.b.h. than with use of the linear model taking into account both d.b.h. and height.

5. From among tree species occurring in the Niepołomice Forest the greatest slenderness in the entire analyzed range of d.b.h. was found for Fraxinus excelsior.

REFERENCES

1. Abetz P., 1985. Ein Vorschlag zur Durchführung von Wachstumsanalysen im Rahmen der Ursachenerforschung von Waldschäden in Südwestdeutschland [A proposal for analyses of tree-growth concerning investigations of damages in forest stands in the Southwest Region of Germany]. Allg. Forst-u. J.-Ztg., 156. Jg., 9/10: 177-187 [in German].

2. Abetz P., 1988. Untersuchungen zum Wachstum von Buchen auf der Schwäbischen Alb [Some investigations towards the growth of beech in the mountain range “Schwäbische Alb”]. Allg. Forst-u. J.-Ztg., 159, Jg., 11/12: 215-223 [in German].

3. Eichkorn Th., 1986. Wachstumanalysen an Fichten in Südwestdeutschland [Growth analyses of spruces in the south-west of the Federal Republik of Germany]. Allg. Forst-u. J.-Ztg., 157, Jg., 7: 125-139 [in German].

4. Gerecke K.-L., 1986. Zuwachsuntersuchungen an vorherrschenden Tannen aus Baden-Württemberg [Growth analyses on predominant firs in Baden-Württemberg]. Allg. Forst-u. J.-Ztg., 157, Jg., 3/4: 59-68 [in German].

5. Jaworski A., 2004. Podstawy przyrostowe i ekologiczne odnawiania oraz pielęgnacji drzewostanów [Increment and ecological foundations of regeneration and tending of stands]. PWRiL. Warszawa, 375 [in Polish].

6. Orzeł S., Socha J., 1999. Smukłosc swierka w szescdziesięcioletnich drzewostanach Beskidów Zachodnich [Slenderness feature in 60-year-old spruce stands of the Western Beskidy Mountains]. Sylwan 4: 35-43 [in Polish].

7. Orzeł S., Socha J., Forgiel M., Ochał W., 2005a. Struktura biomasy podszytu występujacego w drzewostanach Puszczy Niepołomickiej [Undergrowth biomass structure in the stands of Niepołomicka Forest]. Sylwan 4: 40-47 [in Polish].

8. Orzeł S., Socha J., Forgiel M., Ochał W., 2005b. Biomass of underbrush and conditions for its occurrence in stands of the Niepołomice Forest. EJPAU Forestry 8(1) www.ejpau.media.pl

9. Petty J.A., Swain C. 1985. Factors influencing stem breakage in hight winds. Forestry 58: 75-84.

10. Rymer-Dudzińska T., 1992a. Smukłosc drzew w drzewostanach sosnowych [Slenderness of Trees in Pine Stands]. Sylwan 11: 35-44 [in Polish].

11. Rymer-Dudzińska T., 1992b. Zależnosc sredniej smukłosci drzew w drzewostanach sosnowych od różnych cech taksacyjnych drzewostanu [Dependence of the Mean Slenderness of Trees in Pine Stands on Various Taxation Characteristics of Stand]. Sylwan 12: 19-25 [in Polish].

12. Rymer-Dudzińska T., Tomusiak R., 2000. Porównanie smukłosci drzewostanów bukowych i dębowych [Comparison of slenderness in beech and oak stands]. Sylwan 9: 45-52 [in Polish].

13. StatSoft, Inc., 2004. STATISTICA (data analysis software system), version 6. www.statsoft.com

14. Thren M., 1985. Erste Ergebnisse von Wachstumsanalysen an vorherrschenden und herrschenden Kiefern in Südwestdeutschland [First results of growth-analysis on predominant and dominant Scots pines in Southern West-Germany]. Allg. Forst-u. J.-Ztg., 156. Jg.,11: 215-224 [in German].

15. Wang Y., Titus S.J., Le May V.M., 1998. Relationships between tree slenderness coefficients and tree of stand characteristics for major species in boreal mixedwood forests. Can. J. For., 28(8): 1171-1183.

16. Zajaczkowski J., 1984. Postępowanie hodowlane a odpornosc drzewostanów sosnowych na szkody powodowane przez snieg [The silvicultural procedure and the resistance of Scoth pine stands to damage caused by snow]. Sylwan 9: 19-26 [in Polish].

17. Zajaczkowski J., 1991. Odpornosc lasu na szkodliwe działanie wiatru i sniegu [Resistance of forest to harmful action of wind and snow]. Wyd. Swiat. Warszawa. 221 [in Polish].

18. Plan Urzadzania Lasu Nadlesnictwa Niepołomice na lata 2002-2011 [Plan of the Niepołomice Forest District for the period 2002-2011] [in Polish].

Accepted for print: 12.04.2007

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.