Al)
'
y
/r
y
1
r l
-,
1
tI
fir
ny
.
a
..
I',
° IA
#
rf
1
'
E
,
la z
I'
-
r\
c
,'
',
In
rJ
;L
'Ii
lid
-,
E
?
'
1
.
., '
'
`
1
rt-a
4
.°
[
,, "
I:
'
°
,
:1411
fi
,w'tya
-
71'.1
December 1952
1
r
1K j ,-tea
RESEARCFL,-NOTE NO,: 9- °
r
Y
L
a
..
IM
4
'
>:
;
'
sir
I
I
K
1
1
r.)
.2 A
r
1
.. E._
4
y.r
u
f
E
..I
Pn'
fo
.. r,
,
''
j.
17
Kv
n
.-
QI:4
.
4'
J
rl
f
M
UR I' -
-=a I
..c. q1tr
_
.
,n
Ir
r, .
d_, °
'rr`.'
11/1+/VP
L
I
.Yi- ..'
1-
,,
,
..
'`
G
t "; 1 Jai Ue'
-
+AJ
1
.
1'
y t"..
-}
1
'
err
'' E-t,
r
t
fl
i
°:t
:/
-
LS.
{
Y:
,ylA
v.lrf it
E
o
Research
p.Y.
°"9a
,F.
r
r
r
.A
1
-t
E@.
4
I
}
r
gX111,
u
'k
"
,
.-
-
,_..J
4
'
,
O''y a
J{
,' .,
.'s1..
-r
I'*-,r« c
.
'
'
5I'
r,
..
-
:
!
n
'{'
SP
f
'
t
k
4
l'
iF
- 'rh ..,sE
fl
r.
CY
rv
_j 1r
n'47
1
,
WLL
7.
I.
nY
.
y..
.,
t
a
!
1h
.- 1
.. Yr/.Y
.c,j4t
7
X
.i
r
EI i
,.r
_
r
`t?Irr
\
"
+E,
,%
{
r.
r
-
1
G
.I
r
>
_
}
Lj
/+i'a'
T1, a7_
{`I
..
r
-
n.
I
If
L44
,
-,,,
.I
'"
a
r
.1
µ
'tT.
;puaeeer
Stt2 gl,;; ,
t
Sal.e1,B,.pregpn
'
r"'
.'
f1
U
'
51
-
-'
J 1A
1
i
'r{
c
.I'F'
TAT'E BOARD OF 'ORES
-
T.v.,'-
-a'fiF
,:
. L,
1.
,
-
4
(30
e;r
'
c
George Spaur,
Dick Berry, F1CIsea 'c11. Dire
d
h
r.'
°
?
^
P
E
,,r.
' h_. 4
'
.
i' .'1
,.l..lx
j`
.!
:..
k
.ar N.1
l
r.l
ar
'
ft l
!T'
:e
. d r'
-_
r!)
,,
r
°
Y
\
. 1 al
i. r o--
'',
'
r/.. .1
,
' r'W
4
[
1
r T[J '.
-
1
Jam.
DAr'N
BEER
E
4
i
I<
F
'
E
S
-;fir"f' ' '
'
II
1'
ti
.
ll`"Z
41
! 2.
-
'
r
1
I 'aE` I
'd
r
I
[
r . .c} r
.'
.
1
x III-
r
t
Y
,
'c ^,
n.
'E1F
-
P
y
71 !
,J
-
ES''
+
'1
4
'a1 `'-'11
F
('
n
'
i
iRT.CLI}7, PER ACRE ON
I'
;
Ys
-
rr1+ i +
1'
t
''
11
n
,
r4 c
t
-
hy'
I
,II`r
E
' F:
ll-
},'y+
vya['ER OF
.(-L}
.-
>7TC
G.'.
5i
REPdON9{TP_0F`
x7HE°,,CKTNG'PEFif,f
1
f
'/w
a
,,'
rE
' ,111( `
r
-°.'.a /,
!I
4
pa
tl:l.
This repoA madre-= assltrl.e ,,by fltnds der 8d ` hroug Wthe
Forest Research and
.'° y1
'
a,v
-
,
®.ntalTT'ax. Aa.t .af 1 L.1
. I,
1J
r
}
G
' Ir
is .r--, :a
"
it
7°
rat
i.:-ia
t
l
a r+
c
{
n1°
.
f u.
'!
dW
I
.
7- r
-
+s
iI
-
t 911
`
-
'+d.
'
- . -. -r =..=.i
,}
7:
-}
- __a
_
. c V.
!
'''
9
-
I
«a
a. {I
..
1
,1? lE
v
'q
t
,. '},'
J,
rr
!3w'
'S
+`
c
. (w
r
I
--lilt
/1
-
,L
,YUr.- --
R
1
..y..IL`°_
F
..
-
_ 4w
c
,.+ w L: -ta u.
INTRODUCTION
In January 1949 "Research Bulletin No. 1 --- A Study of a Stocking
Survey System and The Relationship of Stocking Percent as Determined by
This System to Number of Trees Per Acre" was issued by the Oregon State
Board of Forestry.
The curves found in that publication made possible the
conversion of stocking percent to number of trees per acre.
The curves
have seen considerable use since that time and have been found to be quite
reliable.
The curves, however, were constructed from data taken in the
field on areas which were restocked from natural seed source and were found
to be inaccurate when applied to areas which were restocked as a result of
artificial broadcast seeding either by hand or by aerial methods.
At the
time Bulletin No. 1 was published there was not sufficient data to be found
anywhere in the Douglas fir region to permit the construction of a curve
for areas restocked by artificial means.
There has, however, since that
time been sufficient experimental work and actual projects in direct seeding
so that this type information is now available.
PURPOSE OF THE STUDY
The purpose of this study is to develop a curve on which the conversion from stocking percent" to number of trees per acre can be made.
It will
apply only to Douglas fir in Western Oregon which has been established from
some type of artificial broadcast seeding.
*The stocking percent referred to in this publication is that
derived from the use of the stocking survey system employed by
the Oregon State Board of Forestry and explained in detail in
"Research Bulletin No. 1, January 1949".
REVIEW OF LITERATURE
This note supplements "Research-Bulletin No. 1, Oregon State Board
of Forestry, January 1949".
STUDY AREAS
Approximately 13,000 acres of direct seeding are represented in
the 43 samples used for the construction of the curve.
the majority is in the "Tillamook Burn".
Of this acreage
The intensity of sampling varied
from 120 to 480 milacre samples to a forty acre subdivision.
CONSTRUCTION OF THE CURVE
Field Data
Table I
Sample , No. Milacre
No.
1
Plots
Milacre
Total Number
Found
Stocking %
of Trees Per Acre
No. Milacre I Total Trees
Plots Stocked
1.
660
209
341
31.7
517
2.
692
71
101
11.3
146
3.
932
150
192
16.1
206
4.
568
73
85
12.9
150
5.
1828
226
263
12.4
144
6.
544
148
191
27.0
351
7.
616
145
174
23.6
282
8.
464
87
124
19.0
267
9.
452
77
122
17.0
270
10.
240
67
111
27.9
463
11.
240
82
122
34.2
508
12.
240
90
144
37.5
600
2
Sample
No.
No. Milacre
Plots
No. Milacre
Plots Stocked
Total Trees
Milacre
Total Number
Found
Stocking %
of Trees Per Acre
13.
480
47
62
9.8
129
14.
692
61
74
8.8
107
15.
688
56
70
8.1
102
16.
456
79
125
17.3
274
17.
1040
81
97
7.8
93
18.
1084
183
253
16.9
233
19.
116
22
32
19.0
276
20.
308
49
63
15.9
205
21.
308
57
77
18.5
250
22.
516
61
80
11.8
155
23.
444
39
48
8.8
108
24.
1280
65
74
5.1
58
25.
320
22
26
6.9
81
26.
300
115
265
38.3
883
27.
320
16
18
5.0
56
28.
320
36
57
11.3
159
29.
204
21
24
10.3
118
30.
640
112
157
17.5
245
31.
960
133
187
13.9
195
32.
800
135
184
16.9
230
33.
1120
135
167
12.1
149
34.
320
23
28
7.2
88
35.
320
26
30
8.1
94
36.
320
26
30
8.1
94
37.
320
17
18
5.3
56
38.
700
106
157
15.1
224
3
Sample
Total Number
of Trees Per Acre
No.
No. Milacre
Plots
No. Milacre
Plots Stocked
39.
880
137
157
15.6
178
40.
1120
69
77
6.2
69
41.
880
233
371
26.5
422
42.
280
29
34
10.4
121
43.
640
40
42
6.3
65
Total Trees
Fo und
Milacre
Stocking %
Sample
Using the above data a free hand curve was drawn and balanced.
The standard error of estimate was
number 26 was omitted by inspection.
computed (See Table II).
All remaining samples fell within 21 times the
standard error of estimate so that the original curve became the final curve,
and no further adjustments were necessary.
The curve was completed by addi-
tion of fiducial limits of 12 and 2; times the standard error of estimate
and a straight line curve representing the practical lower limit of the number
(See Table III for cal-
of trees per acre for any selected stocking percent.
culation of fiducial limits.)
STEPS IN THE COMPUTATION OF THE STANDARD ERROR OF ESTIMATE
Table No. II
Sample
No.
% Stocked
Milacres
No. Seedlings
Per Acre
Computed
No. Seedlings
Per Acre
(Est. from Curve)
Deviations
Deviation %
(Deviation
1.
31.7
517
487
+
30
6.2
38.44
2.
11.3
146
145
?
1
.7
00.49
3.
16.1
206
218
-
12
5.5
30.25
4.
12.9
150
169
-
19
11.2
125.44
5.
12.4
144
160
-
16
10.0
100.00
4
2
No. Seedlings
Per Acre
I'Iilaeres
No. Seedlings
Per Acre
Computed
(:Est. from Curve)
6.
27.0
351
399
-
48
12.0
144.00
7.
23.6
282
339
-
57
16.8
282.24
8.
19.0
267
265
+
2
.8
00.64
9.
17.0
270
233
r
37
15.9
252.81
10.
27.9
463
415
+
48
11.6
134.56
11.
34.2
508
533
-
25
4.7
22.09
12.
37.5
600
600
0
0.0
00.00
13.
9.8
129
122
7
5.7
32.49
14.
8.8
107
108
1
.9
.81
15.
8.1
102
98
4
4.1
16.81
16.
17.3
274
238
36
15.1
228.01
17.
7.8
93
95
-
2
2.1
4.41
18.
16.9
233
232
+
1
.4
.16
19.
19.0
276
265
+
11
4.2
17.64
20.
15.9
205
217
-
12
5.5
30.25
21.
18.5
250
256
-
6
2.3
5.29
22.
11.8
155
153
+
2
1.3
1.69
23.
8.8
108
108
0
0.0
00.00
24.
5.1
58
56
4
2
3.6
12.96
25.
6.9
81
83
-
2
2.4
5.76
26.
38,3
883
617
T 266
5.0
56
55
1
1.8
3.24
28.
11.3
159
145
+
14
9.7
94.09
29.
10.3
118
132
-
14
10.6
112.36
30.
17.5
245
242
+
3
1.2
1.44
Sample
No.
27.
% Stocked
2
Deviations
t
.
5
Deviation %
(Deviation %)
Omit by inspection
No.
Milacres
No. Seedlings
Per Acre
Computed
31.
13.9
195
186
9
4.8
23.04
32.
16.9
230
232
2
.9
81
33.
12.1
149
156
7
4.5
20.25
34.
7.2
88
85
3
3.5
12. 25
35.
8.1
94
98
-
4
4.1
16.81
36.
8.1
94
98
_
4
4.1
16.81
37.
5.3
56
58
2
3.4
11.56
38.
1..5.1
2 24
2"11
4
20
9.8
96,04
39.
15.6
178
211
-
33
15.6
2 43,36
40.
6,2
69
70
-
1
1.4
1,96
41.
26.5
422
390
+
32
8.2
67.24
!; 2
10.4
121
133
12
9.0
81.00
43
6.3
65
73
8
11.0
1 21.00
'Sample
% Stocked
Noe Seedlings
Per Acre
(Est. from Curve)
2
Deviations Deviation %
-
(Deviation %)
2 410.50
+ 262
- 287
The standard error of estimate is computed by the formulad u =f4.(d%)
ill
vrhere.-;'u is the standard error of estimate, _(d%)2 is the sum of the squared
deviations in percent and N is the number of samples.
V/ 2410.50
---
j'u\/ 57.39
7.58
42
6
l1X-lu= 11.37
2 Xdu=18.95
FIDUCIAL LIIIIITS
Table No. III
1
AVE
4
5
6
u
2; u
2X3
2X4
3
2
l;
8
7
Upper lz
2
5
5
55
11.37
18.95
6
10
61
10
127
11.37
18.95
14
24
141
15
202
If
tl
23
38
20
280
11
1!
32
25
364
30
Lower 12
2-5
9
10
Upper 21
Lower 22
2+ 6
2- 6
65
45
113
151
103
225
179
240
164
53
312
248
333
227
41
69
405
323
433
295
452
51
86
503
401
538
366
35
550
63
104
613
487
654
446
40
650
74
123
724
576
773
527
4
USE OF THE CURVE
The Curve is the final result of the study.
It can be used to convert
percent of stocking to number of trees per acre on areas restocked by artificial
broadcast seeding.
Inasmuch as the curve is based on samples from Douglas fir
seeding in western Oregon it rill be of most use in this area and with this
species.
stocking.
The data available will support conversions up to 35-40 percent of
It is not felt that an extension of the curve beyond that point
could be justified.
The samples used in this curve represent areas seeded
at the rate of 1/4 pound per acre to 1-1/2 pounds per acre.
Inasmuch as
there was no discernible difference in the ratio of stocking percent to number
of trees per acre found in these samples it seems reasonable to assume that
for practical purposes the amount of seed broadcast per acre makes no difference
7
i.RMeM.MEe.e..e...neeM.iii.e..e..uraEMON
.EMNMM..Oer.R.R..
.raR
aa...u.O...... rEa 0.
Ml
750
700
65
..
.
.....r....
,
®pmmO0.. O.reumm1 i NM...
MEMMUN:
............. ................................................ ........Runs
.......................r
... .MEMO.
eree.e.0..ee
.uu errRa._...RN.M
NOM.Or..eMMNee.M..
m7mSS7m
.MM.....
Re.au....
.......RrNe.
0 .RSE.
..a...r.
rere..ee..rRe
...e.a.e.e
err0
iii Ti:n.rQ
.ee.e...eRe..e.NauMer.
-.rr
..rM.NM.
.NeNN..N...MMEE.Rw
e.RR...aera...rMR.s
a.reR.e.M.eEe DiR ..ar
1!!!!!!!!!!!!!!.!P!
M.eer..
r..uMReJe.Oe. rMeeO. .. /i....r0
...............
_::::::::::::::UU::
...ME'e....a..ra.y
/
Re...e.ee.eeeeees....,
.e.......e.........E........ + ...0..e.e.0
/eer..
R....!r.t Y..
...ua.an
f7
ae
I /iGF
/
7
I ea
.e.r."ON.NrNE..N.e.e..OR.NNeEo
0.meNReMN.M.a.NNO..MMRRrM
m.eL].
::::Ee::::::::::::ee
reer...
NNR.uMe..M.rr
®mm7ROU.R.RR.u..u
,_.
..............................rr..rrr.E.rrEr.ErB.
.............................NO.O.er......
.
aI
/
Aa
................OO.R.
., ...rrMRR
.e.OOrE.O.
/:
550.r.e
........................I.......................
...
.
......
'
O.M.N......e............e.
.mi
rMN.M.eeR
/
.y
r.een.'
'.
i
/
..u.M.EMaEa.
/..........N..r
A IGi ,"e.eeE.
......rORe'neeeeN.nOr
Jr
.. . . . . . .. . . . . . . . .. .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .
600:::::
..
mm
ME,
............ ..
:M1111111mom
0..,/ 1 .r..r
-% .
rR
/ir
..e..,
a
MOONS
SJO.
.........................................................`
.
I
1111.
a,
U...NNe
1111
1111
lUUUUU...e.MEN
50
S
........LJ......e[
tell
.e
a. ear.eeeeeeraRR
................................................... ,
®®rRir.e.e.ee..ef
...EeerNr.E..y...
450
..M......r.
.......
err.r.............
Ie .IU ;t
..00. 000..... . rr ........
rr.
qz
LU
0.
351
ti
........
immium
.........r.....aN.MNNe-y'
..F, Era
.......e
....r.
a.
won::
V
............
1111I
1 /7II!i!!U!!UU
........
1111
...11.11.
.
'J o
amannommossums
i 6 /
/
UIUUUUUUU::::::I000U
,
+iO. ....e.o.. .eE w
E ON
NNNNNNNNNNNN NNNNNNNNNeN
®mo
/ Srraa
I
4f
25'
Or
iti ®
ENR y
Rr05
/
/
/
........ .................
Essumass
',
tin....
:
r. e /
-FEM. .
.
'...
NONE _
Sam
M
'
30 I..
0:00
Yp
000
...
OR
......
...........................
ee........RM'aaauNOu
!,iuuuuuuuuuuuunuar
uun RM.
a u
a
.eM
.I..re.e......ee...R.rar
'..........4
.....
.....a..............r.
rMRerMR..nNe.N.NR.
.u,
.Muu.EMu.r..uaurmNr
.r.// RrN.R
N.a
uuYuo.u.
Hiiiii "'
.....ar.
""""""""'
e... ..rrr.
....................:
I"e.'
".e / eeR.M
wommomom
200 ..... ................../_
.NN.eMER 4Ok//
uouuua..j/
......t.
r
N.ea_
5'0
i ......................
.
/ei
1111
::....UU............: :::.......... y'//SQ,
G
150
.e..ee.r
ee.e®.....
1111
1111
/
/
I _/rP-
d
a
LeiNm..e.EEEEaE
Rro00........
L.Mm.Re.
..RMNRMeN. }
Iree.err
ORN..OM...OI-5L
r r .ee
a.a
'
.....
51r.ErEO..r.
........
... .............................
I...
'ge ........
............
ORO.RO.e..OeOR
,_Err .Errr.r rrr
ReeErr.r %
SOMEONE
0
1111
1111
1111
mmmmmmmmmmmmm
.......................................
...SO....R....a..
........I.......
J/. ....................
M.aeNeONr
.............e..
®.rR...R.
j.M
J.
.
/
RONN0eaMR..MER.
nEONENnneNnRM.EOrurn
...a...
OEON
OEM
.rNNRMeNMrr
1111
'tin
+/
1.E. ..NNUNN
L.e.e..U....
'ROME
rR rI
400I.NNMRM.
SI/
.1
.0
...
e.u
t
Y
_'
-
"'
.......e...rr
....UE.r...a
ae.U.Err.
A /
RATIO OF MILACRE STOCKING PERCENT TO
NUMBER OF TREES PER ACRE ON
:::::::EMMIM.:::::
ARTIFICIALLY SEEDED ACRES
:00111:60 :111:01:60:00 00HUMMIN: MOORE
uuun.u"uuuu"uanuYuu
0
STATE BOARD OF FORESTRY -SALEM, ORE.
e".""".r
Ue..e
:
OREGON
5
10
IS
(DOUGLAS FIR
WESTERN OREGON)
CURVE OFAVERAGE VALUES
20
STOCKING
FIDUCIAL LIMITS I'/z HN!
UPPER FIDUCIAL LIMIT 2V26u-
25
30
PERCENT
35
40
Manor am
45
SO
to the ratio.
Financial considerations at the present time preclude a great
increase in the amount of seed per acre it would be possible to use.
If,
however, for experimental reasons an area were to be seeded to 3, , or even
8 pounds of seed per acre and a milacre stocking of 40% or less were obtained
it is quite possible that the curve ratio might need some adjustment.
Fiducial limits of 1
standard errors of estimate and 22 standard
errors of estimate have been placed on the curve for the convenience of the
user.
The fiducial limits of 12 standard errors of estimate include 86.6
percent of the probabilities within those limits.
Fiducial limits of 22
standard errors of estimate include 98.8 percent within those limits.
SUM&ARY
This research note is being published to make available a curve that
can be used to convert from milacre stocking percents to numbers of trees per
acre on areas of western Oregon which have been artificially restocked to
Douglas fir by some means of broadcast seeding.
This report supplements "Research Bulletin No. 1 - Oregon State Board
of Forestry, January 1949" which furnished similar curves for use on areas in
the Douglas fir type which have been restocked from natural seed sources.
The curve, produced here, based on field surveys of approximately
13,000 acres of direct seeding, is usable for the conversion of milacre
stocking percent to number of trees per acre for stocking up to 35-40 percent.
There is not available at the present time sufficient data to permit construction of a curve for the higher percentages.
Fiducial limits of 11, and 22 standard errors of estimate have been
placed on the curve for the convenience of the user.
8
These limits represent
86.8 and 98.8 percent of the probabilities within those limits respectively.
If direct seeding continues to expand as a forest practice at its
present rate and the results of the more successful seedings become available
this curve should be, in the near future, enlarged to encompass the higher
stocking percents.
9