Volume 8
Issue 4
Forestry
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume8/issue4/art10.html
PRODUCTIVITY OF SELECTED PROVENANCES OF GRAND FIR IN THE PROVENANCE EXPERIMENT IN THE KRYNICA EXPERIMENTAL FOREST
Marian Kulej^{1}, Jarosław Socha^{2}
^{1} Department of Forest Tree Breeding,
Agricultural University of Cracow, Poland
^{2} Department of Forest Mensuration,
Agricultural University of Cracow, Poland
The productivity of grand fir (Abies grandis Lindl.) was estimated under mountain conditions of Poland. Investigations concerned 7 provenances of this species from the regions of its natural range (Salmon River, Indian Creek, Buck Creek, Bear Mountain, Eagle Creek, Crescent Creek, Santiam Summit). It was found that provenance (origin) has a decisive effect on the productivity of grand fir. The results of a 27year study on its genetic and silvicultural values unmistakably indicate that under site conditions of the Beskid Sądecki Mts. the provenances from the Salmon River, Indian Creek, Buck Creek and Bear Mountain are characterized by a better growth. The provenance Salmon River from the Vancouver Island in British Columbia in Canada turned out to be especially valuable in respect of productivity. Its stand volume reached 143 (m^{3} ha). While the provenances Crescent Creek and Santiam Summit reached the smallest volume, 41.5 and 77.0 (m^{3} ha) respectively.
Key words: Abies grandis, volume increment, productivity, provenance experiment.
INTRODUCTION
The introduction of foreign species to enrich the native arborescent flora should be proceeded by a thorough analysis of requirements and possibilities, as well as long term provenance experiments. A NorthAmerican grand fir (Abies grandis Lindl.) is one of foreign species which have been tested in Poland for a long period of time. It has already been successfully introduced in many countries of Europe [6, 14, 15, 10, 8, 9].
A large natural range of grand fir, growing under various climatic and soil conditions, and the existence of many geographical races, as distinguished by Müller [16, 17] as well as the occurrence of definite provenances [8, 11, 14, 15, 24], result in necessity to select populations of this species proper for given site conditions.
Studies on a genetic and silvicultural variation of grand fir have been conducted by the Department of Forest Tree Breeding of the Agricultural University of Cracow since 1977. The results obtained so far indicate a considerable variability of tested partial populations of grand fir in respect of tree survival and growth [12, 13].
The purpose of the study presented in this paper was to estimate productivity of various provenances of grand fir growing under mountain conditions of Poland. The estimation of productivity was accomplished on the basis of stand volume (m^{3 }ha) reached by analyzed partial populations under conditions of the provenance experiment established in the Krynica Experimental Forest.
MATERIAL
A study comprised seven provenances of grand fir. In their selection variable climatic conditions existing in the area of its natural occurrence were taken into account, basing on the regions distinguished by Müller [16, 17] and height above the sea level. The mother stands grew at altitudes ranging from 25 to 1400 (m) (Table 1). Their location is shown in Fig. 1.
Table 1. Data on mother stands in which seeds of analyzed provenances of Abies grandis [7] 
Number of provenance according to IUFRO 
Name of provenance 
Location of parental stands 

Region, country, locality 
Latitude 
Longitude 
Altitude (m) 
Region acc. to Müller 

12O4O 
Salmon River 
Brit. Columbia. Canada Sayward 
50°20’ 
125°56’ 
25 
I 
12OO3 
Indian Creek 
Washington, USA 
48°04’ 
123°38’ 
140 
I 
12OO1 
Buck Creek 
Washington, USA 
48°15’ 
121°21’ 
400 
I 
12OO5 
Bear Mountain 
Washington, USA 
47°59’ 
123°02’ 
825 
I 
12OO7 
Eagle Creek 
Washington, USA 
47°39’ 
123°30’ 
1200 
II 
12O2O 
Crescent Creek 
Oregon, USA 
43°28’ 
121°57’ 
1375 
II 
12O16 
Santiam Summit 
Oregon, USA 
44°26’ 
121°52’ 
1400 
II 
The experimental area is situated in the Carpathian Forest Region at the altitude of 700–720 (m), i.e. in the middle part of the lower montane belt, within the range of the mountain forest. It is located in the Wojkowa Forest Section of the Krynica Experimental Forest (Fig. 1). It is exposed towards the south and southeast and its geographic coordinates are 49°27’ north latitude and 20°58’ east longitude. In terms of site type, the whole area is in the range of the mountain forest type [12]. Trees of the provenances tested in the experiment were planted in random arrangement of blocks in four replications (28 plots, 20x20 (m) each).
Fig. 1. Location of the mother stands of the examined provenances of Abies grandis in North America (area of occurrence of Abies grandis indicated by solid line) and the experimental area in Poland 
The investigations were based on data obtained by measuring d.b.h. and height of 27yearold grand fir trees of the tested partial populations of this species. D.b.h. was measured on all trees present in plots, while 10 trees were selected at random in each plot (replication) for height measurement. In the case of each provenance a section diameter measurement was made on 20 trees selected at random (i.e. 5 trees in each replication). The measurements were taken directly with the use of a caliper, and each tree was climbed for measurements to be taken. Diameter measurements were taken at the following heights: 0.00 (m); 0.5 (m); 1.3 (m); 2.0 (m); and then every 2 (m) to the top. The last measurement was usually taken approximately 2 (m) from the top. Altogether, 1202 sets of heightdiameter variables were measured.
In total d.b.h. of 1654, and height of 280 trees were measured. Stem section diameters were measured on 140 trees.
The diameter at breast height (dbh) of the measured trees ranged from 2.5 to 28.7 (cm), and their height (h) from 2.5 to 15.5 (m) (Table 2).
Table 2. D.b.h. and height of individual provenances of Abies grandis 
Characteristic 
Provenance 
Mean 
Number of measurements 
Standard deviation 
Minimum 
Maximum 
Height (m) 
040 
10.8 
40 
3.05 
2.8 
15.5 
003 
9.1 
40 
3.21 
1.6 
16.3 

001 
9.2 
40 
2.89 
2.4 
13.7 

005 
10.3 
40 
2.31 
4.6 
13.4 

007 
9.8 
40 
2.56 
4.3 
15.4 

016 
7.9 
40 
2.70 
2.0 
12.6 

020 
8.0 
40 
2.58 
2.2 
11.8 

total 
9.3 
280 
2.93 
1.6 
16.3 

D.b.h. (cm) 
040 
13.5 
270 
5.64 
1.0 
30.6 
003 
12.3 
330 
5.60 
0.7 
27.1 

001 
12.6 
261 
5.44 
0.6 
28.6 

005 
14.3 
245 
5.33 
2.2 
33.5 

007 
12.9 
251 
5.49 
0.7 
28.7 

016 
12.5 
197 
5.55 
1.5 
27.2 

020 
12.9 
100 
5.71 
0.7 
24.5 

total 
13.0 
1654 
5.55 
0.6 
33.5 
METHODS
Partial populations of grand fir tested in the experimental area in the Krynica Experimental Forest are characterized by a considerable variability of the tree stem form [21]. Application of a common empirical equation for calculation of stem volume of individual provenances causes that negative errors are in majority in the case of populations of the region I, and positive errors in the case of populations of the region II. Also according to cited references the application of empirical equations worked out for grand fir by Dik [4] in Holland and Øen et al. [18] in Norway causes the occurrence of considerable errors in volume calculations. In the case of Dik equation the mean error in calculation of volume of a single tree was from 6.3% (provenance 020) to 21.37% (provenance 040), while in the case of the equation of Øen et al. it was from –3.6% to 10.9% for the same provenances respectively. Due to large values of errors in determination of volume by empirical equations used in Europe, and lack of such data in Poland, the authors have worked out new equations for calculation of volume of a single tree of analysed provenances of grand fir. Subsequently these equations were used to determine the provenance volume (m^{3} ha). For this purpose for trees, in the case of which a section measurement of diameter was made, the stem volume (v) was calculated by the section method of Smalian [26]. The empirical equation to determine volume of stem was constructed on the basis of the allometric function [24]:
(1) 
where: v – dependent variable (volume of the stem)
X_{1}, X_{2}, ... X_{n} – independent variables
b_{0}, b_{1}, b_{2}, ... b_{n} – equation parameters
ε – random error of a normal distribution.
In general, in the case of allometric relationships there occurs a phenomenon of heteroscedasticity of residuals, consisting in increase of residual variances of the dependent variable, along with increase of values of independent variables. In order to obtain homoscedasticity of residuals the equation of an allometric function (equation 1) was linearized by logarithmic transformation (equation 2) [22].
(2) 
Independent variables occurring in the empirical equation were selected on the basis of the corrected coefficient of determination (adjusted R^{2}), the value of which indicates a proportion of variance explained by the variables used (equation 1). Due to differences in the tree stem form, as mentioned above, connected with the provenance of grand fir, the empirical equations have been worked out separately for two (I and II) regions of its natural range.
Height of individual trees was necessary for calculation of stand volume in individual plots. Since height of only some trees was measured it was necessary to plot height curves for individual provenances of grand fir. The relationship between height and d.b.h. was smoothed by the Näslund equation (equation 3) [2].
(3) 
where: h – tree height
d – d.b.h.
α, β – equation parameters.
Using the height curve, height of unmeasured trees was determined. Then, using empirical equations volume of stem each tree was calculated.
Summing up stem volume in individual plots, and converting it to volume per hectare the stand volume (V) of individual provenances was obtained within their replications. A subsequent step of the analysis was to determine the effect of the provenance on stand volume. For this purpose a bifactor analysis of variance was used with a provenance and a replication as the two factors. It turned out that the replication affects the stand volume, and to eliminate this effect standardization of stand volume within individual replications was used. Stand volume of tested provenances was standardized within a given replication according to the equation 4.
(4) 
where: V_{sij }– standardized value of stand volume of provenance (i) in repetition (j)
V_{ij} – stand volume of provenance (i) in repetition (j)
δ_{vj} – standard deviation of stand volume of individual provenances in repetition (j)
V_{j} – mean stand volume of repetition (j).
Elimination of the effect of a replication permitted to make a one factor analysis of variance used to test occurrence of differences in mean values of standardized stand volumes (V_{s}) of individual provenances. The analysis of variance was preceded by testing homogeneity of variance in individual provenances using the BrownForsyth test [27]. In order to distinguish groups which significantly differed between one another the RIR test of Tukey was used [27].
RESULTS
To determine stem volume, the empirical equations were worked out, with tree d.b.h. and height as independent variables (equation 5, Table 3).
(5) 
where: v – stem volume
h – tree height
d – d.b.h.
b_{0}, b_{1}, b_{2}, b_{3} – equation parameters
ε – random error
Table 3. Parameters and basic statistics of empirical equations for determination of stem volume (v_{s}) of Abies grandis of tested provenances 
Volume 
Region 
Parameters of equation 
R 
R^{2} (adjusted) 
pvalue 
Durbin Watson Statistic 
Serial correlation 

b_{0} 
b_{1} 
b_{2} 
b_{3} 

v_{s} 
I 
0.0000680 
1.2123560 
0.2738699 
0.9037535 
0.996 
0.992 
0.0000 
1.9567 
0.0102 
II 
0.0000206 
3.6625117 
2.2694781 
0.8921409 
0.997 
0.993 
0.0000 
2.1321 
0.0736 
The equations worked out explained over 99% of variation of stem volume, since the adjusted coefficient of determination was 0.992 for provenances from the region I, and 0.993 for provenances from the region II. The DurbinWatson test showed no residual autocorrelation. Residuals of the equations were characterized by homoscedasticity since there was no increase in residual variance with increase in values determined by the equation (Figs. 2a and 2b).
Fig. 2. Residuals (actualpredicted) against predicted stem volumes of Abies grandis (for the data converted into logarithm) using equation (2) (a – region I, b – region II) 
To determine volume according to these equations the height of each tree has to be known. In order to obtain heights of individual trees, the parameters of the height curve were calculated (equation 3).
There was a strong correlation between tree height and d.b.h. within a provenance. The correlation coefficient of the regression equation varied from 0.872 to 0.984 (Table 4).
Determination of height of individual trees permitted to calculate their volume. Volume of stems was calculated according to equation 5.
Table 4. Parameters of height curve and the coefficient of correlation between tree height and d.b.h. of individual provenances of Abies grandis 
Provenance 
Parameter of Näslund curve 
Coefficient of correlation 

a 
b 

040 
1.6996 
0.2043 
0.947 
003 
1.6200 
0.2284 
0.889 
001 
1.9021 
0.2068 
0.944 
005 
1.5199 
0.2360 
0.906 
007 
1.8938 
0.2093 
0.872 
016 
2.3682 
0.2101 
0.920 
020 
2.2583 
0.2175 
0.948 
The provenance 016 from Oregon state in the USA (Santam Summit) had the smallest mean stem volume, while this value for the provenance 040 from British Columbia in Canada (Salmon River) was the greatest (Fig. 3). The partial populations of grand fir, tested in this experiment, may be divided into three statistically homogeneous groups in respect of volume of a single tree. In the main, grand firs from eastern (016, 020, and 001) and western (003) slopes of the Cascade Range in Washington and Oregon states were characterized by the smallest volume of a single tree.
Mean volume (V) of individual provenances varied considerably (Fig. 4) from 43.7 (m^{3} ha) (provenance 020) to 151.3 (m^{3} ha) (provenance 040).
Fig. 3. The mean single tree stem volume of Abies grandis of individual provenances 
Fig. 4. Mean volume of individual provenances of Abies grandis 
It was found, on the basis of analysis of variance, that the provenance as well as the replication had a significant effect on stand volume of analysed provenances of grand fir. Besides differences between provenances, there were also differences between replications in respect of stand volume (Table 5).
Table 5. Results of analysis of the dependence of stand volume (V_{s}) on the provenance and replication 
Effect 
V_{s} 

F 
df 
P 

Free term 
611.4 
1 
0.000000 
Provenance 
7.03 
6 
0.000003 
Replication 
5.53 
3 
0.000437 
Elimination of variation caused by replications, attained by standardization of volume, permitted to use a one factor analysis of variance to determine the effect of the provenance. This was preceded by the test of homogeneity of variance (Table 6).
Table 6. Comparison of mean stand volumes (V_{s}) of provenances using the analysis of variance preceded by the test of homogeneity of variance 
Variable 
Test of variance homogenity 
Analysis of variance 

DF 
Chisquare 
P 
SS 
DF 
MS 
SS 
DF 
MS 
F 
P 

model 
model 
model 
error 
error 
error 

V_{s} 
6 
5.351118 
0.499630 
21.18923 
6 
3.531538 
2.81077 
21 
0.133846 
26.38502 
0.000000 
In the case of stand volume (V) the variance in individual provenances was homogeneous (Table 6), while the probability level indicated that the tested hypothesis about equality of mean stand volumes in a plot (V) in individual provenances should be rejected (Table 6). In order to distinguish homogeneous groups the RIR test of Tukey was used.
Table 7. Comparison of mean standardized stand volumes (V_{s}) of individual provenances of Abies grandis using the RIR test of Tukey 
Provenance 
040 
003 
001 
005 
007 
016 
020 
plevel 

040 

0.7676 
0.0385 
0.4773 
0.2510 
0.0002 
0.0002 
003 
0.7676 

0.4880 
0.9988 
0.9620 
0.0005 
0.0002 
001 
0.0385 
0.4880 

0.7774 
0.9515 
0.0289 
0.0002 
005 
0.4773 
0.9988 
0.7774 

0.9993 
0.0013 
0.0002 
007 
0.2510 
0.9620 
0.9515 
0.9993 

0.0033 
0.0002 
016 
0.0002 
0.0005 
0.0289 
0.0013 
0.0033 

0.0266 
020 
0.0002 
0.0002 
0.0002 
0.0002 
0.0002 
0.0266 

The analyzed provenances may be divided into four homogeneous groups in respect of standardized stand volume (V_{s}) (Table 7, Fig. 5). The provenance 020 from Crescent Creek decidedly had the smallest volume (per ha), at the difference in respect of the general mean amounting to 1.72 (V_{s}) of standard deviation. Also the provenance 016 from Santiam Summit had relatively small V_{s}, smaller than the mean for the entire study material by 0.80 of standard deviation. The third group comprised provenances 001, 007, 005, and 003. While decidedly the highest values of V_{s} higher than the mean by 0.98 of standard deviation, had grand fir from Salmon River (040) from British Columbia in Canada.
Fig. 5. Mean standardized stand volumes of individual provenances of Abies grandis – data are arranged according to increasing altitude of mother stands 
DISCUSSION
This study showed that partial populations of grand fir tested under mountain conditions of the Beskid Sądecki Mts are strongly diversified in respect of stand volume attained. The results permit to make a hypothesis that elements of location of mother stands, i.e. altitude and latitude, strongly affect stand volume of individual provenances. With increase of altitude the stand volume of almost all provenances, with the exception of grand fir from Bear Mountain (005), decrease. In respect of latitude, grand fir of the most northerly (latitude 50°0’) provenance 040 from Salmon River in British Columbia is characterized by the greatest productivity. While the smallest volume was attained by the most southerly provenances, i.e. from Santiam Summit (016) and Crescent Creek (020) situated on eastern slopes of the Cascade Range. Moderate volumes were attained by populations of grand fir from the area between latitudes 47°39’ and 48°15’.
The mean annual increment of large wood volume of 27yearold Abies grandis ranged from 1.6 (m^{3} ha) (provenance 020) to 5.6 (m^{3} ha) (provenance 040). In comparison with Abies alba, which under Polish conditions attains the mean annual volume increment of about 4.2 (m^{3} ha) (site quality class I) [25], the investigated provenances of Abies grandis attain in general a higher volume increment. Only in the case of provenances 016 and 020 the mean annual volume increment was smaller, and it was equal to increment of Abies alba of quality classes II and III.
A 100yearold grand fir of the eastern Cascade Range attains the stand volume ranging from 476 to 1330 (m^{3} ha) [3], while in northern Idaho, where it grows together with Pinus strobus, it attains volume ranging from 470 to 1078 (m^{3 }ha) [5]. While the mean annual increment of grand fir is from 8 to 13 (m^{3 }ha) in Idaho [23], and from 6 to 10 (m^{3 }ha) in Montana [19]. Considerably higher volume increments of grand fir, i.e. from 18 to 20 (m^{3 }ha) when trees were 40 years old, were recorded on fertile soils in England [1]. These examples, as well as the results that have been obtained till now, permit to suppose that also under mountain conditions of Poland the productivity of grand fir would be quite good. However, the productivity depends on the provenance, and therefore the origin of planting material is very important.
SUMMARY OF RESULTS AND CONCLUSIONS
The tested provenances of grand fir are characterized by diversified volume attained by a single tree, as well as in respect of stand volume. The greatest volume of a single tree was found in the case of the provenance 040, and the smallest in the case of the provenance 016. The group characterized by smaller mean volume of a single tree includes provenances 016, 003, 020, and 001, while the group characterized by greater mean volumes comprises provenances 007, 005, and 040.
As far as the volume per area unit is concerned the greatest values of V, i.e. mean 151 (m^{3 }ha) were observed in the case of the provenance 040. While the smallest stand volumes were observed in the case of provenances 020 (V – 43.7 (m^{3 }ha)) and 016 (V – 81.4 (m^{3 }ha)). Taking all provenances tested into account, grand firs from the region I were characterized by higher volumes, while trees from the region II by smaller volumes. The mean annual volume increment ranged from 1.6 (m^{3 }ha year) (provenance 020) to 5.6 (m^{3 }ha year) (provenance 040).
It may be concluded that the provenance (genotype) has a decisive effect on productivity of grand fir growing under mountain conditions of Poland. The results of a 27year study on genetic and silvicultural values of grand fir of different provenances indicate that under site conditions of the Beskid Sądecki Mts provenances from the first (I) region are characterized by more favourable growth characteristics than provenances from the second (II) region of their natural range, as distinguished by Müller. In respect of productive capacity under mountain conditions of Poland the provenance from Salmon River in British Columbia is especially valuable.
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Marian Kulej
Department of Forest Tree Breeding,
Agricultural University of Cracow, Poland
Al. 29 Listopada 46, 31425 Cracow, Poland
phone: +48126625124
email: rkulej@cyfkr.edu.pl
Jarosław Socha
Department of Forest Mensuration,
Agricultural University of Cracow, Poland
Al. 29 Listopada 46, 31425 Cracow, Poland
email: rlsocha@cyfkr.edu.pl
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