Table 1—Management regime that maximizes
land expectation value in mixed loblolly pine—
hardwood stands on medium-size site”

Table 2—Management regime that maximizes diver-
sity of tree size and species, in mixed loblolly pine—
hardwood stands on medium site

Volume (trees/acre)

Volume (trees/acre)

i Soft Hard i Soft Hard
eet heron Softwoods hardwoods __ hardwoods piame height Softwoods hardwoods _ hardwoods
(in.) Stock Cut Stock Cut Stock Cut (in.) Stock Cut Stock Cut Stock Cut
2 13730 — 796 796 72.3 72.9 2 893 — 942 43 93.0 3.1
4 65.0 — 11.8 11.8 12.0 12.0 4 23.9 04 236 1.1 235 1.0
6 40.30 — 1.6 16 19 1.9 6 10.3 0.3 10.2 02 102 02
8 29.8 — 0.2 02 03 0.3 8 §8 02 57 0.1 57 0 —
10 247 0 — _ - _ _ 10 37 01 3.7 01 3.7 0.1
12 16.9 16.9 - _ _ _ 12 26 01 25 — 25  —
14 85 85 od _ _ > 14 19 04 19 01 1.9 0.1
16 3.1 3.4 _— _— _ - 16 140 — 14.0 — 140 —
18 08 08 _— _ _ _ 18 110 11 — 1140
20 0.2 0.2 - _— — _— 20 09 — O09 — 09 —
22 - -_ _ _— _— _ 22 08 01 O08 — 07 > —
24 _ - - - _— _ 24 06 — O06 — 06 —
26+ _ _ _ _ _ _— 26+ 05 — 05 — 05 —
Cutting cycle 13 years Cutting cycle 1 year
H 1.5 H 3.7
Sawtimber 338 board ft/acre/year Sawtimber 71 board ft/acre/year
LEV $1,1314/acre LEV ~$2,698/acre

* His stand diversity; LEV is land expectation value.
Source: Schulte and others (1998a).

Economic Objective

There are many sustainable regimes. The most desirable can
be selected from a wide range of choices. For example, the
desired regime may be the best sustainable one in a purely
economic sense. The economic criterion is the land value
that results from a specific management regime, sometimes
called the land expectation value (LEV). The LEV is the
present value of all future returns, over an infinite horizon,
minus the value of the growing stock needed to produce this
return. The problem with a purely economic objective for
uneven-aged management then consists in finding the stand
state y, and the corresponding harvest h, that maximize LEV,
while satisfying growth Model | and the steady-state
constraints.

Table | provides an example of economic sustainable man-
agement. The regime of highest LEV is a diameter-limit
cut, taking all the softwoods 11 in. in diameter at breast
height (dbh) and larger every 13 years, and taking all the
hardwoods regardless of size. This will lead to a constant
production of 4,398 board ft/acre each cutting cycle, repre-
senting an average annual production of 338 board ft/acre
per year. The drawback of this regime is that the diversity

Source: Schulte and others (1998a).

of the stand is low in terms of trees of different species
and size.

Ecological Objective

A variety of ecological objectives can be expressed at stand
level, based on the diameter distribution of trees, y,. The
diversity of tree species and tree size is commonly measured
with Shannon’s index, H (Pielou 1977). In this application,
His largest when there is an equal proportion of tree basal
area in each species and size class.

A stand management policy with a purely ecological objec-
tive can then be sought by finding the values of the stock y,
and harvest h, that maximize stand diversity H while satisfy-
ing the sustainability constraints and the growth Model 1. An
example of a solution that maximizes diversity is shown in
Table 2. The best solution is to cut few trees, doing practi-
cally nothing. According to the model, in the long run, natu-
ral processes alone would produce a steady state or climax
with a stand of highest possible diversity, in Shannon’s
sense. The diversity index H would be more than double that
obtained by maximizing economic returns. The opportunity
cost of this regime compared with the economic regime is
quite high; $1,131 + $2,698 = $3,829/acre.

SORTA


The parameters are (1) the probability that a live tree of a
particular species and size remains alive and grows from that
size to a larger size during the interval f to #1, (2) the
probability that a live tree of a particular species and size
remains alive and stays in that same size class from ¢ to t+],
and (3) parameters representing the effects of the trees in
each size class on the recruitment rate from f to +1. Typi-
cally, recruitment is an inverse function of stand density and
a direct function of the number of trees of the same species
in the stand (Buongiorno and Michie 1980). The growth
matrix can distinguish between species and may be a vari-
able function of the stand state (Kolbe and others 1999).
Variants of this model have been successfully applied to
many different forests, and much is known on how to esti-
mate them (Mengel and Roise 1990, Osho 1991, Lin and
others 1996).

The model of loblolly pine-hardwood stands in the U.S.
South was initially estimated with data from 796 naturally
regenerated, mixed-aged, re-measured FIA plots of the
loblolly pine forest type in seven U.S. states (Lin and others
1998). These lots were selected randomly from the 991 plots
available. The resultant model was then used to predict the
state of the remaining 20% plots at the time of the second
inventory, given their state at the first inventory. There was
little difference between the means of the predicted and
observed number of trees in each size class. Figure | shows
the predicted and actual number of trees for the softwood
species.

The long-term validity of the model was also tested by simu-
lating species succession over 300 years. For example,
Figure 2 shows that without disturbance the stand basal area
on a good site would stabilize at around 200 fi’/acre and the
stand would become primarily soft hardwoods. This is con-
sistent with prior knowledge (Quarterman and Keever 1962,
Switzer and others 1979).

Choosing Target Stand

Within Model 1, the number of trees in each size class and
species group that the manager desires to maintain defines
the target state. This state will usually be chosen on the basis
of various economic and ecological criteria.

One fundamental criterion is that the stand state be sustain-
able, given the prescribed harvest and the potential growth
of the forest. In terms of Model 1, this means that the stock
vector y,, and the harvest vector h, must satisfy a sustainabil-
ity constraint, according to which the stand state at the end
of the cutting cycle, of length 7 years, must be the same as
the beginning state (Fig. 3).

1000.0 F Pine and other softwood

Observed
Predicted

100.0 N:

Tree/acre
3
o
T

0.1
2 6 10 14
DBH (in.)
Figure 1—Observed and predicted average number of
trees per acre on 195 plots in loblolly pine-hardwood
stands in the South (Lin and others 1998).

350 Good site
300 k ~~ Fotal “7% Softwood

_ Soft hardwood **++-* Hard hardwood

& 250

&

‘= 200

8

150

o

& 100

a ?

a
3

0 50 100 150 200 250 300
Year

Figure 2—Basal area growth of undisturbed loblolly
pine-hardwood stand on good site (Lin and others 1998).

Yt YteT

t hat

>

Cutting cycle

Figure 3—The steady-state regime is such that
growth just replaces harvest over the cutting cycle.



Table 3—Management regime that maximizes eco-
nomic returns and keeps diversity at least 75% of its
maximum, in mixed loblolly pine—-hardwood stands

Volume (trees/acre)

. Soft Hard
hroaet height Softwoods hardwoods —_ hardwoods
(in.) Stock Cut Stock Cut Stock Cut
2 112.7 0.0 941 68.6 883 58.5
4 52.4 00 208 113 21.3 99
6 32.1 0.0 69 27 79° 27
8 23.5 0.0 3.1 1.2 40 1.2
10 19.4 0.0 18 04 27 0.1
12 14.0 10.4 14 0.0 2.2 0.0
14 7.9 74 1.0 0.4 1.7 0.7
16 3.4 3.3 0.6 0.3 14 07
18 11 11 0.3 0.2 06 04
20 0.3 0.3 0.1 0.0 03 0.2
22 0.1 0.1 0.1 0.1 0.1 0.1
24 —- -—- -— = O14 —
26+ — ee
Cutting cycle 13 years
H 28
Sawtimber 321 board ft/acre/year
LEV $882/acre

Source: Schulte and others (1998a).

Mixed Objectives

The purely economic or ecological managements are ex-
tremes. More often, managers seek target stand states for the
transformation that would yield both ecological and eco-
nomic results. One might seek the target tree distribution and
harvest that would maximize the land expectation value LEV
while maintaining the diversity index H above a preset ac-
ceptable level. Or, symmetrically, one could search for the
solution that would maximize diversity, subject to a lower
bound on LEV.

For example, Table 3 shows a management regime that
maximizes economic returns while maintaining diversity at
75% of its maximum. Thus, H must equal at least 2.8. The
best cutting cycle is 13 years and the best cutting regime
takes all the trees 11 in. dbh and larger, like in the purely
economic regime. However, many more hardwood trees are
left. The result is an LEV of $882/acre, 78% of the
maximum LEV obtained without diversity constraint

(see Table 1).

Converting Stand to Desired State

Like the target stand state, the transformation from the cur-
rent state to the desired state can also be optimized
(Buongiorno 2000). However, a simple heuristic procedure
for the transformation consists in comparing the current
stand state with the desired post-harvest state and cutting
trees in the classes that have more trees than the desired
state, while doing nothing in those classes that have less.

The SouthPro computer software (Schulte and others 1998b)
can be used to make predictions of the economic and eco-
logical consequences for this type of management strategy,
for mixed loblolly pine—hardwood stands. An example of
SouthPro output appears in Figure 4, which shows the evolu-
tion of the size distribution of softwood trees under a com-
promise regime, seeking both economic returns and ecologi-
cal diversity. Figure 5 shows that the number of trees below
size class 10 would decrease during the simulated 18 years,
while the number in size class 10 and above would increase,
thus increasing the size diversity of the stand.

Another example of SouthPro output appears in Figure 5,
which shows the economic consequences of high grading
compared with a diameter-limit cut. Only the commercial
trees were harvested for high grading, thus producing a
higher initial income. Diameter-limit cutting applied a re-
gime very similar to the one described in Table 1. Figure 5
shows that the periodic income produced with the diameter-
limit cutting policy was much greater in the long run than
that obtained by high grading.

Conclusion

This research demonstrates that quantification of biological
processes and management decisions is helpful for predict-
ing the effects of different regimes for managing uneven-
aged loblolly pine-hardwood stands in the southern United
States. Quantification also facilitates the selection of the
most appropriate regime for multiple objectives. Current
models are still imperfect, but rigorous quantitative models
are better than no model at all, because assumptions are
transparent and can be improved by future research.

It is essential that management models, regardless of their
form, lead to prescriptions that are practical, or else they

will not be used. In that respect, the simplicity of the man-
agement prescriptions derived from this research (such as
diameter-limit cuts) is encouraging. The strategy of
developing general cutting guides and applying them regard-
less of the stand initial condition is also desirable. Even
though this strategy may be sub-optimal, its simplicity of
implementation may well make it the superior approach for
practitioners.

E



USDA eve" Quantifying Trade-Offs
~~ Between Economic and
ues” Ecological Objectives

General

r.. in Uneven-Aged Mixed-

FPL-GTR-145

& | Species Forests in the
Southern United States

Joseph Buongiorno
Benedict Schulte
Kenneth E. Skog



180 Softwood tree distribution
160 Compromise regime
Poor site
140
120
g Minitial state
8 100 BYear 6
3 80 mYear 12
Fil DYear 18

2 4 6 8B 10 12 14 16 18 20 22 24 26+
DBH (in.)

Figure 4—Evolution of diameter frequency distribution,
as predicted by SouthPro for mixed economic and
ecological objectives (Schulte and others 1998c).

2500

 High-grading Ml Diameter-limit cutting

2000
_ 1500
@
£
&

1000

500

0 20 40 60 80 100 120 140 160 180
Year

Figure 5—Periodic income obtained with a high-grading

or a diameter-limit cutting policy for a loblolly pine—
hardwood stand on site 4, over 180 years (Schulte
and Buongiorno 1998).

Literature Cited

Buongiorno, J. 2000. Quantifying the implications of trans-
formation from even to uneven-aged forest stands. Forest
Ecology and Management. 5447: 1-12.

Buongiorno, J.; Michie, B. 1980. A matrix model of un-
even-aged management. Forest Science. 26(4): 609-625.

Holling, C.S.; Dantzig, G.B.; Winkler, C. 1986. Determin-
ing optimal policies for ecosystems. In: Kallio, M. [and
others] (eds.). Systems analysis in forestry and forest indus-
tries. North Holland, Amsterdam: TIMS Studies in Man-
agement Science. 21: 463-473.

Kolbe, A.; Buongiorno, J.; Vasievich, M. 1999. Geo-
graphic extension of an uneven-aged, multi-species matrix
growth model for northern hardwoods. Ecological Modeling.
121: 235-253.

Lin, C.R.; Buongiorno, J.; Vasievich, M. 1996. A multi-
species, density-dependent matrix growth model to predict
tree diversity and income in northern hardwood stands.
Eological Modeling. 91: 193-211.

Lin, C.R.; Buongiorno, J.; Prestemon, J.; Skog, K. 1998.
Growth model for uneven-aged loblolly pine stands—
Simulations and management implications. Res. Pap. FPL-
RP-569. Madison, WI: U.S. Department of Agriculture,
Forest Service, Forest Products Laboratory. 13 p.

Mengel, D.L.; Roise, J.P. 1990. A diameter-class matrix
model for southeastern U.S. coastal plain bottomland hard-
wood stands. Southern Journal of Applied Forestry.

14: 189-195.

Osho, J.S.A. 1991. Matrix model for tree population projec-
tion in a tropical rain forest of south-western Nigeria. Eco-
logical Modeling. 59: 247-255.

Pielou, E.C. 1977. Mathematical ecology. Toronto, Canada:
John Wiley & Sons. 132 p.

Quarterman, E.; Keever, C. 1962. Southern mixed hard-
wood forest: Climax in the southeastern coastal plain, U.S.A.
Ecological Monographs. 32(2): 167-185.

Schulte, B.; Buongiorno, J. 1998. Effects of uneven-aged
silviculture on the stand structure, species composition, and
economic returns of loblolly pine stands. Forest Ecology and
Management. 111: 83-101.

Schulte, B.; Buongiorno, J.; Skog, K. 1998a. Optimizing
uneven-aged management of loblolly pine stands. In:
Proceedings, Society of American Foresters, national con-
vention; 1998 September 19-23; Traverse City, MI. Be-
thesda, MD: Society of American Foresters: 306-318.

Schulte, B.; Buongiorno, J.; Lin, C.R.; Skog, K. 1998b.
SouthPro, a computer program for managing uneven-aged
loblolly pine stands. Gen. Tech. Rep. FPL~GTR~112. Madi-
son, WI: U.S. Department of Agriculture, Forest Service,
Forest Products Laboratory. 47 p.

Schulte, B.; Buongiorno, J.; Skog, K. 1998c. Simulating
the uneven-aged management of southern loblolly pine:
features of the SouthPro computer program. In: Proceedings,
9th biennial southern silvicultural research conference,
Clemson, SC. Gen. Tech. Rep. SRS-GTR-20. Asheville,
NC: U.S. Department of Agriculture, Forest Service,
Southern Station: 515-521.

Switzer, G.L., Shelton, M.G.; Nelson, L.E. 1979. Succes-
sional development of the forest floor and soil surface on
upland sites of the East Gulf Coast Plain. Ecology.

60(6): 1162-1171.

Usher, M.B. 1969. A matrix model for forest management.
Biometrics. 25: 309-315.


Abstract

This paper summarizes research on the management of
uneven-aged loblolly pine-hardwood stands in the southern
United States. This research was composed of three
elements: (1) modeling of biological growth of uneven-aged
stands of mixed loblolly pine and hardwood trees, (2) opti-
mization to discover sustainable regimes that would best
meet economic and ecological objectives such as stand
diversity, and (3) simulations to predict the effects of
optimal management guides, when applied to stands in
different initial conditions. The findings suggest that uneven-
aged systems are feasible for the mixed loblolly pine—
hardwoods forest type. An infinite number of sustainable
management regimes are possible, with different cutting
cycles and/or cutting intensities. Regimes with the highest
financial returns would lead to pure pine stands, a cutting
cycle of about 13 years, diameter-limit cuts at 12 in. diame-
ter at breast height for pines, and total removal of hard-
woods. Near-maximum diversity of species and size of trees
would be produced by a “hands off” policy, at a high oppor-
tunity cost. Intermediate regimes were designed to maximize
income, while leaving a sufficiently diverse stand. A simple
effective method for converting stands from their initial state
to a desired future state is to cut all the trees and only the
trees that currently exceed the desired state.

Keywords: uneven-aged, loblolly pine, hardwoods, south,
silviculture, economics, linear programming, simulation,
biometrics.

February 2004

Buongiome, Joseph; Schulte, Benedict .J.; Skog, Kenneth B. 2004. Quanti-
fying trade-offs between economic and ecological objectives in uneven-aged
mixed-species forests in the Southern United States Gen. Tech. Rep.
FPL-GTR-145. Madison, WI: U.S. Department of Agriculture, Forest
Service, Forest Products Laboratory. 5 p

A limited number of free copies of this publication are available to the
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Acknowledgments

This research was supported in part by the Wood Utilization
for Ecosystems Management Project; USDA Forest Service,
Forest Products Laboratory; Southern Forest Experiment
Station; and the School of Natural Resources, University

of Wisconsin, Madison. We thank Jeff Prestemon and
Ching—Rong Lin for their collaboration.

Conversion
Inch-pound unit factor SI unit
inch (in.) 25.4 millimeter (mm)
square foot (ft?) 0.093 square meter (m*)
cubic foot (ft*) 0.0283 cubic meter (m’)
acre 0.4047 hectare (ha)

Contents

Introduction...

Modeling Forest Growth...

Choosing Target Stand..

Economic Objective....

Ecological Objective...

Mixed Objectives...

Converting Stand to Desired State..
Conclusion ..

Literature Cited .



Quantifying Trade-Offs Between
Economic and Ecological Objectives in
Uneven-Aged Mixed-Species Forests
in the Southern United States

Joseph Buongiorno, Professor
Benedict Schulte, Research Assistant

Department of Forest Ecology and Management, University of Wisconsin, Madison, Wisconsin

Kenneth Skog, Project Leader
Forest Products Laboratory, Madison, Wisconsin

Introduction

There is a strong worldwide interest in management of un-
even-aged forests. The main reason for this is the perception
of uneven-aged systems as working “close to nature.” These
systems maintain a constant ground cover and use mostly
natural regeneration. Uneven-aged systems favor a mix of
many species and are meant to keep trees of very different
ages on small tracts of land. The result is dramatically differ-
ent from homogeneous plantations of a single species, which
are even-aged and managed by clear cutting and artificial
regeneration. The aesthetic quality of uneven-aged systems
is appreciated by the general public, and the gain in biologi-
cal diversity is well documented.

If uneven-aged systems are to be applied more extensively,
their economic and ecological consequences must be pre-
dicted. This paper presents some results of research aimed at
rigorously analyzing the transformation, with the ultimate
goal of obtaining guidelines that could be applied readily in
the field. Although this type of research has been done for
several forest types, we were restricted to results obtained by
the Wood Utilization for Ecosystems Management Project
that pertain to mixed softwood—hardwood stands in the
southern United States.

Quantification is important to clarify some issues pertaining
to uneven-aged management. With mathematics and num-
bers, all the assumptions underlying a particular result and
recommendation can be fully disclosed. Careful specification
of all the equations helps improve communication between
researchers. The gain in understanding facilitates critical
review and should lead ultimately to faster progress. The
availability of a quantitative model to experiment with, i-e.,
to “bring the world to the laboratory” (Holling and others
1986), also facilitates the relationship between researchers
and practitioners. Nonetheless, quantification is useful only

if it leads to improved practice, i.¢., to operational manage-
ment guidelines. In that spirit, the approach to quantifying
the implications of uneven-aged stands proposed here has
three steps:

Modeling the growth of the stand. This step involves the
formulation of a particular model structure, i.e., a theory of
growth and calibration of the model parameters with growth
data from the particular ecosystem of interest.

Optimizing the target stand. Optimization of the stand is
meant to help the selection of a particular management goal,
given the growth model and management criteria, which
may be purely economic, purely ecological, or a mix of

the two.

Simulating the conversion to the desired state. Simulation
is meant to quantify the economic and ecological effects of
going from the initial stand to the desired target, according
to a particular rule. The rule proposed here is simple heuris-
tics, based on the choice of target in step 2.

Modeling Forest Growth

A particular class model (Model 1) that has been applied to a
wide range of conditions uses a vector and matrix represen-
tation of stand state and growth (Usher 1969):

Yin =G(y,—h,) +e

where y, is a vector describing the stand state at instant /.
The vector elements are the number of trees of different
species and size per unit of land area. Sizes are categorized
in a finite number of size classes. The variable h, is the
harvest vector, i.e., the number of trees of each species and
size that are cut at time 7. G, is a matrix of parameters, and ¢
is a constant vector.