Estimating productivity on sites with a low stocking capacity

Historic, archived document

Do not assume content reflects current
scientific knowledge, policies, or practices.

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Uns USDA FOREST SERVICE RESEARCH PAPER PNW ~152
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1973

CORE LIST

IMATING PRODUCTIV!
ON SITES WITH A LOW
STOCKING CAPACITY.

T

U.S, DEPT. OF AGRICULTURE enn
U tf [AGI Age WS ae e

25
COLIN D. MACLEAN
AND

CHARLES L. BOLSINGER

EO REST AND

IeULTURE RANGE EXPERIMENT STATION» 475//

oe FOREST SERVICE
PORTLAND OREGON

OR Tar ee Te Oey RMR PAL Raa. Tara se SPU IDOIO

ABSTRACT

In most areas, normal yield tables are the only tools
available for estimating timber productivity and establishing
stocking standards. However, the stocking capacity of
naturally sparse stands in the arid West is often lower than
was found in the stands sampled by the makers of normal
yield tables. Normal yield table estimates, therefore, may
indicate high productivity and understocking for stands that
are really well stocked but not very productive.

About half of the commercial forest land in the areas
studied--eastern Oregon and northern California--appears
unable to support normal yield table stocking levels. Two
methods are presented for identifying and quantifying this
limitation. The first method is to develop factors to dis-
count the normal yield tables in habitat types where a stock-
ing limitation exists. The second method, for areas where
habitat types have not been classified, is to predict stocking
capacity from multiple regression equations based on site
index, elevation, and the presence of certain indicator plants.

KEYWORDS: Stand density, indicator plants, productivity,
stand yield tables.

CONTENTS

Page
INTRODUCBION ssi". 25. O10 O8O 7 Oke BO ol6 Ae ceifeiaeor rented brelairobhied Be Nesnievt ofits di

IMPACT OF LIMITED STOCKING CAPACITY ON FOREST
LEAR OID UK IEIWAMING “506 oud Cos osGmonOno rere otae aeane, eilelicfmettels ove -ei) ‘etl 'e 2
J (GBIN/LOIRVNIC) EET OVAGIEL so) 485" OF Gms In On ONO) CO NOL Omic IO ROnGnC)CMOnOUONCnOmG . 4
A PROCEDURE FOR EASTERN OREGON ....22.eseecccscececce 5
A PROCEDURE FOR NORTHERN CALIFORNIA ......+2e-2c-eesecc8 8
A Possible Approach e e e e e e e e e e e e e e e e e ‘or 4@)) (0, 70) (0), ce e e e 8
Developing a Multiple Regression Equation ......+..se-eeeee8 9
How Good Are the Equations? e e e e e e e e e e e eo e e e e e e e e e 11
Developing Plot Discount Factors ......2¢seccscseccee Sie 13
Resultspineshastavand MrinityrCOuntieS sie. < ss ee + + 0 «6 « 0 6 e 13

Developing Plot Discount Factors for Three Other

Geographic Units e e e e e e e e e e e eo e e e e e e e e e e e e e e 13
CONC LUSIONS e e e e e e e e e e e e e e e e e e e Oe) Orie: '@ 20,110) He *e e eo e e 15

PRAGUE CED cokes sels ec eee flees 6 eoeeee e @ @ @), {oF 1.6)7<0 16

INTRODUCTION

In the arid West, stands of trees on
the lower forest fringe are often surpris-
ingly sparse, in spite of a moderately
good site index and a history unmarked
by either human disturbance or natural
catastrophe (fig. 1). Such stands appear
to have always been lightly stocked.
Wikstrom and Hutchison (1971), comment-
ing on this condition, observed that

. . . the assumption that the
area being evaluated can support
as many trees as the land on
which the yield table data were
collected. . . is not always
true and is not generally true

on the more arid fringe of the
forest. In areas of low rainfall,

each tree requires more room
than is "normal" to fulfill its
moisture requirements.

Despite their understocked appearance,
such stands are often fully utilizing the
site's capacity to grow trees.

Naturally sparse stands may also
occur where physical obstructions
inhibit tree growth over part of an area.
Trees may be growing in pockets of
deep soil or cracks in the bedrock,
interspersed with small areas where
the soil is too shallow to grow trees.
Such stands also often appear under-
stocked when, in fact, the site may be
fully occupied.

Figure 1.--Ponderosa pine on the Colville Indian
Reservation growing near the lower limits of
tree occurrence. Stands such as this are
naturally sparse.

IMPACT OF LIMITED STOCKING CAPACITY
ON FOREST PRODUCTIVITY

“at. 7 v———— |

In areas where moisture is limited, refer to anormal yield table for the mean
shallow soil and rock outcrops common, annual increment at the point of culmina-
or other extensive limitations on stocking tion for that site index. This estimate of
capacity present, a corresponding reduc- the productive potential for well-stocked
tion in forest productivity is likely--an natural stands forms a basis for compar-
effect often ignored in timber inventories ing the productivity of different areas. “4
(fig. 2). Forest management decisions It is used in this manner by the nationwide
are strongly influenced by the quality of Forest Survey of the U.S. Forest Service.
available estimates of productive potential Many others use site index as a means of
and of current stocking level--the degree ranking productivity without attempting to
of utilization of the potential productivity. quantify the estimates. The soil vegetation
Failure to recognize stands with limited maps of California, 2/ for example, show
stocking capacity may result in costly Dunning's site class (Dunning 1942) for
management errors. For example, if every commercial forest land type island.
stands identified as poorly stocked are The tabulation or mapping of forest land
really sparse stands fully occupying sites into site classes is a widespread practice
with limited stocking capacity, then a among forest managers.

planting program would fail.
Implicit in these approaches is the

In most areas, estimates of produc- assumption that all acres having the same
tive potential are based on normal yield site index are equally productive. The
| tables--the only available sources of widespread acceptance of this assumption
| productivity information. One procedure is evidenced by the importance generally
| used is to measure the site index, then placed on site index information when

making management decisions. However,
the assumption that forest productivity
depends on site index alone and can be
measured by normal yield tables is valid
only when the area of interest has environ-
mental conditions that fall within the range
of those sampled by the maker of the yield
table.

Stocking standards also typically
rest on the assumption that all acres with
a given site index are equally productive--
at least within a forest type. Present
growing stock--usually expressed as basal
area or number of trees per acre--is |
compared to a stocking standard that is
often derived from normal yield tables.
This comparison provides an indication

Y/ Compiled by the Soil- Vegetation Survey conducted
Indian Reservation severely restrict stocking by the Pacific Southwest Forest and Range Experiment Station
capacity. The site index is 60 and the total in cooperation with the University of California for the

5 California Division of Forestry.
basal area is 45 square feet per acre or 26
percent of "normal."

2

of how well the productive potential of

the site is being utilized. However, stock-
ing estimates obtained in this manner are
again only valid for areas that fall within
the range of conditions sampled to develop
the stocking standard.

Areas with patchy stands, nonforest
inclusions, and sparse stands on the forest
fringe are situations that evidently were
not sampled by the makers of yield tables.
Meyer's ( 1961) ponderosa pine (Pinus
ponderosa)— yield table is based on a
sample which excluded all plots with a
stand density index of less than 250 (250
trees per acre when quadratic mean diam-
eter is 10 inches). Data collected by
Hall?/ in the Blue Mountains of eastern
Oregon suggest that substantial areas of
ponderosa pine type will not support this
many trees.

Data gathered for this study suggest
a similar situation in California. Stock-
ing capacity also is obviously limited,
possibly because of soil toxicity, in stands
of Jeffrey pine (Pinus jeffreyt) growing
on serpentine (peridotite and serpentinite
soils) in southern Oregon and northern
California (fig. 3). We have observed
similar restrictions on stand density in
stands of other species growing on dry
sites, and Wikstrom and Hutchison (1971)
report the condition to be widespread in
the intermountain and Rocky Mountain
regions.

The assumption, implicit in most
yield tables, that stocking capacity is
constant for a given site index has been
questioned by several European authors.
Assmann (1959) found substantial varia-
tion in Norway spruce (Picea excelsa)

yields that he was unable to explain by
site index. Bavarian spruce yield tables
(Assmann and Franz 1965) reflect these
findings by dividing each site index class
into three production classes. ' Recent
British tables (Bradley, Christie, and
Johnston 1966) are similarly divided.
Locally, data from Hall's (1971) ecological
study of the Blue Mountain region of east-
ern Oregon indicate that basal area carry-
ing capacity is more closely related to
plant community than to site index.

Under what conditions are the pro-
cedures described above inappropriate ?
One such situation occurs when small
patches of nonforest land, usually avoided
by the makers of normal yield tables, are
included in the forest land sample. Such
patches may be deliberately combined
with forest land because they fail to meet
some previously defined minimum area
standard, or they may be patches of
scabland--nonforest inclusions incapable
of growing trees--that have been mistaken

Figure 3.--Jeffrey pine growing on serpentine
(peridotite soil) north of Grants Pass,

2/ Names of trees according to Little (1953).

3/ Frederick C. Hall, unpublished data on file at the
Regional Office, U.S. Forest Service, Portland, Oreg.

Oregon. The stocking capacity of this area
is severely limited. Although the site
index is 95, the basal area is only 24
Square feet per acre--about 11 percent of
"normal" stocking.

3

for nonstocked forest land. In either case,

conventional procedures based on site
index and a normal yield table will lead

to overestimation of potential productivity
and underestimation of stocking. As
previously pointed out, this combination
of errors, in turn, may lead to the identi-
fication of an apparent treatment oppor-
tunity where none exists.

Conventional procedures are also
inappropriate for assessing the potential
productivity and stocking of sparse stands
near the dry lower forest fringe--the sort
of stands referred to by Wikstrom and
Hutchison (1971). Such stands may have
as few as 15 or 20 trees per acre and no
evidence that stocking has ever been
greater. They are often on deep soil
and display a site index as good as that
found in much denser stands at higher
elevation. Ecologists, silviculturists,
and other forest scientists that we talked
to were in general agreement that such

stands, if uncut and free from catastrophe,
are in fact fully occupying the site even
though stand density is far below that indi-
cated by normal yield tables. This is a
logical assumption if one accepts the
premise implied by the normal yield tables
and accepted by Franz (1967) that stands
allowed to develop in an undisturbed con-
dition tend toward an equilibrium at a

", . . natural basal area [that] is an
expression of the productive capacity of
the site."

A proper method for estimating pro-
ductivity on sites with limited stocking
capacity entails comprehensive site and
yield studies. Since such data are years
away, the urgent need for good productivity
estimates encouraged us to develop some
alternative solutions that would improve
Forest Survey productivity estimates. Two
such solutions are presented here--one for
an area where considerable research data wer
available and one for an area lacking such data.

A GENERAL APPROACH

Before examining specific localized
procedures, let us first consider the
general problem of identifying and quanti-
fying restrictions on stocking capacity.
The easiest part of the problem involves
such obvious restrictions as rock out-
crops. [If half a plot is solid rock, then
a 50-percent reduction in productive
capacity seems logical. Likewise, the
stocking standard for that particular plot
should be only one-half that for a fully
productive plot. If the plot is bisected
by a creek, the answer is not so obvious
since the trees may, to some extent,
utilize the soil under the creek and the
air space over it. Nevertheless, since
creek bottoms are usually either very
stony or saturated with water, it is
probably more reasonable to assume
that the creek is nonstockable than to
assume that the potential productivity

of the acre is unaffected (fig. 4).

Identifying small patches of land with
soil too shallow to grow trees is more
difficult. Fortunately, the plant commun-
ities growing on such scabland areas are
usually distinctly different from those
found on timber growing sites. On the
Modoc plateau in northern California,
for example, Artemtsta arbuscula 4
is an indicator of nonforest land.2/ If,
with the help of ecologists, we can learn
to recognize the plant communities that
occur only on nonforest land, then we can
handle such areas in the same manner as
rock outcrops and streambeds.

= Names of grasses, herbs, and shrubs follow Munz
and Keck (1970).

} Conversation with Frederick C. Hall, range ecologist,
U.S. Forest Service, Portland, Oreg.

Figure 4.--It is reasonable to assume that
this creek bed is nonstockable.

Learning to recognize sites that grow
trees but are limited in stocking capacity
is acomplex problem. If we accept the
premise that undisturbed stands tend to-
ward equilibrium (Franz 1967), we can
seek out such stands and compare their basal
areas with those predicted by a normal
yield table for the same stage of develop-
ment. Those stands with less than "normal"
stocking (including recent mortality) can
be assumed to have a stocking restriction.
By measuring such stands, we could build

anew "normal yield table" for sites with
restricted stocking capacity.

But how can we recognize restricted
stocking capacity when disturbance has
removed part or all of the tree cover?
One way would be to study the effect on
forest stocking of all the various physical
factors which affect the environment: soil,
microclimate, available moisture, slope,
aspect, etc. Such an approach seems
time consuming for an ecologist and
probably hopeless for the average

inventory crew. Even detailed soil infor-
mation, although prospectively highly
useful, is not easy to gather in most
inventory situations.

Fortunately, the plants growing on
a site offer an important alternate source
of information. Plants or plant commu-
nities have often been used as indicators
of environmental factors present, particu-
larly those which are critical to plant
growth on a particular location--e. g.,
moisture, temperature, fertility, etc.
(Daubenmire and Daubenmire 1968,
Dyrness and Youngberg 1966, Griffin 1967,
Poulton 1970, Waring 1969, Youngberg
and Dahms 1970). If plant communities
representing various levels of forest
productivity can be identified, then sepa-
rate yield tables can be developed for
each community, or in place of this,
discount factors computed for existing
yield tables.

A PROCEDURE FOR EASTERN OREGON

The first phase of this study was an
effort to use plant community information
to identify areas where stocking capacity
is restricted and to improve productivity
and stocking estimates on such areas.
Fortunately, F. C. Hall, Range Ecologist
for the U.S. Forest Service's Region 6,
had recently developed a habitat type

(plant community) classification scheme
similar to Daubenmire and Daubenmire's
(1968) for the Blue Mountain region of
eastern Oregon, an area where a Forest
Survey timber inventory was currently
in progress.

Hall also developed a key (see

footnote 3) for determining plant commu-

nity, even when disturbance has destroyed

the climax vegetation. In addition, he
estimated the average basal area and site
index associated with each plant commu-
nity from measurements in undisturbed
stands. Hall's data indicated that six

plant communities grew on sites incapable

of supporting "normal" levels of stocking
(fig. 5). The ratio of Hall's basal area
data to equivalent normal yield table data
provided a basis for discounting normal-
yield-table-derived stocking standards
and productivity estimates as follows:

In addition, nonstockable land was
treated as 0 percent of normal (fig. 6).
Seven other plant communities were iden-
tified but not discounted as no stocking
problem appeared to exist.

Forest Survey field plots sample
approximately an acre with a cluster of F
10 points. In eastern Oregon, each stock-
able point on each commercial forest plot
was placed in one of the 13 plant commu-
nities. On spots where the soil was too
shallow to support tree growth, we found
grasses and herbs that identified nonforest
habitat types in Hall's key. Points falling

Plant community Percent of on such spots were classed as nonstockable,
normal as were those falling on bare rock, water,
Pine/wheatgrass 20 or any other nonstockable condition. The
Pine/bitterbrush/fescue or sedge 54 10 discount factors--one for each point
Pine/bitterbrush/stipa 59 in the 10-point cluster--were then aver-
| Pine/fescue 59 aged to provide a discount factor for the
| Pine/elk sedge 74 entire plot. Productivity was estimated
Pine/shrub/elk sedge 79 for the plot by obtaining the mean annual

i asa Be EN ieee aie “ ; é
Figure 6.--Nonforest (Poa-Danthonia) scablam
in Oregon's Blue Mountain area. The

forest land in the background is a2
pine/wheatgrass community with a stocking
capacity limited to about 20 percent of

"normal" basal area.

igure 5.--This uncut ponderosa pine stand, near
Bend, Oregon, iS growing in a pine/bitter-
brush/fescue plant community. Although the
site index is 70, basal area per acre is only
85 square feet--about 42 percent of "normal."
The growth rate has slowed from six rings per
inch to 30 rings per inch, indicating that
the stand is probably overstocked.

6

increment at culmination from an appro-
priate yield table and multiplying this
amount by the plot discount factor. Plot
stocking was assessed by comparing the
basal area found on the plot with a basal
area standard. This standard was derived
from an appropriate normal yield table
and discounted by the plot discount factor.

We were aware that several writers
(Lynch 1958, Smithers 1961, Curtis and
Reukema 1970) have reported that site
index is sometimes correlated with stand
density--especially in very dense stands.
However, since our major interest in this
study was in relatively low-density stands
where the likelihood of site index-stand
density correlations seemed least, we
assumed that site index is independent of
stand density.

Forest Survey inventoried all forest
land in eight counties of eastern Oregon
(Baker, Grant, Harney, Malheur, Morrow,
Umatilla, Union, and Wallowa), except
for the National Forests. The sample
included 220 field plots distributed over
the area on a rectangular grid. After
discounting for limited stocking capacity,
15 percent of the land that had been classi-
fied as commercial forest was reclassified
as noncommercial because it failed to
meet the minimum productive capacity
for commercial forest as defined by Forest
Survey (20 cubic feet per acre per year).
Half of the remaining commercial forest
area was discounted because the plant
community indicated that the site was not
capable of carrying normal yield table
levels of stocking. The total effect of the
discount was to lower our estimate of the
productive capacity of forest land in the
eastern Oregon inventory unit by 21 per-
cent including the loss due to change in
land class.

The stocking capacity discount had
a similar effect on the basal area by which

plot stocking was judged. On 50 percent
of the commercial forest plots, the basal

area required for full stocking was reduced.

As a result, those plots were judged to be
somewhat better stocked than previously
supposed. Although many of these stock-
ing adjustments were small, the change
was substantial for some plots. The
stocking estimate for one plot in Wallowa
County, Oregon, for example, was in-
creased from 15 percent to 52 percent.

Did the discount factors that we
developed from Hall's data fit the
limited stocking conditions found on
Forest Survey field plots? To test
this, we selected 30 undisturbed or
lightly cut plots in Harney, Grant,
and Baker Counties--areas which
appeared to have substantial limita-
tions on stocking. On each plot, we
tallied the total basal area in trees,
stumps, and recent snags. [If our tally
represents the stocking capacity of the
area sampled, then that area can
Support an average of 96 square feet
of basal area per acre at the current
stage of stand development. An esti-
mate derived from a normal yield
table suggests that the area should
support 186 square feet of basal
area--an overestimate of 94 percent.
Our estimate based on discounted
normal yield table values is 110 square
feet per acre--still an overestimate,
but by only 14 percent. The normal
yield tables overestimated stocking
capacity on each of the 30 plots--in
many cases by a wide margin, On
the seven plots with the most severe
limitations, the stocking capacity aver-
aged only 19 square feet of basal area
per acre, yet the normal yield table
estimate was 183 square feet per acre.
After discounting by plant community,
the yield table estimate was 47 square
feet--again slightly high but much
more reasonable.

_

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A PROCEDURE FOR NORTHERN CALIFORNIA

The procedure used in eastern |
Oregon to identify and quantify restric-
tions on stocking capacity is applicable
only to areas where ecologists have
developed a plant community classifica-
tion scheme. Such studies are still
regrettably few. For other areas, some
alternative procedure was needed. We
undertook to develop such a procedure
for Shasta and Trinity Counties in northern
California where Forest Survey fieldwork
was in progress.

There, productivity estimates
proved more difficult than in eastern
Oregon. The area is a complex mosaic
of contrasting vegetation, geology, and
climate. Plant communities in Shasta
and Trinity County areas are as yet
unclassified. Some indications of pro-
ductivity are provided by the Soil-
Vegetation Survey (see footnote 1). Where
available, survey maps show soil char-
acteristics, principal tree and shrub
Species present, and site class. Unfor-
tunately for our purposes, these maps
are limited in coverage and lack direct
measure of limitations on tree stocking
capacity. Although there is probably a
strong relationship between soil charac-
teristics and timber productivity, we
concluded that this approach was too
complex for our Forest Survey field
assistants.

A POSSIBLE APPROACH

Plant indicators still seemed our
best hope. Griffin (1967) had developed
a vegetative drought index for use in the
vicinity of Redding, California. His
technique was to relate soil droughtiness
to the presence or absence of 172 indi-
cator plants. Since tree density is related
to soil moisture, we reasoned that the
plants used in Griffin's index might also

be useful in estimating stocking capacity.
However, rather than use vegetative
drought index, we related the plant species
growing on a Site directly to its stocking
capacity as measured by stand density
index--that is, the trees per acre that

a site can support when the quadratic
mean diameter is 10 inches.

Our analysis rested on three
assumptions. First, we accepted the
premise (Franz 1967) that undisturbed
stands tend toward equilibrium and that
their natural basal area is an expression
of the site's productivity. Accepting
this, we were able to reasonably estimate
stocking capacity on relatively undisturbed
plots by tallying the trees and adding
recent stumps and snags. Areas with an
obvious history of severe fire or heavy
cutting were not sampled. Second, we
assumed that plant species associated
with a given stocking capacity on undis-
turbed sites are likely to indicate a
similar stocking capacity when found in
heavily disturbed areas. This is in
accordance with Daubenmire and Dauben-
mire's (1968) report that ground vegeta-
tion in the northern Rocky Mountains
grew independent of the overstory, and
with Dyrness'& observations of the
persistence of most plant species even
after clearcutting and burning. However,
we took the advice of Waring and Major
(1964) and Griffin (1967) and restricted
our observations to plant occurrence,
ignoring plant coverage, which they felt
was more likely to be influenced by dis-
turbance. Third, we assumed that stand
density index (Reineke 1933) was a reason-
able measure of stocking capacity that

would enable us to directly compare

LOY oi, oe Dyrness. Early stages of plant succession in

the western Cascades of Oregon. Unpublished manuscript on
file at Pac. Northwest Forest & Range Exp. Stn., Corvallis,
Oreg.

a

maa

stands at different stages of development.
In this we relied on the experience of
others (Curtis 1971) who have found stand
density index to have a wide application.

Stand density index--our choice as
a dependent variable--is the number of
trees per acre that a stand could be
expected to have if it retained its pres-
ent stocking (percent of normal trees
per acre) and its quadratic mean diam-
eter was 10 inches. The relationship
between number of trees per acre
and mean diameter, illustrated in
figure 7, can be described mathematically
as i, = a(D)? (Curtis 1970) where 1
is the expected number of trees in a
normal stand, D is the quadratic mean
diameter of the stand, @ varies with
stand density index, and bd is a constant
power of D. For these study data, }b
approximated -1.6 for true fir and
mixed conifer stands (as in figure 1),
-1.8 for ponderosa pine stands (from
Meyer's (1961) basic data), and -1.4 for
hardwoods (from study data and the red
alder (Alnus rubra) yield table
(Worthington et al. 1960).

DEVELOPING A MULTIPLE
REGRESSION EQUATION

Our sample consisted of 97 regular
Forest Survey plots well distributed
throughout the range of natural condi-
tions found in the commercial forest
zone. Although plots were, as much
as possible, restricted to more or
less homogeneous, relatively undisturbed
stands, some reconstruction from
stump counts proved necessary because
of the area's long history of logging,
mining, and fires. Each location was
visited once during the growing season
in order to measure the stand density
index, measure site index on three
or more dominant trees, and identify
all recognizably mature plant specimens

on Griffin's list. An area of about
an acre was carefully searched to
insure that all plant species were
found. Slope, aspect, elevation, and
physiographic class were also re-
corded. The only plant species not
recorded were those occurring on
small nonforest inclusions such as
rock outcrops and roadbeds. The
area of such inclusions was deducted
from the plot area before calculating
stand density index.

The next step was the multiple
regression analysis. Since 172 var-
iables were far too many, the plant
list was reduced to 40 or 50 by
hand screening. First, the list
was shortened to include only those
plants which were fairly easy to
identify throughout the growing
season. Then, hand plotting was
employed to eliminate plants that
were apparently unrelated to stand
density index. Finally, plants that
Seemed to grow together under
similar growing conditions were
lumped together as single variables.
The plant variables, the physio-
graphic features, Dunning's site
index (1942), and various squares
and interactions were entered in a
stepwise regression program. From
this analysis we developed two
equations for estimating stand den-
sity index capacity: One that in-
cluded Dunning's site as a variable
and one for use where suitable
site trees are not available. The
two equations follow. Elevation is
recorded to the nearest 100 feet
and site index to the nearest foot.
All other variables have a value of
1if present and 0 if absent. Plant
combinations are considered present
if any of the species in the vcom-
bination is present.

10

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AVERAGE DIAMETER (INCHES)

Figure 7.--Stand density curves for true firs and
mixed conifer stands.

INDEX

STAND DENSITY

Ie Stand density index -2 -47X_ - 84x, + 62x, + 99K. + 39x, + 92x + 64x

al! 8 10

+ - 44x + 0.0719X
+ 33X54 + 61%) 5 32%, 3 14 16
+ 0.00045x, — - 0.000008 2x, .,
2s Stand density index = 230 - 105x, - 115x, at 54x, - 46x , + 30Xe + 129%,
+ + + - -
+ 60X, + 39X, 5 57X54 50X, 5 54x, 4 58X, 4 68X)
When: x) = Ceanothus cuneatus (buckbrush), Cercocarpus betuloides, or
Cercocarpus ledifolius (mountain mahogany)
x, = Cercis occidentalis (California redbud) or Ceanothus lemmonii
(lemmon ceanothus)
X, = Quercus garryana (Oregon white oak), QO. garryana var. breweri
3 ata ae: ; :
(Brewer oak) or Q. wislizenii (interior live oak)
xi, = Rhamnus californica ssp. tomentella (coffeeberry) or Prunus
subcordata (sierra plum)
x = Abies magnifica (California red fir)
Xe = Abies concolor (white fir)
Xo = Pinus lambertiana (sugar pine) or Pseudotsuga menziesii
(Douglas-fir)
x = Castanopsis sempervirens (bush chinquapin) or Prunus emarginata
(bitter cherry)
Xq = Rosa gymnocarpa (wood rose)
Xo” Quercus kelloggii (California black oak)
x= Pyrola picta (white vein shinleaf), Trientalis latifolia
(star flower), or Asarum spp. (wild ginger)
X,.= Chimaphila umbellatum (prince's pine), Pterospora andromedea
UZ ‘ : ; §
(pine drops), or Smilacina spp. (false solomon's seal)
X13 Pinus ponderosa (ponderosa pine)
Xi 47 Ceanothus prostratus (squawcarpet)
| Xi5- Berberis pumila (dwarf barberry)
| x6 (elevation) -
q 2
| oe (Dunning's site index) (elevation)
| X37 (Dunning's site mgex)4 (elevation) —

HOW GOOD ARE THE EQUATIONS ?

The stepwise multiple regression programs used to develop the stand density index
equations also provided estimates of the standard error of estimate for each equation
| and the variation it accounted for as follows:

: 2D :
Equation R Standard error of estimate
(stand density index points)
With Dunning's site index 0.77 67

Without Dunning's site index 0.72 70

Since we were aware that stepwise
regression analysis of large numbers of
empirically chosen variables may give
underestimates of variance and inflated
R2's, we also tested the equations against
70 plots that were from the study area but
not used in constructing the equations.
Although many of these plots had been
heavily logged, we were able to recon-
struct their stand density index capacity
by means of stump counts. This gave us
a measure of the equations’ reliability on

However, standard errors of estimate
obtained from the independent test were
5 to 20 percent larger than those obtained
during the regression analysis. Despite
this apparent crudity, the equations pre-
dict stand density index capacity with far
greater precision than is possible from
normal yield tables. When the stocking
capacity of the test plots was estimated
from these tables, the standard error of
estimate was 127 stand density index

points. Furthermore, the yield table
estimates averaged 58 points higher than
field measured stand density indices.

disturbed areas. The results of this test,
on both disturbed and undisturbed sites,
appear in table 1.

It might appear likely that logging
would encourage the replacement of plants
typical of a moist environment by plants
adapted to a hotter, dryer site. If so,
the equations would underestimate the

As expected, the equations, particu-
larly the one without Dunning's site index,
appear slightly less reliable than indicated
by the stepwise regression analysis. Equa-
| tion-based estimates of stand density index stocking capacity of cutover land. We
were neither significantly higher nor lower found no evidence of such underestimation.
| than field measured values. The small Plants that were present before logging
amounts of bias that show on table 1 are seemed generally to have persisted in
| probably a result of sampling accident. spite of heavy disturbance--possibly

| Table 1.--Reliability and bias of stand density equations for cut and uncut stands

a ly,
With Dunning's site—
Number | __With Dunning's site/

of Standard error tk 2/
plots of estimate LEIS

Without Dunning's site

Type of disturbance Standard error

of estimate Bias~

l Undisturbed stands 24 72 15 86 4

| Logged within

| 10 years 21 75 -6 73 0)

1

i Logged more than

| 10 years ago 25 65 8 102 27
Total 70 70 6 88 aa

z/ Dunning (1942).

Average amount by which equation estimates exceeded or fell short of field measured
stand density index.

12

because some undisturbed microsites
usually remain. Although we were not
able to test the performance of the
equations in brushfields on old burns,

we suspect that they may be less reliable
for such areas. Areas that have been
recently clearcut and broadcast-burned
may be lacking plant indicators, although
Dyrness (see footnote 6) found that slash
fires did not destroy all vegetation--small
unburned islands often retained their
original cover.

DEVELOPING PLOT
DISCOUNT FACTORS

Although the stand density index
equation was developed from undisturbed
stands, its usefulness is in predicting
stocking capacity (expressed as stand
density index) on all stands including
those that have been heavily disturbed.
For each stand, the stand density index
capacity is estimated from the equation
and compared to the appropriate "normal"
stand density index (from a normal yield
table). If the stand density index capacity
is significantly below "normal," then
productivity estimates and stocking stand-
ards based on normal yield tables are
too high and should be discounted. The
appropriate discount factor is the equa-
tion stand density index divided by the
"normal" density index.

Normal yield table stocking is the
average of the range of stocking condi-
tions sampled by the builder of the table.
Individual normal stands may exhibit
stocking capacities that are somewhat
less or greater than these tabular values.
Such stands do not have a limited stock-
ing capacity as defined in this paper and
were not discounted. Since data on the
range of stocking conditions sampled for
normal yield tables are scanty, we more
or less arbitrarily assumed that plots
with a stand density index capacity of 80

percent or more of normal fell within
this range. Plots with a lesser predicted
stand density index capacity were appro-
priately discounted.

RESULTS IN SHASTA AND
TRINITY COUNTIES

Productivity was estimated on each
of 315 commercial forest plots in Shasta
and Trinity Counties from appropriate
normal yield tables. Where the predicted
stand density index capacity was less
than 80 percent of "normal," the esti-
mate was appropriately discounted.
Stocking was estimated by comparing the
basal area found on each plot with a
standard based on the appropriate normal
yield table but again discounted where
the equation indicated that stocking capac-
ity was limited. Both productivity esti-
mates and stocking standards were
further discounted for small nonforest
inclusions, when these occurred on the
plot.

Study results indicate that 41
percent of the commercial forest land
in the Shasta and Trinity inventory units
(excluding National Forest) has a limited
stocking capacity. Stocking estimates
on these lands were adjusted upward to
account for the limited stocking potential,
and productivity estimates were revised
downward. The productivity discounts
reduced our estimates of total productive
capacity by 12 percent, and of commer-
cial forest land area by 1 percent (fig. 8).

DEVELOPING PLOT DISCOUNT
FACTORS FOR THREE OTHER
GEOGRAPHIC UNITS

Since completing the study unit,
Forest Survey has developed equations
for calculating stand density index capac-
ity in three other areas in California.
The procedure used was similar to that

igure 8.--Natural sparse stand of Jeffrey pine
near Weaverville, California. This is a
serpentine area with a site index of 95.
Although the stand has only about 28 percent
of "normal" basal area, low growth rates
indicate that the stocking level is at or
near capacity.

used for the study except that the data
were gathered from special temporary
plots instead of the regular inventory

field plots (fig. 9). Since lists of indica-

tor species like that developed by Griffin
(1967) did not exist for these areas, we
recorded all the vascular plant species

that were present and identifiable on each

plot at the time of our visit. Since we
were able to visit each plot only once,
species that were not generally identi-

fiable throughout the growing season were

subsequently dropped from our list of
potential indicators. Development of
equations for the three areas prior to
regular fieldwork made plant identifica-
tion much easier for Forest Survey field
crews, Since they needed to identify only
the relatively few plants appearing in the
final equation--a much easier task than
identifying the 172 plants required for
Shasta and Trinity Counties,

14

Figure 9.--A low density stand of Jeffrey 4
near Aden, California. Scattered stands
such as this are common on the Modoc
plateau in northeastern California. There
is no evidence that they have ever supporié
"normal" stocking levels.

Estimates of the reliability of the
three equations appear in table 2. In
addition, independent tests of reliability
were made in the central Sierra and in |
the Modoc plateau-northeast Sierra units. |
The standard error of estimate was 88
stand density index points for the central
Sierra test and 113 points for the Modoc
unit when site index was one of the inde-
pendent variables in the equation. When
site index was deleted, results were sub-
stantially poorer. Although the Modoc
test results were somewhat disappointing,
the equation was still a much better pre-
dictor of stocking capacity than was the
normal yield table. Still, we were dissatis-
fied with the result. We suspect that the
equations would have proved more reliable
if we had separated the area into two or
more nearly homogeneous units. Anyway,
it points up the advisability of making an
independent test of each equation before
putting it to use.

Table 2.--Standard error of estimate and variation accounted for by stand density

index equations developed for northern California

Unit and county

Dunning 's—
included

Re Standard error R?
of estimate

1/

site

Dunning's site
deleted

Standard error
of estimate

West Sacramento ORFZ mS 0.70 78
(Tehama, Colusa,
Glenn, and Lake)
Modoc Plateau - Northeast Sierra 69 91 - 66 94
(Modoc and eastern portions
of Lassen, Plumas, Sierra,
Nevada, Placer, and El Dorado)
Central Sierra 5 72 106 5 7hb 106
(Yuba and western portions
of Sierra, Nevada, Placer,
and El Dorado)
Shasta and Trinity 577) 67 a2 70
4 Dunning (1942).
CONCLUSIONS

During the course of this study,
field crews visited 535 plots spread over
eight counties in eastern Oregon and two
counties in northern California, all
capable of producing at least 20 cubic
feet per acre per year according to the
normal yield tables. After field exami-
nation, we concluded that 255 of these
plots were incapable of carrying normal
yield table levels of stocking. In other
words, normal yield table based esti-
mates of productivity were too high and
similar stocking estimates were too low
on almost half of the study area. Clearly,
a forest manager with funds to invest in
silvicultural treatment needs better
information if he is to spend his
money wisely.

Long-range studies may, Someday,
result in yield tables that are stratified
by plant community. Development of such
yield tables over large areas would re-
quire a massive effort, since they would,
of necessity, be quite local in nature.
Because such a massive effort is not
likely to be undertaken soon, cruder
approximations of yield will have to suf-
fice. The method tested in eastern
Oregon--developing yield table discount
factors for plant communities--is rela-
tively simple to apply and yields much
more realistic estimates of productivity
on problem areas than does the undis-
counted normal yield table. Unfortunately,
its use depends upon the existence of
an ecological study of the plant communities

in the area to be inventoried. Although with limited stocking capacity seems

such studies are still comparatively few unacceptable. For areas where plant
in number, their potentialusefulness ex- community information is not available,
tends well beyond the scope of this study. the regression approach developed in
northern California is an alternative.
Even where long range studies are Although admittedly crude, we believe
lacking, continued use of undiscounted it will yield a substantially closer approxi-
| normal yield table values to estimate the mation of true productivity than the use
| productivity and stocking level of stands of an undiscounted normal yield table.

LITERATURE CITED

Assmann, E.
1959. Hodhenbonitat und wirkliche Ertragsleistung. (Height-site and actual yield. )
Forstwes. cbl. 78: 1-20. (Translated by Robert O. Curtis.)

and F, Franz
1965. Vorlaufige Fichten-Ertragstafel fir Bayern. (Preliminary spruce yield
tables for Bavaria.) Forstwes. cbl. 84 (1/2): 13-43. (Translated by
Robert O. Curtis. )

Bradley, R. T., J. M. Christie, and D. R. Johnston
1966. Forest management tables. For. Comm. Bookl. No. 16. London: H. M.
Stationery Off., 218 p., illus.

Curtis, Robert O.
1970. Stand density measures: An interpretation. Forest Sci. 16: 403-414, illus.

1971. A tree area power function and related stand density measures for Douglas-
fir. Forest Sci. 17: 146-159, illus.

and Donald L. Reukema
1970. Crown development and site estimates in a Douglas-fir plantation spacing
test. Forest Sci. 16: 287-301, illus.

Daubenmire, R., and Jean B. Daubenmire
1968. Forest vegetation of eastern Washington and northern Idaho. Wash. Agric.
Exp. Stn. Tech. Bull. 60, 104 p., illus.

Dunning, Duncan
1942. A site classification for the mixed conifer selection forest of the Sierra

Nevada. USDA Forest Serv. Calif. Forest & Range Exp. Stn. Res. Note
28, 21p., illus.

Dyrness, C. T., and C. T. Youngberg
1966. Soil-vegetation relationships within the ponderosa pine type in the central
Oregon pumice region. Ecology 47: 122-138, illus.

16

Franz, Friedrich
1967. Verfahren zur herleitung von Ertragsniveau-Schatzwerten {fiir die Fichte
aus einmalig erhobenen Bestandesgroben. (Methods for derivation of
production class estimates for spruce from single measurements of stand
values.) IUFRO XIV Congr., Munich. Sec. 25. VI: 287-303. (Translated
by Robert O. Curtis. )

Griffin, James R.
1967. Soil moisture and vegetation patterns in northern California forests. USDA
Forest Serv. Res. Pap. PSW-46, 22 p., illus. Pac. Southwest Forest &
Range Exp. Stn.

Hall, Frederick C.
1971. Some uses and limitations of mathematical analysis in plant ecology and
land management, p. 377-395. In Statistical ecology. Vol. 3, Many
Species populations, ecosystems, and systems analysis. E. P. Patil,
E. C. Pielou, and W. E. Waters (eds.). University Park: The Pa. State
Univ. Press.

Little, Elbert L., Jr.
1953. Check list of native and naturalized trees of the United States (including
Alaska). U.S. Dep. Agric. Handb. 41, 472 p.

Lynch, Donald W.
1958. Effects of stocking on site measurement and yield of second-growth
ponderosa pine in the inland empire. USDA Forest Serv. Intermountain
Forest & Range Exp. Stn. Res. Pap. No. 56, 36 p., illus.

Meyer, Walter H.
1961. Yield of even-aged stands of ponderosa pine. USDA Tech. Bull. No. 630
(Eve), Oops) lllus:

Munz, Philip A., and David D. Keck
1970. A California flora. 1,681 p., illus. Berkeley: Univ. Calif. Press.

Poulton, Charles E.
1970. Practical applications of remote sensing in range resources development
and management, p. 179-189. In Range and wildlife habitat evaluation--
a research symposium. USDA Forest Serv. Misc. Pub. No. 1147.

Reineke, L. H.
1933. Perfecting a stand-density index for even-aged forests. J. Agric. Res.
46: 627-638, illus.

Smithers, L. A.
1961. Lodgepole pine in Alberta. Can. Dep. For. Bull. 127, 153 p., illus.

18

Waring, R. H.

1969. Forest plants of the eastern Siskiyous: Their environmental and vegetational
distribution. Northwest Sci. 43: 1-17, illus.
and J. Major

1964. Some vegetation of the California coastal redwood region in relation to

gradients of moisture, nutrients, light, and temperature. Ecol. Monogr.
34: 167-215, illus.

Wikstrom, J. H., and S. Blair Hutchison
1971.

Stratification of forest land for timber management planning on the western

National Forests. USDA Forest Serv. Intermountain Forest & Range Exp.
Stn. Res. Pap. INT-108, 38 Pes illus.

Worthington, Norman P., Floyd A. Johnson, George R. Staebler, and William J. Lloyd
1960.

Normal yield tables for red alder. USDA Forest Serv. Pac. Northwest
Forest & Range Exp. Stn. Res. Pap. 36, 29p., illus.

Youngberg, C. T., and W. G. Dahms
1970. Productivity indices for lodgepole pine on pumice soils.

J. For. 68: 90-94,
illus.

wx G.P.O.: 1973 797-392/85

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iD A LG OS RA ARAL

The mission of the PACIFIC NORTHWEST FOREST
AND RANGE EXPERIMENT STATION is to provide the
knowledge, technology, and alternatives for present and
future protection, management, and use of forest, range, and
related environments.

Within this overall mission, the Station conducts and
stimulates research to facilitate and to accelerate progress
toward the following goals:

1. Providing safe and efficient technology for inventory,
protection, and use of resources.

2. Development and evaluation of alternative methods
and levels of resource management.

3. Achievement of optimum sustained resource produc-
tivity consistent with maintaining a high quality forest
environment.

The area of research encompasses Oregon, Washington,
Alaska, and, in some cases, California, Hawaii, the Western
States, and the Nation. Results of the research will be made
available promptly. Project headquarters are at:

Fairbanks, Alaska Portland, Oregon
Juneau, Alaska Olympia, Washington
Bend, Oregon Seattle, Washington
Corvallis, Oregon Wenatchee, Washington
La Grande, Oregon

STRAT LOLA SSR AER

The FOREST SERVICE of the U. S. Department of Agriculture
is dedicated to the principle of multiple use management of the
Nation’s forest resources for sustained yields of wood, water,
forage, wildlife, and recreation. Through forestry research, co-
operation with the States and private forest owners, and man-
agement of the National Forests and National Grasslands, it
strives — as directed by Congress — to provide increasingly greater
service to a growing Nation.