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A Simple Model to Predict Snag Levels In
Managed Forests1
Norm Cimon2
Abstract.--The need for quantitative estimates of snag
levels is discussed. A simple model to predict snag levels
in managed forests is developed. Projections of standing ·
snags in two diameter classes for a typical managed stand
are developed. The model, once verified, may prove its
usefulness when incorporated within existing stand
simulations.
Thomas (1979) detailed the specific
requirements, by diamet~r and tree species, for
each of the cavity using birds ~nd mammals.
INTRODUCTION
Snags as Habitat
Snags are an essential component of the
habitat requirement for many species of
wildlife. In the Blue Mountains of Oregon, for
example, it is known that upwards of 60
different birds and mammals are cavity users
(Thomas 1979).
Need for a Predictive Hodel
It starts to become evident that what is
needed is a model that would project snag
levels over time for all relevant species and
diameter classes. With such a model, and the
species specific requirements mentioned above,
the wildlife manager would have the tools at
hand to protect required levels of wildlife by
protecting the needed snag habitat.
Current Snag Research
The importance of snags leads quite
naturally to a series of questions: What type
of snags are important? How many snags per
acre, and of what species and diameter class,
does it take to meet the specific requirements
of a given species of bird or mammal? What
role does forest succession play? Does the
stage of decay of the snag have a significant
impact on potential cavity users? I am certain
that the reader could add many more to the
list.
The rudiments of such a model were
originally described in a paper by Bull et al.
(1980). In this paper, I have extended the
1980 model by developing separate equations for
each diameter class, and by including
provisions for the growth of live trees from
one diameter class to the next. This model
explicitely attempts to predict the number of
snags available, for a given tree species per
acre by diameter class, over a series of
planning intervals.
In fact, questions like these are the
source of much of the active research in the
field of snag management (Balda 1976, Conner
1973, Hannan 1977, McClelland 1975, Scott
1978). Many of these questions either have
been or are in the process of being answered.
To retum to the case of the Blue Mountains,
METHODS
Requirements for the Hodel
In this simplified model, prediction
involves knowledge of certain basic information
at each stage of the planning process. First
of all a planning interval must be selected.
For the purposes of the example given below,
the interval chosen was 10 years. This is to
say that the model will be updated in 10 year
increments.
lpaper presented at the Snag Habitat
Management Symposium, Flagstaff, Arizona,
7-9 June 1983.
2Norm Cimon, 1207 Y Avenue, La Grande,
Oreg.
200
Once a planning interval is in hand, this
determines the the magnitude of the various
rates which are used in the equations for the
model. Here is a list of these rates:
Pd
veterans from the snag population. In
mathematical terms, the equation is:
= the
probability that a snag in
diameter class d will remain
standing over 1 ttme interval
(this is 1-Fall Rate)
Pd and Md are as described previously,
while S (n) and Td (n) represent,
respectively, the number of snags and the
number of live trees in diameter class d at the
start of ttme interval n.
the probability that a live tree
in diameter class d will die
over 1 time interval
Qd
= the
Rd
= the
Suppose we know that at time 0 we have,
for the 10-20" diameter class which we will
arbitrarily call class 2, a certain number of
snags and live trees of that diameter class
(S2(0) and T2(0)). We would like to project
the number of snags in this class 10 years, or
1 time interval, into the future. Then:
probability that a live tree
in diameter class d will move to
diameter class d+1 in 1 time
interval
probability that a tree in
diameter class d will remain in
diameter class d over 1 time
interval
If we now assume that we have a way of
obtaining the number of live trees that will be
available at the start of time interval 1 for
that diameter class we may then project 20
years into the future by calculating:
As is obvious, there is a heavy emphasis
placed on a diameter structure for the model.
There are reasons for this. First, it is a
fact that there are definite preferences among
certain species of woodpecker, for example, for
snags that are of a certain minimum diameter
(Thomas 1979). Wildlife management for such
species thus requires insight into the diameter
composition of the available snag habitat.
Thus, recursive calculations can be used
to estimate the number of snags in each
diameter class for successive time intervals.
Second, existing studies (Keen 1955, Dahms
1949, VanSickle 1978, Lyon 1977, Bull in
publication) have shown that, in general, snag
fall rates follow a nonlinear pattern by
diameter class. This is to say that we cannot
expect a snag in the 10-20" class to stay up
half as long on the average as a snag in the
20-30" class. The reality is that trees that
are about twice as big across stay up more than
twice as long.
The Live Tree Equation
Somewhat more tenuously, we may write down
a simple equation to project live tree growth
over time so that we might continue to update
the snag equation described above. This
equation starts with the number of live trees
in a given diameter class which are available
at the beginning of a time interval and which
might be expected to remain in that diameter
class over the interval (Td(n) x ~)). To
this is added the number of trees from the
immediately preceding diameter class which
would grow into this diameter class during the
time·interval (Td-l(n) x Qd-1)). The equation
is:
In the same fashion, transition rates for
live trees from one diameter class to the next
are nonlinear (i.e. big trees have less
diameter increment than small trees over the
same time interval). So one equation for all
of the diameter classes will not do. That is
why we empahsize the diameter structure.
At this point, we should pause to examine
more closely the equations stated above. There
are certain implicit assumptions which limit
their usefulness. This is especially true for
the second, or live tree, equation. This is
not as crucial as it might first appear,
however, since there exist far superior models
to predict tree growth. One such model, the
Stand Prognosis Model (Stage 1982), will be
discussed below. Access to such a model would
preclude the need to make use of the live tree
equation, since mortality figures could be
obtained directly from this more comprehensive
modelling process.
Defining the Equations
The Snag Equation
The snag equation is quite simple to
state. To determine the number of snags in a
given diameter class at the start of a planning
interval, we start with the number of snags
that remain standing from the start of the last
planning interval. To this we add the number
of live trees that were in that diameter class
during the previous interval which we would
expect to die off. So the snag pool is made up
of recruits from the living population and
201
Table 1.-Comparison of predicted number of
live trees by diameter class over a 100
year period for the SPM and live tree
equations (LTE).
The real value of this live tree equation
may be in its ability to mimic the much more
complicated processes of models like the Stand
Prognosis Model (SPM). In situations where
there is a specific management regime imposed
on a stand, the live tree equation seems to
hold very closely to the growth estimates of
the stand prognosis model. The relationship
between the live tree equation given above and
models like the SPM could be the subject of
future research.
Predicted no. of trees
by diameter class
SPM/LTE
Year
10"-20"
>20"
70
29 I 29
0 I 0
80
23 I 23
4 I
90
18 I 16
6 I 8
100
11 I 10
11 I 11
110
5 I 7
15 I 14
120
2 I
4
16 I 14
(M) •
130
0 I 3
17 I 15
A potentially more serious problem arises
with the so called transition ra tea, Q and R.
Stocking density will have a definite impact on
these rates. In the SPM, for example, diameter
growth for a specific tree is made functionally
dependent upon the total basal area/acre of all
trees greater in diameter than the target
tree. In other words, for a given diameter
class, Q and R are not constant but are density
dependent parameters.
140
0 I 2
16 I 16
150
0 I
14 I 15
160
0 I
13 I 15
Assumptions
At this point we would do well to list
the assumptions we have made in developing the
above system of equations. Specifically, we
have assumed that the rate factors are
constants, independent of stand density or
distribution. While this may have validity for
the snag retention rates (P) (this may be less
applicable where the stand has been opened up
and wind throw becomes a factor), it would seem
to have less merit for calculating mortality
4
snag levels (per acre) for the 10"-20" and >20"
classes are outlined in table 2.
The transition rates (Q and R) were
obtained from a fit of data for the SPM
predicted live tree numbers of table 1.
Mortality for the live trees (M) was a
by-product of this fit and, along with snag
retention rates (P), was used to continuously
update the snag equation to produce table 2.
While these limiting assumptions might
seem to limit usefulness of the live tree
equation, in fact, this is not the case. Let
us consider managed stands, for example.
Example
To summarize, if the user has access to
reliable estimates of stand distribution by
diameter class over time, or better yet actual
mortality figures by diameter class over
time, then these, when combined with snag fall
rates and a set of initial stand conditions,
allow for an estimate of snag distribution, by
diameter class over time.
In managed stands, periodic thinnings
insure that individual trees have enough
growing space to minimize competition. We
might then expect the transition factors, Q and
R, to be more nearly constant. When the live
tree equation was fitted to the SPM predicted
values for a managed stand, 3 and the resulting
rate factors used in the live tree equation,
the results were quite close to the SPM
predicted values (table 1).
In lieu of actual mortality figures in our
example, we estimated the mortality rates, snag
retention rates and transition rates, based on
outputs from the SPM and produced the simulated
live tree and snag numbers from the equations
pre sen ted here.
Values for s, M, R and Q for both diameter
classes were obtained using regression
techniques with data from the SPM model. With
these estimators, the m9del equations could be
updated as a system. The resulting values for
DISCUSSION
Any model such as this one must be subject
to intense scrutiny. As a first step, it is in
need of field validation, as opposed to
validation based on another model, such as the
30btained from the Wallowa Valley Ranger
District of the Wallowa-Whitman National
Forest, Joseph, Oregon.
202
Table 2.--Snag numbers over a 100 year period
for two diameter classes.
estimates of the number of snags available over
time, by species and diameter class. This
would provide a starting point for maintenance
of viable amounts of habitat for the many
cavity users.
Number of snags by
diameter class
Year
10"-20"
>20"
70
0.0
80
2.6
o.o
o.o
90
3-3
0.1
100
2.9
0.3
110
2.2
0.5
120
1.5
0.6
130
1.0
0.8
140
0.7
0.9
150
0.4
1.0
160
0.3
1.1
LITERATURE CITED
Balda, Russell P., and James B. Cunningham.
1976. Snag selection and use by
secondary cavity nesters of the
ponderosa pine forest. Report
submitted to the U.S. Forest Service.
103 p.
Bull, Evelyn L., Asa D. Twombly, and Thomas
M. Quigley. 1980. Perpetuating snags
in managed mixed conifer forests of
the Blue Mountains, Oregon. p. 325336. In Management of western forests
and gr.aislands for nongame birds.
Workshop Proceedings. USDA Forest
Service General Technical Report
INT-86. Intermountain Forest and
Range Experiment Station, Ogden,
Utah.
Bull, Evelyn L. In press. Longevity of
snags and their use by woodpeckers.
In Snag Habitat Management Symposium.
SPM. This is especially true of the snag
levels, since the SPM does not project these
figures at all. In fact one of the
recomendations that I would like to make is
that models such as the Stand Prognosis Model
have incorporated into them a simple equation
to project snag levels. But first there must
be validation.
Conner, R. N. 1973. Woodpecker
utilization of cut and uncut
woodlands. M.S. thesis. Virginia
Polytechnical Institute and State
University.
In addition, data collection efforts
should center on the determination of snag
retention rates. These are of the utmost
importance to accurate predictions of snag
levels. This determination should be made for
all tree species and diameter classes which are
of importance to wildlife managers as potential
habitat. At the very least, a literature
search should be conducted to obtain all of
those studies for which these rates might be
computed.
Dahms, Walter G. 1949. How long do
ponderosa pine snags stand? USDA
Forest Service, Pacific Northwest
Forest and Range Experiment Station
Research Note 57, 3 p. Portland,
Oreg.
A useful source of future determination of
snag retention rates might be the existing
forest inventory stands managed by the u.s.
Forest Service. These inventories in the Blue
Mountains track the number of downed snags.
But there is no tagging, by diameter class or
·otherwise, and thus no possibility of
determining over what period a specific snag
may have fallen. If the inventory process
could be modified to incorporate this knowledge
then a large step would have been taken in
gathering accurate data for the prediction of
snag levels •
Lyon, L. Jack. 1977. Attrition of
lodgepole pine snags on the Sleeping
Child Burn, Montana. USDA Forest
Service Research Note INT-219, 4 p.
Intermountain Forest and Range
Experiment Station, Ogden, Utah.
Keen, F. P. 1955. The rate of natural
falling of beetle-killed ponderosa
pine snags. Journal of Forestry
53:720-723.
Hannan, R. W. 1977. Use of snags by
birds, Douglas-fir region, western
Oregon. M.S. thesis. Oregon State
University, Corvallis. 114 p.
McClelland, B. Riley, and Sidney S.
Frissell. 1975. Identifying forest
snags useful for hole-nesting birds.
Journal of Forestry 73:414-417.
I am convinced that with this important
bit of information a simple model like the one
described above would allow for reasonable
203
U. S. Depa r tmen t of Agriculture
Agricultu re Handbook No . 553 .
(Published in cooperation with the
Wildlife Management Institute and the
U. S . Department of t he Interior Bureau
of Land Management . ) Washington, D. C.
Stage, Albert R., Nicholas L. Crookston,
and William R. Wykoff . 1982 . User's
guide to the stand prognosis model .
USDA Forest Service General Technical
Report INT- 133. Intermountain Forest
and Range Experiment Station, Ogden ,
Utah.
Van Sickle, Charles, and Robert E. Benson.
1978. The dead timber resource-amounts and characteristics . p. 127146. In Proceedings of symposium on
the dead softwood timber resources.
Washington State Univer sity, Pullman.
Thomas , Jack Ward, Ralph G. Anderson, Chris
Maser , and Evelyn L. Bull. 1979 .
Snags. p. 60- 77 . In Wildlife
habitats in managed-rorests--the Blue
Mountains of Oregon and Washington.
\
204