Data sources
Three long-term data sets spanning up to three decades of repeated measurements were used for these analyses. These data sets are rare in that the data were collected across the range of developmental stages that can be statistically analyzed. The three data sets were collected from an initial planting density study for Alnus rubra Bong. and two levels of growing stock studies: one established in three naturally regenerated, Pseudotsuga menziesii var. menziesii stands and another in an artificially regenerated Pinus resinosa Ait. plantation. For all, dendrometric data were collected repeatedly on trees growing at different spacings. In the A. rubra study, trees were planted at four square spacings (1.8 m, 2.8 m, 4.2 m, and 6.4 m) and allowed to develop without interference. In the P. menziesii and the P. resinosa studies, trees were thinned to a series of growing-stock levels. The growing-stock levels in the P. menziesii study were set relative to four, fixed percentages of plot growth relative to the unthinned control plots. These percentages were 10%, 30%, 50%, and 70%. In the P. resinosa study, growing stock was defined as basal area per hectare. Five levels of growing stock were assigned to the plots established in this study (7, 14, 21, 28, 35 m2/ha) plus an unthinned control.
The biological characteristics of A. rubra are described by Harrington (1990). Alnus rubra is a common hardwood species that is native to the coastal region of the northern Pacific coast in North America. It is relatively short lived, maturing between 60 to 70 years old, and it is intolerant to shade. It is unique in that it fixes nitrogen. Height growth is rapid when young, slowing significantly after the juvenile stages. Typical heights at 50 years old range between 18 to 37 m.
The A. rubra study was established by the Hardwood Silviculture Cooperative at Oregon State University. Details of the study were described by Weiskittel et al. (2009). Plots varied from 0.13 ha to 0.20 ha and were measured every 3-5 years beginning at age 3 years. Within the 22 installations, one replicate of each planting density was randomly assigned to a plot. Measurement protocols are also described by Weiskittel et al. (2009) and summarized by Dean et al. (2013). The number of trees measured in each plot varied by planting density and age, ranging from a maximum of 688 at age 4 in the plots with the closest initial spacing to a minimum of 45 at age 13 in the plots with the widest spacing (Table 1).
Table 1
Minimums, maximums, and means of numbers of trees per plot, total tree height, and diameter at breast height (dbh) for each measurement period by treatment. Only data from one installation is shown for Pseudotsuga menziesii because measurements were collected at different ages at the other 2 installations. Data shown for the Rocky Brook installation is typical.
|
|
|
Age
|
|
|
|
4
|
7
|
10
|
13
|
Species
|
Spacing
|
|
Min
|
Median
|
Max
|
Min
|
Median
|
Max
|
Min
|
Median
|
Max
|
Min
|
Median
|
Max
|
Alnus rubra
|
6.4 m
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
32
|
51
|
86
|
32
|
50
|
83
|
32
|
51
|
82
|
45$
|
49
|
53
|
|
|
Height (m)
|
0.3
|
3.0
|
3.0
|
0.8
|
7.4
|
15.3
|
3.2
|
9.2
|
19.5
|
8.4
|
14.6
|
17.6
|
|
|
dbh (cm)
|
0.5
|
1.8
|
6.6
|
0.5
|
7.1
|
18.5
|
2.0
|
11.7
|
26.9
|
9.1
|
20.8
|
30.5
|
|
4.2 m
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
65
|
97
|
138
|
59
|
94
|
136
|
57
|
96
|
133
|
80
|
94
|
110
|
|
|
Height (m)
|
0.4
|
3.0
|
7.4
|
1.7
|
7.4
|
14.4
|
2.6
|
11.0
|
18.0
|
6.8
|
14.7
|
20.6
|
|
|
dbh (cm)
|
0.5
|
1.8
|
7.1
|
0.5
|
7.1
|
17.8
|
1.3
|
11.9
|
23.9
|
5.6
|
17.0
|
27.9
|
|
2.8 m
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
129
|
203
|
296
|
129
|
200
|
294
|
139
|
204
|
292
|
189
|
192
|
195
|
|
|
Height (m)
|
0.3
|
3.3
|
8.2
|
1.4
|
8.0
|
14.3
|
2.3
|
10.4
|
18.8
|
6.4
|
13.7
|
22.6
|
|
|
dbh (cm)
|
0.5
|
1.8
|
7.4
|
0.5
|
7.1
|
17.5
|
1.0
|
10.4
|
22.1
|
3.6
|
14.7
|
24.9
|
|
1.8 m
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
195
|
388
|
688
|
192
|
374
|
683
|
218
|
367
|
658
|
287
|
310
|
332
|
|
|
Height (m)
|
0.3
|
3.4
|
7.9
|
1.7
|
7.4
|
14.4
|
2.6
|
9.2
|
18.6
|
3.9
|
11.1
|
21.1
|
|
|
dbh (cm)
|
0.5
|
2.0
|
7.1
|
0.5
|
6.3
|
14.7
|
1.3
|
8.4
|
18.3
|
2.3
|
11.2
|
20.3
|
Table 1
|
|
|
Age
|
|
Growing stock
|
|
28
|
39
|
45
|
58
|
Pseudotsuga menziesii
|
10%
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
63
|
63
|
79
|
20
|
24
|
35
|
14
|
17
|
25
|
9
|
11
|
15
|
|
|
Height (m)
|
5.6
|
9.2
|
13.4
|
9.8
|
15.2
|
19.8
|
11.6
|
19.1
|
23.2
|
18.7
|
25.7
|
32.0
|
|
|
dbh (cm)
|
6.9
|
11.2
|
17.3
|
11.9
|
19.8
|
29.0
|
13.7
|
25.1
|
35.3
|
23.1
|
35.3
|
45.7
|
|
30%
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
73
|
74
|
78
|
37
|
49
|
51
|
32
|
45
|
45
|
25
|
32
|
35
|
|
|
Height (m)
|
5.7
|
9.4
|
21.7
|
9.5
|
15.1
|
19.7
|
11.6
|
18.0
|
23.6
|
13.7
|
22.9
|
31.0
|
|
|
dbh (cm)
|
5.3
|
11.2
|
18.8
|
8.6
|
17.8
|
25.9
|
10.4
|
20.8
|
31.2
|
14.2
|
27.4
|
39.4
|
|
50%
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
63
|
73
|
73
|
52
|
63
|
69
|
45
|
59
|
66
|
35
|
38
|
60
|
|
|
Height (m)
|
5.0
|
9.5
|
14.4
|
7.9
|
14.8
|
21.1
|
9.2
|
17.6
|
25.0
|
10.4
|
22.0
|
30.3
|
|
|
dbh (cm)
|
6.4
|
11.2
|
18.8
|
8.9
|
16.4
|
26.7
|
8.9
|
18.9
|
31.8
|
9.9
|
22.6
|
40.1
|
|
70%
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
78
|
78
|
80
|
72
|
75
|
75
|
69
|
72
|
75
|
56
|
65
|
72
|
|
|
Height (m)
|
5.2
|
9.8
|
13.8
|
8.8
|
16.1
|
21.3
|
10.4
|
19.1
|
24.6
|
12.2
|
24.6
|
31.7
|
|
|
dbh (cm)
|
5.6
|
11.2
|
19.1
|
9.4
|
17.1
|
28.4
|
9.7
|
20.1
|
33.0
|
11.2
|
24.6
|
41.7
|
|
100%
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
168
|
178
|
212
|
158
|
158
|
207
|
134
|
138
|
187
|
95
|
100
|
127
|
|
|
Height (m)
|
4.4
|
8.7
|
16.1
|
5.8
|
13.0
|
23.5
|
6.8
|
15.3
|
26.5
|
9.2
|
20.7
|
33.7
|
|
|
dbh (cm)
|
4.1
|
8.6
|
22.9
|
3.8
|
11.4
|
31.0
|
4.1
|
13.5
|
34.0
|
4.8
|
17.8
|
40.4
|
Table 1 (cont’d)
|
|
|
Age
|
|
Basal area
|
|
50
|
65
|
70
|
80
|
Pinus resinosa
|
7 m2/ha
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
8.0
|
12.0
|
23.0
|
8.0
|
12.0
|
23.0
|
7.0
|
12.0
|
23.0
|
7.0
|
12.0
|
23.0
|
|
|
Height (m)
|
12.8
|
17.8
|
20.7
|
14.0
|
20.1
|
22.9
|
14.3
|
21.0
|
22.7
|
17.4
|
23.5
|
26.5
|
|
|
dbh (cm)
|
10.9
|
22.6
|
32.3
|
14.5
|
30.5
|
40.6
|
16.3
|
33.9
|
44.5
|
19.6
|
39.1
|
50.3
|
|
14 m2/ha
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
16.0
|
24.0
|
41.0
|
16.0
|
24.0
|
41.0
|
16.0
|
24.0
|
41.0
|
16.0
|
24.0
|
41.0
|
|
|
Height (m)
|
15.9
|
18.0
|
20.1
|
16.2
|
20.9
|
23.2
|
18.9
|
22.1
|
23.5
|
20.7
|
23.9
|
26.2
|
|
|
dbh (cm)
|
10.7
|
22.6
|
35.1
|
14.5
|
29.7
|
42.7
|
15.7
|
32.5
|
45.7
|
17.0
|
36.6
|
49.8
|
|
21 m2/ha
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
30.0
|
42.5
|
66.0
|
21.0
|
30.0
|
48.0
|
16.0
|
24.0
|
39.0
|
13.0
|
16.5
|
31.0
|
|
|
Height (m)
|
10.7
|
17.9
|
19.5
|
15.4
|
20.9
|
23.5
|
16.2
|
22.0
|
24.1
|
17.6
|
23.7
|
26.8
|
|
|
dbh (cm)
|
9.4
|
21.6
|
31.5
|
10.2
|
27.1
|
38.4
|
10.2
|
29.2
|
41.4
|
11.2
|
32.5
|
45.7
|
|
28 m2/ha
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
44.0
|
55.0
|
72.0
|
34.0
|
42.0
|
56.0
|
28.0
|
33.0
|
48.0
|
21.0
|
25.0
|
39.0
|
|
|
Height (m)
|
15.7
|
18.0
|
20.1
|
18.4
|
20.9
|
23.9
|
19.4
|
22.0
|
26.8
|
20.9
|
23.8
|
26.8
|
|
|
dbh (cm)
|
10.7
|
22.4
|
32.0
|
11.9
|
26.9
|
36.1
|
12.7
|
28.7
|
38.1
|
13.5
|
32.3
|
40.9
|
|
35 m2/ha
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
63.0
|
75.0
|
99.0
|
49.0
|
55.0
|
78.0
|
41.0
|
48.0
|
65.0
|
33.0
|
40.0
|
57.0
|
|
|
Height (m)
|
14.9
|
17.9
|
20.8
|
17.4
|
17.4
|
24.7
|
18.3
|
22.0
|
24.8
|
19.8
|
23.8
|
28.1
|
|
|
dbh (cm)
|
10.7
|
21.3
|
30.5
|
11.7
|
25.1
|
35.6
|
11.7
|
27.2
|
37.3
|
14.7
|
30.0
|
40.4
|
|
Control
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Trees/plot
|
76.0
|
89.0
|
118.0
|
73.0
|
84.5
|
109.0
|
69.0
|
82.0
|
105.0
|
66.0
|
74.5
|
91.0
|
|
|
Height (m)
|
14.3
|
18.0
|
22.0
|
18.6
|
20.9
|
25.6
|
19.8
|
22.0
|
27.1
|
22.1
|
23.8
|
29.9
|
|
|
dbh (cm)
|
9.9
|
22.5
|
32.3
|
12.2
|
25.4
|
36.3
|
12.2
|
26.9
|
37.8
|
16.3
|
29.0
|
40.1
|
$The minimum number of trees increased from age 10 to 13 because some plots across the installations were not measured at age 13. The number of trees per plot decreased or remained the same through time for individual installation.
The biological characteristics of P. menziesii are described by Hermann and Lavender (1990). The levels of growing stock study was established in coastal P. menziesii, var. menziesii which is a different variety than P. menziesii var. glauca growing east of the Cascade Mountains in the northwest region of North America. Coastal P. menziesii is considered intermediate in shade tolerance and is very long lived, commonly living for 500 years. Old-growth trees can reach 76-m tall. Highest height increments are reached between 20 and 30 years of age.
The P. menziesii data used in this study was collected in the three installations of the Levels of Growing Stock Study established on National Forests in the Pacific Northwest region of the United States (Harrington 2018). These installations and others established by Weyerhaeuser Company, Oregon State University, and the Canadian Forest Service comprised the Douglas-fir Levels of Growing Stock Study (LOGS) described by Curtis and Marshall (1986). The three USDA Forest Service installations were established in Washington and Oregon on the Olympic (Rocky Brook installation), Gifford Pinchot (Iron Creek installation), and the Umpqua (Stampede Creek installation) National Forests. Within each installation, levels of growing stock were randomly assigned to three, 0.08-ha plots. Trees in the plots had naturally regenerated. Measurement frequency varied by installation because thinning intervals were set according to height increment. The number of trees measured at the Rocky Brook installation varied from a maximum of 212 at age 28 years for the unthinned control to a minimum of 9 at age 58 years for the 10% level of the growing stock (Table 1). These numbers are typical of the other two locations.
The biological characteristics of P. resinosa are described by Rudolf (1990). The biological range of P. resinosa is in the northeastern and north central regions of North America. P. resinosa is intolerant to shade, but it does not seem to be as intolerant as A. rubra. Trees as tall as 43 m have been recorded, but heights of 21 to 24 m are more typical at maturity. Height increment slows significantly after 100 years of growth. The maximum life span of P. resinosa is substantially shorter than that of P. menziesii and is at least twice as long as that of A. rubra.
The P. resinosa study was also designed to examine the effects of maintaining fixed levels of growing stock on tree and stand growth. This study was established in the Birch Lake plantation planted with 2,500 trees per hectare on the Superior National Forest in northern Minnesota, USA. The six basal area treatments were assigned at random to 18, 0.8 hectare plots. These plots were split into thirds to accommodate three thinning methods: low, crown, and combined. Plots were thinned about every 10 years, and trees were measured every 5-10 years. The number of trees measured at each measurement period varied from a maximum of 118 at age 45 in the unthinned plots to a minimum of 7 at age 80 for the 7 m2/ha basal area treatment (Table 1).
Variables
Relative height increment was calculated for each tree surviving between measurement periods. Equations to calculate missing heights were developed with height data that were measured on a subset of trees during each measurement period. The height equation for A. rubra was developed by the OSU Hardwood Research Cooperative. Equations to calculate missing heights for P. menziesii and P. resinosa are described by Dean et al. (2021). Relative height increment for these analyses is simply height increment per initial height at the beginning of each measurement period.
Volume increment per meter of height growth was calculated for each tree in the plot. Tree-volume equations for A. rubra, P. menziesii, and P. resinosa are described by Hibbs et al. (2007), Bruce and DeMars (1974), and Fowler (1997), respectively. Volume increment per height increment was calculated for each tree that survived between measurement periods.
Net leaf area added per meter of height increment was calculated for each tree that survived between measurement intervals. Leaf area per tree was calculated with regression equations based on combinations of dbh and height. The equation for A. rubra was developed by Helgerson et al. (1988). The equation for P. menziesii was developed by Dean et al. (2021) based on data collected by Maguire and Bennett (1996), and the equation for P. resinosa was developed by Penner and Deblonde (1996).
Dominance indexes were calculated from cumulative proportions of the height increment versus initial height or relative height growth (Gdh), marginal height cost for height ranked trees (Gdv/dh), and marginal height benefit for height-ranked trees (GdAl/dh) for each plot for each measurement period. Forrester (2019) calculated growth dominance for relative basal area growth, for example. The three dominance coefficients were calculated with the alternative equation proposed by Fernandez et al. (2011).
Analyses
Tests for competition effects on Gdv/dh and Gdh were conducted with linear mixed models with repeated measures suggested by Littell et al. (2006). The null hypothesis of no competition effect on the least-square means of Gdv/dh and Gdh was rejected if the probability of greater values of F exceeded 0.10. The least-square means represented age-adjusted means values of Gdv/dh and Gdh for each level of competition. Post-hoc means testing was conducted by calculating the probability of greater values of t for all pairs of means. Standard errors of the age-adjusted means allowed t-tests of the null hypothesis that the mean equal to zero. Data for the mixed-model analysis were the mean values across installation for each initial planting density and measurement period for the A. rubra data; the values averaged over the three replications of each level of growing stock, installation, and measurement period for the P. menziesii ; and the values averaged over the three replications of each residual basal area, thinning method, and measurement period for the P. resinosa data. Standard errors of these means were used to conduct two-tailed, t-tests for the null hypothesis of no difference with zero.
The existence of competition-induced tradeoffs between marginal height cost and marginal height benefit was tested with linear, mixed-model regression analysis with repeated measures with competition treatment as a categorical variable. The growth dominance index for marginal height cost (Gdv/dh) was regressed on GdAl/dh with individual plot as the repeated unit. A simple tradeoff between costs and benefits would be indicated with either a zero or negative slope between the variables.