FORE
REf EARCH LABORATORY
REIEAPCI:IATE 66
n_.
AN EVALUATION OF EIGHT
INTERTREE COMPETITION INDICES
r~.
S. NOONE
JOHN F. BELL
INTRODUCTION
Intertree competition
indices have been
important in growth simulation methodology
since Newnham (1964) introduced a distancestand model
for Douglas-fir.
dependent
Indices developed by other authors also
1.
TABLE
BASIS OF COMPUTATION FOR THE EIGHT
INTERTREE COMPETITION INDICES.
Crown or
adjusted
require data on intertree
however, their calculations vary for crown
distances;
and
diameter
angle measures,
ratios
of
height
(d.b.h.)
breast
competitors to subject trees. The purpose
of this study was to evaluate the ability
of eight such indices to predict diameter
Those tested
growth in thinned stands.
fall into two groups, one basing the
overlap,
indices on crown or adjusted crown overlap
and the other on diameter, or distance to a
neighboring tree (Table 1).
A set
of
algorithms developed by
Research
Centre,
Forest
FORTRAN
Pacific
B.C., to evaluate the competition
indices were made available to the School
of Forestry at Oregon State University.
the
Victoria,
crown
Author
Date
overlap
Arney
1971
X
Bella
1970
X
Ek and
1973
X
Diameter/
distance to
neighboring
tree
Monserud
Hegyi
1973
Lin
1969
Newnham
1964
X
Staebler
1951
X
Quenet
1975
GROWTH DATA USED IN THE EVALUATION
indices were
stand age was 20
taken from a study by Berg and Bell (1979)
established in 1963 on land near Hoskins,
Average
Oregon owned by Starker Forests.
to
Data
used
to
evaluate
OCTOBER 1990
the
was
designed
years.
examine
The Hoskins study
the effect of
different levels of growing stock on wood
production, tree size, and ratios of growth
OREGON STATE UNIVERSITY, SCHOOL OF FORESTRY
CORVALLIS. OREGON 97331 503-753-91 66
2
to growing-stock.
It comprises eight
treatments and a control, each replicated
three times.
A calibration thinning was
made in 1963 and treatment thinnings were
made in 1966 and 1970.
We used data from
treatments 1, 3, 5, and 7, representing
four levels of growing stock in descending
order from heavy to light thinning, and
from two growth periods, 1966-1970 and
1970-1973.
An interior square (50 x 50 ft) was used to
any trees outside
model growth; therefore,
the interior that could
(crown overlap) could be
inhibit
growth
accounted for
The
interior square also
accurately.
contained a large enough number of trees
for a reasonable growth analysis repre-
senting different thinning treatments.
trees within the 0.2-acre plots had
All
been
numbered and stem mapped.
Each of the four treatments contained three
square 0.2-acre plots (93.33 x 93.33 ft).
DATA ANALYSIS
The data were analyzed in two ways.
First,
we regressed periodic increment in d.b.h.
initial diameter, initial competitive
stress index, and change in the competitive
stress index due to different thinning
treatments on individual plots at the
beginning of each growth period.
The
correlation coefficient (R ) and mean
square error
(MSE)
for each thinning
treatment were then averaged. Second, we
combined data for all trees on alI plots
on
and regressed periodic diameter Increment
on the associated initial diameter, initial
competition
index,
and
change
competition Index due to thinning.
in
The basic growth model for the comparison
analysis is that used
The
that Smith (1977) tried.
following are his results using data from
models
the Hoskins study:
Growth model AD = f (DO, CSIO, ACSIO).
R2
MSE
1966-1970
1970-1973
0.674
.094
0.808
.042
In our analysis, we substituted CIO for
CSIp and ACID for ACSIO, where CIO refers
to one of the
being compared.
eight competition indices
Therefore, our basic growth model is
by Smith (1977):
AD = a + bD0 + c(Cl0) + d(ACIO)
[11
AD = a + bD0 = c(CSIO) + d(ACSIO)
Open-grown crown width
where
AD = the change in d.b.h. (in.),
d.b.h. at the beginning of the
growth period (in.),
no = the
is used by Arney,
Bella, Ek, Newnham, Lin, and Staebler in
determining their competition indices. The
crown width formula is that used by Arney
(1973) in his analysis combining data from
British Columbia and Oregon:
CW = 4.0223 + 2.1223 (DOB) - 0.0220 (DOB)2
Competitive Stress Index at the
beginning of the growth period, and
CSIO = the
ACSIO = the change in CSI due to thinning
before the beginning of the growth
period.
This model was chosen because it had the
highest R2 and the lowest MSE of all the
where
ON = crown width (ft), and
DOB = diameter outside bark (in.).
Input
data
to
the
coordinates of each
initial
diameter
at
program
were
x-y
the tree number,
breast height (DO),
tree,
3
diameter at breast height (D1) at the end
of the growth period, and plot number. The
output contained plot number, tree number,
the author's assigned number, DO, AD, CIO,
growth model, Equation 1, was
We
averaged
to the data.
R2
each treatment (three
and MSE over
plots for the two
and over all
plots)
basic
The
fitted
then
growth periods.
and ACID.
CORRELATING PREDICTION WITH MEASURED GROWTH
In the analysis by treatment (Table 2), the
model using Lin's competition index had the
highest correlation with measured growth
lowest R2, 0.616 and 0.695, and the highest
MSE, 0.125 and 0.044.
for both growth periods, 0.684 and 0.804,
and
lowest
the
Quenet's
MSE,
competition
in the 1966-1970 growth period, growth data
heaviest thinning treatments, 1
0.104 and 0.029.
index produced the
from the
and
3,
fit the model best with R2 0.759 and
TABLE 2.
CORRELATION OF GROWTH MODELS USING EACH OF EIGHT COMPETITION INDICES (CIO)
WITH GROWTH DATA FOR FOUR THINNING TREATMENTS IN THE HOSKINS STUDY. MEAN
SQUARE ERROR IN PARENTHESES.
Average
sample
Treat-
meet
size per
plot
Arney
Bella
Ek
1966-1970 GROWTH MODEL:
12
1
0.801
(.062)
16
3
.755
(.092)
17
5
.571
(.195)
18
7
Mean
0.778
(.068)
6
11
3
12
16
7
Mean
Treatment
average
0.759
)
0.699
0.82a
0.750
0.652b
0.796
(.083)
(.049)
(.072)
(.100)
(.063)
.755
.786'
(.076)
(.100)
.736b
.741
.743
.757
.753
(.093)
(.090)
(.092)
(.092)
.566
(.188)
.569
.582
.558
.567
(.186)
(.194)
(.180)
(.190)
.616
.614
.613
(.089)
(.089)
(.092)
.677
.678
.678
.670
(.111)
(.110)
(.109)
(.111)
.623a
(.086)
.684a
(.104)
D = a + hD0
.572
(.100)
.657
(.115)
0.786
0.784
0.802
0.887a
0.750b
(.023)
(.027)
(.027)
(.022)
(.016)
(.038)
.700
.767
(.028)
.772
(.027)
.686
(.039)
.833'
(.024)
(.036)
.763
.765
(.027)
(.027)
.754
(.047)
.755
(.046)
.755
(.047)
.515b
.602a
(.203)
(.189)
.554b
(.105)
.616b
(.125)
.566
(.191)
.565
.593
(.101)
(.095)
.680
.668
(.111)
(.112)
0.787
0.798
(.031)
(.027)
= c(Clo) + d(C1)
0.813
(.037)
(.071)
(.097)
.753
(.093)
.700
0.771
(.034)
.574b
(.051)
.677
.714
(.042)
(.036)
(.030)
.813a
.791
.766
(.020)
(.022)
(.027)
.732
(.037)
.737
(.040)
.737
.706
(.048)
(.054)
.744
(.047)
.704b
(.054)
(.045)
.740
(.037)
.695b
(.044)
.744
.754
(.040)
(.035)
.750
.768
.769
.760
(.036)
(.032)
(.032)
(.032)
a Highest R2 for the treatment.
bLowest R2 for the treatment.
Staebler
(.070)
.584
.731b
Quenet
0.774
(.096)
(.038)
5
Newnham
AD = a + boo + c(Cl ) + d(ACl
1970-1973 GROWTH MODEL:
1
Lin
Hegyl
.804a
(.029)
.773a
.762
.741
(.049)
4
0.753,
respectively.
Treatments 5 and 7
had
correlations of 0.566 and 0.593,
respectively.
In the 1970-1973 growth
period, the growth model for each of the
eight authors fit observed growth nearly
equally.
Treatment 1, the most heavily
thinned, had a correlation of 0.798.
We
combined
data
growth
and
competition-index
1970-1973 and for
treatments 1, 3, 5, and 7 for analysis by
author only.
Criteria for evaluating the
effectiveness of each index were R2 and
MSE.
Four models were fit to the data:
for
1966-1970
and
AD = f (ACID)
AD = f (CIO)
AD = f (CIO, ACID)
AD = f (D0, CIO, ACID)
For the two growth periods, the fourth
model
the highest correlation and
had
However, among the eight
lowest MSE.
overall averages for authors, no one index
is clearly superior to the others.(Table 3).
COMPUTATION TIME
important criterion for selecting a
competition index is the computation time
required. Table 4 lists the time required
with each index to evaluate a forest plot
An
50 by
50 feet in a stand of approximately
280 trees per acre. Six indices are within
40 percent of the fastest model (the Hegyi
model).
The Staebler
competition index was
notably slower.
LIMITATIONS OF DATA
The reader should note that this analysis
was performed on a single set of plots and
a single
tree species within a restricted
set of conditions. A direct comparison of
the results by no means establishes the
true relationship among
the methods.
Alemdag (1978), in a similar study, found
that although some competition indices gave
better results with a given data set, there
was
no consistent pattern among sets.
He
believed the order of results might have
been purely accidental. This study seems
However,
to support Alemdag's findings.
least
required
the
model
Hegyi's
computation time.
TABLE
II
3.-- -
-
-
--
CORRELATION OF FOUR GROWTH MODELS AND EIGHT COMPETITION
INDICES WITH COMBINED GROWTH DATA FROM THE HOSKINS STUDY
PLOTS.
DATA IN LEFT COLUMNS 'BENEATH EACH VARIABLE ARE FOR
187 TREES, 1966-1970; IN RIGHT COLUMNS FOR 133 TREES,
1970-1973. MEAN SQUARE ERROR IN PARENTHESES.
Model Variables
Author
Arney
ACID
0.102
(.236)
Hegyi
0.114
0.314
(.233)
(.124)
0.298 0.453
(.185) (.099)
0.592
0.718
(.108)
(.052)
.735
.025
.006
.371
.578
.511
.697
(.179)
(.165)
(.076)
(.129)
(.055)
(.106)
(.049)
.016
(.258)
.013
(.178)
.379
(.163)
.574
.513
.696
(.077)
(.129)
(.055)
.598
(.107)
.732
(.049)
.030
(.255)
.012
(.178)
.441
.685
.566
(.147)
(.057)
(.115)
.729
(.049)
.603a
(.106)
.741a
(.047)
.060"
.015
(.177)
.381
.542
.533
.651
.585
.681
(.247)
(.163)
(.083)
(.123)
(.062)
(.110)
(.058)
.052
(.249)
.326
(.177)
.579
(.076)
.496
.686
(.180)
(.133)
(.057)
.599
(.107)
.728
(.050)
.003
(.180)
.221
.450
.348
.475
.546b
.660b
(.205)
(.099)
(.173)
(.095)
(.121)
(.062)
.274
(.132)
.588
.709
(.110)
(.053)
Ln
Newnham
0.034
(.173)
D0, CIO, &CIO
(.256)
"gBjeJ'A
Ek
C10, ACID
CIO
Quenet
.052
(.249)
Staebler
.001
.135
.080
.015
.131
.135
(.259)
(.166)
(.228)
(.-157)
(.211)
.603a
11
11
aHighest R2.
bLowest R2.
1I
TABLE 4.
11
AVERAGE COMPUTATION TIME USING
THE EIGHT COMPETITION INDICES IN
THE EQUATION AD = f(D0, C10, ACIO).
Percent slower than
fastest time
Author
Seconds per plot
Hegyi
0.369
Quenet
0.386
4.5
Lin
0.391
5.8
0.425
15.2
Ek
0.444
20.3
Arney
0.462
25.2
Newnham
0.515
39.6
Staebler
2.182
491.5
"Sella
6
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