Stand Density
NASP IMDS
THE BIG THREE:
• Absolute stand density
• Quadratic Mean Diameter
• Basal Area
Graphical Guides
Size-Density Relationship
The predictable relationship between
mean size of trees and their associated
density in crowded (i.e., stem exclusion)
populations
Density

Age
Boundary Line Examples
(AKA: “-3/2 Power Law”)
Log-log
Scale
Growth Trajectories
Wiley 1976
Stand Density Index
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
Stand Density Index (SDI) – Woodard paper
Reineke (1933)
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SDI
Species-specific upper limit
Density when the stand has a standardized QMD
Calculated as:
Imperial
 QMD 
 TPA  

 10 
1 . 605
SDI
Metric
 QMD 
 TPH  

 25 . 4 
1 . 605
Stand Density Index Values
Suggested Maximum SDI by species and source. English units are number of
10-inch trees per acre. Metric units are number of 25.4cm trees per hectare.
Species
White fir
Red fir
Mixed conifer for CA
Douglas-fir for WA-OR
Douglas-fir for CA
Eucalyptus
Redwood
Ponderosa Pine
Loblolly Pine
Longleaf Pine
Slash Pine
Shortleaf Pine
Upland Oak
Ponderosa Pine
Lodgepole pine
Douglas-fir
Western Hemlock
Maximum SDI Maximum SDI
(English)
(metric)
830
2050
1000
2470
750
1850
595
1470
600
1480
490
1210
1000
2470
800
1980
450
1110
400
990
400
990
400
990
230
570
830
2050
690
1700
587
1450
790
1950
Source
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Reineke, 1933
Schnur, 1937
Long, 1985
Long, 1985
Long, 1985
Long, 1985
Long, J. N. 1985. A pratical approach to density management. Forest Chronicle 61:23-37.
Reineke, L. H. 1933. Perfecting a stand density index for even-aged forests. Journal of Agricultural Research 46(7):627-638.
Schnur, G. L. 1937. Yield, stand, and volume tables for even-aged upland oak forests. USDA Technical Bulletin No. 560, 87p.
Stocking
Charts & Guides
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Size vs. Density
Log-Log scale
SDI on the “third axis”
SDImax = 1000
Taylor Woods
Level-of-Growing-Stock
Study
Flagstaff, AZ
Relative Density Index

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Relative Density Index (RDI)
Basically the percent of maximum SDI
Communication across species (species have
maximums)
Intuitive feel
Magic thresholds for stand dynamics

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0.15 - 0.30 for crown closure
0.40 for scheduling of growing space thinnings
0.55 for entering “the zone of imminent competition”
0.80 for certain mortality agents
Density
Guides
Density Management Diagrams
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Packaging the concepts
together
Simple management tool
Old GSL “boat” diagrams
Additional information on
the diagrams
INTERPRETING CHANGES
6”
(800 TPA, 5.1”)
4”
340 TPA
653 TPA
Density
Guides
Density Effects on Growth
Density Effects on Growth
Taylor Woods: Four decades of TREE DIAMETER growth; 1962 - 2002
4
y = -1.3146Ln(x) + 7.106
R2 = 0.97
y = -1.415Ln(x) + 7.6447
R2 = 0.9793
DBH growth (inches/decade)
3
2
y = -1.4821Ln(x) + 8.2557
R2 = 0.9873
GSL40 1962-1972
GSL60 1962-1972
GSL80 1962-1972
GSL100 1962-1972
y = -1.1867Ln(x) + 6.8112
R2 = 0.9767
GSL120 1962-1972
GSL150 1962-1972
1962-1972
1
1972-1982
1982-1992
1992-2002
Log. (1962-1972)
Log. (1972-1982)
Log. (1982-1992)
Log. (1992-2002)
0
0
20
40
60
80
100
basal area (sf/ac) at decade's beginning
120
140
160
Density Effects on Growth
Taylor Woods: Four decades of TREE HEIGHT growth; 1962 - 2002
10
height growth (feet/decade)
8
y = -2.3839Ln(x) + 16.391
R2 = 0.6455
y = -2.1886Ln(x) + 14.675
R2 = 0.6736
6
GSL40 1962-1972
GSL60 1962-1972
GSL80 1962-1972
4
y = -1.4543Ln(x) + 11.654
R2 = 0.3773
GSL100 1962-1972
y = -1.8418Ln(x) + 13.568
R2 = 0.6672
GSL120 1962-1972
GSL150 1962-1972
1962-1972
1972-1982
1982-1992
1992-2002
2
Log. (1962-1972)
Log. (1972-1982)
Log. (1982-1992)
Log. (1992-2002)
0
0
20
40
60
80
100
basal area (sf/ac) at decade's beginning
120
140
160
Density Effects on Growth
PER ACRE
Taylor Woods: Four decades of CUBIC FOOT VOLUME growth; 1962 - 2002
1200
GSL40 1962-1972
GSL60 1962-1972
GSL80 1962-1972
y = 444.4Ln(x) - 1246.2
R2 = 0.8503
GSL100 1962-1972
GSL120 1962-1972
1000
GSL150 1962-1972
1962-1972
MCF Volume growth (cf/ac/decade)
1972-1982
1982-1992
1992-2002
800
Log. (1962-1972)
Log. (1972-1982)
Log. (1982-1992)
Log. (1992-2002)
600
y = 278.49Ln(x) - 516.98
R2 = 0.7585
y = 240.24Ln(x) - 387.18
R2 = 0.8335
400
y = 209.37Ln(x) - 241.19
R2 = 0.8082
200
0
0
20
40
60
80
100
basal area (sf/ac) at decade's beginning
120
140
160
Density Effects on Growth
Taylor Woods: Three decades of BOARD-FOOT VOLUME growth; 1972 - 2002
PER ACRE
5000
GSL40 1972-1982
GSL60 1972-1982
y = -0.2786x2 + 71.106x - 626.9
R2 = 0.8283
GSL80 1972-1982
Scribner Board-Foot Volume growth (bf/ac/decade)
GSL100 1972-1982
GSL120 1972-1982
4000
GSL150 1972-1982
1972-1982
1982-1992
y = -0.3955x2 + 56.14x + 847.11
R2 = 0.6366
1992-2002
Poly. (1972-1982)
3000
Poly. (1982-1992)
Poly. (1992-2002)
2000
y = -0.2407x2 + 33.39x + 1134.4
R2 = 0.31
1000
0
0
20
40
60
80
100
basal area (sf/ac) at decade's beginning
120
140
160
DENSITY EFFECTS ON GROWTH
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
Tree vigor and mortality rates
Plasticity of the trees – think about this at
“Hoskins” LOGS study (chapter 7)
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Live Crown Ratio and “canopy depth”
Crown Radius (branch length/size) and crown closure
Height:Diameter and “stability” (e.g., in wind and snow)
Wood utilization products; size and quality
Understory richness, diversity and abundance
Net Primary Productivity distribution
Ecosystem “stuff”
OTHER DENSITY MEASURES

CURTIS’ “RELATIVE DENSITY”
RD = BA
√QMD

RELATIVE or “AVERAGE SPACING”:
(can be relative to heights, as well)

TREE-AREA RATIO: area occupied by tree crowns
per unit land area; TA can be estimated from D or D2

CROWN COMPETITION FACTOR;
TA relative to open grown trees
Spacing impacts
Example calculations - Douglas-fir (SDImax = 600)
QMD
TPA
BA
SDI
RDI
CRD
6
50
9.8
22
0.04
4
6
200
39.3
88
0.15
16
crown closure
6
400
78.5
176
0.29
32
well-stocked
10
50
27.3
50
0.08
9
10
200
109.1
200
0.33
34
well-stocked
10
400
218.2
400
0.67
69
moved into "the zone"
15
50
61.4
96
0.16
16
crown closure
15
200
245.4
383
0.64
63
moved into "the zone"
15
400
491
767
1.28
127
24
50
157.1
204
0.34
32
24
200
628
815
1.36
128
impossible, would have self thinned
24
400
1257
1630
2.72
257
completely crazy idea
Description
low-density young plantation
low density, but great tree growth
impossible, would have self thinned
well-stocked
UNEVEN-AGED structures?
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
SDI calculated by
diameter class
from a stand table
BUT don’t stretch
too far…why?
2
6
10
14
18
22
TPA BAPA
50
1
10
2
0
0
60
64
80
141
20
53
220
261
SDI
4
4
0
103
205
71
388