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.
INCORRECT HEIGHT-AGE CURVES
AND BIAS IN BULLETIN 201
•
McArdle
and Meyer's Douglas-fir
(Pseudotsuga menziesii) yield tables,
first published in 1930 (McArdle and
Meyer 1930) with later revisions
(McArdle et al. 1961), were a milestone
in Douglas-fir management. Their
demonstration of Douglas-fir produc­
tive potential was a major factor in the
transition from an extractive economy
to one based on planned timber man­
agement. For many years these tables
were the bible that shaped foresters'
conceptions of Douglas-fir stand
growth patterns. They still have an in­
fluence despite recognition that "nor­
mal" stands are not the goal of man­
agers and despite recent development
of a number of simulation programs
that generate alternative yield tables.
Mean annual increment (MAl) is to­
tal yield divided by stand age. Age of
culmination of MAl, the age at which
maximum average production is at­
tained, is a reference point useful in
forest management. MAI at culmina­
tion is used by some as an expression
of site productivity. The National For­
est Management Act requires that ro­
tations on national forest lands shall
not be Jess than approximate culmina­
tion age. And, with current interest in
extended rotations as a possible strat­
egy for reconciling timber production
with recreation, aesthetic, and wildlife
needs, there is also a need to evaluate
the effect of such policies on yields.
Inferences on shape of the MAl curve
and age of culmination drawn from
McArdle et al. (hereafter referred to as
B201) have had and still have a consid­
erable influence on forest managers'
thinking.
This note (1) recapitulates the state­
ments of B201 regarding culmination
of MAl, (2) calls attention to an appar­
ent bias in B201, and (3) points out ef­
fects of this bias on estimates of MAl
culmination ages.
1
Pacific Northwest Research Station, For­
estry Sciences Laboratory, 3625 93rd Ave­
nue SW, Olympia, WA 98502.
0
Table 1. MAl culmination ages (as taken from
8201 tables 2, 3, and 4).
Site II
Site Ill
Site IV
MAl culmination ages (as taken from B201 tables 2, 3, and 4) are shown in Table 1. The merchantability limit
used obviously has a strong effect on
age of culmination, and this effect is
much greater on poor sites because of
the longer time required to reach any
given lower merchantable size limit.
All
trees
Trees
7" + dbh
Trees
12" + dbh
65
65
65
65
70
80
80
95
115
CULMINATION OF MAI
ACCORDING TO B201
Total stand volumes in cubic feet by
total age and site index are presented
in B201 in three tables:
Table 2: for all trees 1.6" + dbh
Table 3: for all trees 7" + dbh
Table 4: for all trees 12" + dbh
Of these, table 2 corresponds to bio­
logical production of stemwood, table
3 to very close utilization (sometimes
approached today), and table 4 to a
utilization standard common at the
time but lower than is common today.
The basic procedure used to prepare
normal yield tables in the B201 era was
to (1) fit an average height-age guide
curve to a collection of temporary plot
data, (2) derive a family of height
curves from this guide curve by pro­
portion or otherwise, (3) use this fam­
ily of curves to assign site index values
to field plots measured for volume, (4)
group plot volumes by site index
classes, and (5) draw average curves of
volume over age for each site index
class.
It is now generally recognized that
guide curve procedures are often seri­
ously biased, because they depend on
the untestable and often incorrect as­
sumption that the sample contains
equal representation of all sites at all
ages (Monserud 1985). Any bias in the
estimate of height-age trends is neces­
sarily reflected in estimates of volume­
age relationships.
Since McArdle's time, stem analysis
methods have generally replaced the
old guide curve methods for construc­
tion of height growth curves. Several
sets have been constructed-for coastal
Douglas-fir, notably those of King
(1966) from western Washington data,
20000
18000
16000
'Vi'
(!)
(!)
14000
'ia
12000
0
til
10000
(!)
8000
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ai
'-
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::::,
E
:l
:g
Ill
6000
4000 2000 0
0
20
40
60
80
100
120
Total Age (yrs)
Figure 1. Volume yield curves for all trees from B201 table 2 (1) as published (solid) ' and
(2) adjusted to King (1966) height curves (dashed), sites II, III, and IV.
WJAF 7(4)1992
97
200
I
v... I.·······
.
..
7
7· v .. .
/71 ..1-'
111// .. 1 .......
if?. . .
lf..··
180
.
160
(ij'
(I)
140
=;a
120
(I)
.....
100
(;)'
80
<(
:E
60
-
....-.
tion for converting McArdle's site in­
dexes (100-yr base) to equivalent King
site indexes (50-yr base):
i""oo.t..
.
..
.
.
40
.
•
41 • ••
••
.
..
--
II ..
Ill
'·
.:.k
\
..
..
·
..:..:..s
IV
.
•
20
0
I
0
20
40
I
I
60
80
I
100
120
Total Age (yrs)
Figure 2. Mean annual increment curves for all trees from B201 table 2 (1) as published
(solid), and (2) adjusted to King (1966) height curves (dashed), sites II, III, and IV. currently the most widely used; and
those of Hann and Scrivani (1987)
from southwest Oregon data. Means
and Helm (1985) and Means and Sabin
(1989) have also constructed curves
from stem analysis data from localized
areas. Bruce (1981) constructed curves
from region-wide periodic permanent
plot remeasurement data.
The newer curves differ consider­
ably from McArdle's, generally show­
ing height growth patterns with rela­
tively slower early growth but with
growth sustained to greater ages. The
Hann and Scrivani (1987) curves differ
most, while the King (1966) and Bruce
(1981) curves are intermediate and
closely resemble each other.
REVISED B201 VOLUMES
ADJUSTED FOR BIAS IN
HEIGHT-AGE CURVES
Volumes given in B201 can be ad­
justed to remove the bias introduced
by differences in height growth
curves.
King (1966) gives a regression equa­
200
180
:2
.0
"0
r:: (I)
(I)
..:
..... ()
<(
:E
160
140
120
Ill
100
••
80
...
,t, •• • •
..
IV
60
40
20
0
0
20
40
60
80
100
120 Total Age (yrs)
Figure 3. Mean annual increment curves for trees 7'+ dbh from B201 table 3 (1) as pub­
lished (solid), and (2) adjusted to King (1966) height curves (dashed), sites II, III, and IV.
98
WJAF 7(4)1992
S50
=
21.5 - 0.18127
(TOTAL AGE)
+ 0.72114 * S100.
*
Starting with values given in B201 ta­
bles 2, 3, and 4, S100 values were con­
verted to King site indexes (S50) by the
above equation. For each age, volumes
were plotted over King site index, and
values were estimated by linear inter­
polation for King site indexes of 126,
104, and 83 to produce new yield ta­
bles based on King's curves. (These
site index values correspond to McAr­
dle site indexes 170, 140, and 110, and
are referred to hereafter as sites II, III,
and IV.)
Figure 1 compares the original B201
table 2 volumes (all trees) with the cor­
responding volumes after the above
adjustment. These values were con­
verted to MAis and plotted over age.
Figure 2 compares the original B201
values for table 2 (all trees) with the
adjusted values. Figures 3 and 4 do the
same for table 3 (trees 7'' +) and table 4
(trees 12" +). Revised culmination ages
are shown in Table 2.
Figure 5 displays all the above ad­
justed curves on a single graph, illus­
trating the effect of merchantability
limits on shape of the volume growth
curves.
CONCLUSIONS
1. The patterns of volume develop­
ment and age of culmination of
MAI are strongly influenced by the
minimum merchantable size limit
adopted, particularly on poor sites.
This fact is self-evident though
sometimes not recognized by those
with little mensurational back­
ground.
2. Differences in height growth pat­
tern have a strong influence on vol­
ume growth trends and on age of
culmination of MAL (Differences
from B201 estimated volumes and
culmination ages would have been
even greater had the Hann and
Scrivani curves been used instead
of King's.) This fact is not generally
appreciated and emphasizes the
importance of accurate measure­
ment and estimation of height
growth trends. It also implies dif­
ferent culmination ages for sites
which have height growth trends of
different shapes although nomi­
nally of the same site index.
3. Adjustment of B201 values t o
King's height growth curves results
in substantially later culmination of
MAI, and produces MAI curves
that are considerably flatter in the
vicinity of the culmination point.
These characteristics indicate that
200
rotations to enhance aesthetic, rec­
reational, and wildlife values
would not necessarily reduce long­
term timber production.
180
160
:2
.a
"0
+
140
N
..-
V)
a>
a>
!:> 111
100 ..:
a>
...
u
--- ...
120
80
--
"""'"'_,.
IV
60
::E
40
20
0
0
20
60
40
80
100
120
Total Age (yrs)
Figure 4. Mean annual increment curves for trees 1 2"+ dbh from B201 table 4 (1) as
p ublis h ed (solid), a n d (2) a djusted to King (1966) h eig ht curves (dashed), sites II, III, and
IV.
Table 2. MAl culmination ages, as read from
curves shown in Figures 2-4.
Site II
Site Ill
Site IV
All
trees
Trees
7"+ dbh
Trees
12"+ dbh
70
80
90
75
85
105
90
105
120+
yield reductions associated with
very short rotations are greater
than indicated by B201 and that
there is a fairly wide range of ages
in the vicinity of the culmination
point with .substantially the same
yield. This in turn suggests that
some lengthening of conventional
200
160
a>
Cl)
!=
140
'iij
120
Cl)
.....
100
..:
I
::E
LITERATURE CITED
D. 1981. Consistent height-growth and
growth-rate estimates for remeasured plots.
For. Sci. 27(4):711-i25.
BRUCE,
R. 0. 1992. Levels-of-growing-stock coop­
erative study in Douglas-fir: Report no. 11­
Stampede Creek: A 20-year progress report.
USDA For. Serv. Res. Pap. PN\A.'-RP-442. 52 p.
CURTJS,
D.W., AND J.A. SCRIVANl. 1987. Dominant
height growth and site index equations for
Douglas-fir and ponderosa pine in southwest
Oregon. Oregon State Univ., Cell. of For., For.
Res. Lab Res. Bull. 59. 13.
HANN,
180
V)
The later culmination of the ad­
justed values is consistent with obser­
vations in a number of long-term per­
manent plot studies (e.g., Curtis 1992)
that seem to indicate culmination ages
greater than shown by B201. It is also
considerably closer to predictions of
the ORGANON simulator (Hester et
a!. 1989) which uses height growth
curves markedly different from those
of B201.
"Normal" stands are not usually a
management goal, and treatments
(stocking control, fertilization, etc.)
applied to managed stands will intro­
duce other factors (mortality differ­
ences, gross volume increment differ­
ences, diameter increment differences)
that will alter the shape of the volume
growth curve and time of culmination
in undetermined ways. But the two
factors of merchantability limits and
height growth patterns will necessar­
ily also have strong effects in managed
stands.
0
II
Ill
A.S., D.W. HANN, AND D.R. LARSEN,
1989. ORGANON: Southwest Oregon growth
and yield model user manual. Version 2.0. Or­
egon State Univ., Coli. of For., For. Res. Lab.,
Corvallis. 59 p.
HESTER,
J.E. 1966. Site index curves for Douglas-fir
in the Pacific Northwest. Weyerhaeuser For.
Res. Center, Centralia, WA. Weyerhaeuser
For. Pap. No. 8. 49 p.
KING,
I
.,.,
I.,...-
80
IV
r
60
R.E., AND W.H. MEYER. 1930. The
yield of Douglas-fir in the Pacific Northwest.
USDA For. Serv. Tech. Bull. 201. 64 p.
McARDLE,
R.E., W.H. MEYER, AND D. BRUCE,
1961. The yield of Douglas-fir in the Pacific
Northwest. USDA For. Serv. Tech. Bull. 201
(rev.). 72 p.
MEANS, J.E., AND M.E. HELM. 1985. Height
growth and site index curves for Douglas-fir on
dry sites in the Willamette National Forest.
USDA For. Serv. Res. Pap. PNW-341. 17 p.
McARDLE,
40
20
0
0
20
40
60
80
100
120
Midperiod Age--yrs
Figure 5. Mean annual increment curves from B201 tables 2, 3, and 4 adjusted to King
(1966) height curves (1) all trees (solid), (2) trees 7"+ dbh (dotted), and (3) trees 12"+ dbh
(dashed), sites II, III, and IV.
J.E., AND T.E. SABIN. 1989. Height
·growth and site index curves for Douglas-fir in
the Siuslaw National Forest, Oregon. West. J,
Appl. For. 4:13&-142.
MEANS,
R.A. 1985. Comparison of Douglas­
fir site index and height growth curves in the
Pacific Northwest. Can. J, For. Res. 15:673-679.
MoNSERUD,
W}AF 7(4)1992
99