---:a United States :-p - $, : $& Department A of 

gr~culture 

OAKSIM: 

Forest Service An Individual-Tree Growth and 

Northeastern 

Station Yield Simulator for Managed, 

Research Paper 

NE-562 Even-Aged, Upland Oak Stands 

1985 

Donald E. Hilt 
The Author 

Donald E. Hilt, research forester, received a B.S. degree in forestry from 

Iowa State University in 1969, and an M.S. degree in forestry from Oregon 

State University in 1975. He joined the Northeastern Forest Experiment 

Station in 1975 and since 1976 has been engaged in research on the growth 

and yield of managed upland oaks at the Northeastern Station's Forestry 

Sciences Laboratory at Delaware, Ohio. 

Manuscript received for publication 21 September 1984. 

Abstract 

OAKSIM is an individual-tree growth and yield simulator for managed, 

even-aged, upland oak stands. Growth and yield projections for various 

thinning alternatives can be made with OAKSIM for up to 50 years. 

Simulator components include an individual-tree diameter growth model, a 

mortality model, height prediction equations, bark ratio equations, a taperbased volume system, and a mathematical thinning rule based on actual 

data. The range of age, site, and stand conditions to which OAKSIM can be 

applied is discussed, and a numerical example is used to demonstrate 

computer output generated by the simulator. 

Preface 

This version of OAKSIM gives users a functional individual-tree growth 

and yield simulator for managed, even-aged, upland oak stands. A user's 

guide is in preparation. Improvements to OAKSIM will continue. A 

comprehensive statistical validation of growth and yield projections will be 

made when an improved mortality model and an ingrowth model are 

completed in the near future. A method of projecting individual-tree 

quality changes in relation to residual stocking after intermediate thinnings 

will also be incorporated into OAKSIM. Information on tree quality is 

essential input to an economics subroutine that will be added to determine 

optimum management alternatives in the upland oak timber type. 

Users are encouraged to submit useful changes, extensions, or identified 

errors to the author for inclusion in the next version of OAKSIM. OAKSIM 

can become a valuable tool for forest managers only through close 

cooperation and coordination between researchers and users. 

NOTE: 

The computer program described in this publication is available on request 

with the understanding that the U.S. Department of Agriculture cannot 

assure its accuracy, completeness, reliability, or suitability for any other 

purpose than that reported. The recipient may not assert any proprietary 

rights thereto nor represent it to anyone as other than a Governmentproduced computer program. For cost information write Donald E. Hilt, 

Northeastern Forest Experiment Station, USDA Forest Service, 359 Main 

Road, Delaware, OH 43015. 

The use of trade, firm, or corporation names in this publication is for the 

information and convenience of the reader. Such use does not constitute an 

official endorsement or approval by the U.S. Department of Agriculture or 

the Forest Service of any product or service to the exclusion of others that 

may be suitable. 
Introduction 

Forest land managers need reliable growth and yield information to 

manage efficiently the nearly 109 

million acres of upland oak timber 

type in the United States. This paper introduces the initial version of 

OAKSIM, an individual-tree growth 

and yield simulator for managed, 

even-aged, upland oak stands. 

OAKSIM is designed specifically to 

help land managers evaluate management alternatives. Although 

many cultural treatments must be 

considered for the management of 

upland oak stands, OAKSIM addresses that silvicultural treatment 

which has the most potential for 

influencing tree and stand growth 

and yield-intermediate thinning. 

The timing, intensity, and frequency 

of intermediate thinnings for a wide 

range of age, site, and stand conditions can be studied in detail with 

OAKSIM. 

Growth and yield projections for 

up to 50 years after various thinning 

alternatives can be made with OAKSIM. Existing data bases do not 

support longer projections. Since 

OAKSIM is an individual-tree simulator, it provides valuable information on the species and size class of 

trees in the projected stand. This 

information is critical for determining the value of trees in the projected stand. Tree values are an essential ingredient for evaluating the 

economic aspects of thinning, especially in hardwood stands. 

OAKSIM is written in FORTRAN 

and is flexible enough to accommodate a variety of user demands. 

Input and output program commands 

make OAKSIM easy to use while 

preserving the detail that is characteristic of individual-tree simulators. This paper deals primarily 

with the development and structure 

of the simulator; a forthcoming 

user's guide will provide easily understood operating instructions. 

OAKSIM can be used to make 

growth and yield projections for a 

single stand or group of stands of 

particular interest, but a more logical approach may be to develop 

management guidelines by running 

the simulator for broader categories 

of age, site, and stand conditions. 

Management guidelines developed in 

this manner could be very useful, 

especially to forest land managers 

who do not have access to highspeed computers. 

Data 

Data used to develop the individual-tree diameter growth and mortality models were collected on 77 

permanent growth and yield plots in 

southern Ohio and southeastern 

Kentucky. Species composition 

ranged from nearly pure white oak 

on some Kentucky plots to a mixture of black and scarlet oaks on 

some Ohio plots.1 Hickory 

1~ee Little (1978) for scientific 

names of all species referred to in 

this paper. 

constituted a minor component of 

the overstory on some plots. 

Understory species consisted 

primarily of dogwood, red maple, 

yellow-poplar, sourwood, and 

serviceberry. The even-aged plots 

ranged from 29 to 93 years in age, 

and from 60 to 77 in site index 

according to Schnur's (1937) site 

index curves. Percent stocking 

after initial thinnings in 1962 ranged 

from 16 to 94 according to 

Gingrich's (1967) tree-area-ratio 

equation2 (Fig. 1). Many plots have 

received a second or third thinning 

since 1962. The complete data set 

consists of remeasurements made 

periodically for 20 years on 9,455 

trees that were larger than 2.5 

inches d.b.h. after thinning in 1962. 

2~ercent stocking (PS) contributed 

by the ith tree in the stand is calculated as follows: 

PSI = -.005066 +.016977*DBH 

+.003168*DBH*DBH. 

Figure 1.--White oak plot in Kentucky, age 33. Stocking was 

reduced to 37 percent. 
The method used to thin the 

growth and yield plots is best 

described as "free thinning1'--the 

marker was free to remove trees 

from all crown classes. The 

objective was to leave the specified 

stocking distributed on the best 

trees as evenly spaced as possible 

throughout the plot. In general, the 

larger cull and defective trees were 

cut first, then the competing trees 

of poor form and quality, then the 

intermediate and suppressed trees 

of lower quality and value. Finally, ' if necessary, lower value species 

and even some high-quality 

desirable species were removed 

from the main canopy to achieve a 

uniform spatial distribution. This is 

the most realistic, practical 

thinning method that can be applied 

at the present time by professional 

foresters in even-aged upland oak 

stands. 

Developing all growth and yield 

components from one data base is 

most desirable. Unfortunately, this 

is seldom possible. A total of 2306 

felled-tree and 2313 standing-tree 

heights were measured on unmanaged even-aged plots in six midwestern states to develop the height 

prediction equations. Bark-ratio 

equations were developed from data 

collected over the entire upland oak 

range. A total of 1619 trees, representing 10 species groups were sampled. The taper-based volume system was developed from measurements on 418 felled upland oak trees 

in five midwestern states. Since the 

height, bark, and volume equations 

were based on data collected from 

unmanaged stands, the effects of 

residual stocking on these components could not be assessed. This is 

not considered detrimental to 

OAKSIM1s performance, however, 

because individual-tree diameter 

growth and mortality are by far the 

most important components affecting growth and yield projections in 

managed stands. 

Program Structure 

A generalized flow chart of the 

programming logic used in OAKSIM 

is shown in Figure 2. The control 

information specifies: (1) type of 

input data, (2) timing, intensity, and 

frequency of thinning, (3) tree volume calculations, and (4) type of 

output. If a stand table is provided 

in lieu of a tree list, OAKSIM generates a tree list as described later. 

A summary of initial stand 

conditions by species and size 

classes is then computed and printed 

(Table 1). The stand may be thinned 

initially or at any 5-year interval to 

a specified stocking level. A 

maximum of ten 5-year growth 

projections may be made. The 5- 

year intervals provide adequate 

resolution of growth and yield 

projections over time for most 

users. Linear interpolation may be 

used for estimates between the 5- 

year intervals. 

Diameter growth of each residual 

tree is predicted for each 5-year 

period. The probability of mortality 

for each tree is then determined 

from this growth, the initial size of 

the tree, and the species of the 

tree. If the tree is classified as 

dead on the basis of this probability 

and a draw from a random number 

generator, it is removed from the 

list. If the net stand basal area 

growth is not within stand-level 

growth limitations, a modifier (described later) is applied to the diameter growth calculations and the 5- 

year growth cycle is repeated. 

Inside-and outside-bark volumes 

to specified top diameters are 

calculated for individual trees from 

a predicted total tree height, the 

appropriate bark ratio equation, and 

a taper-based volume system. Stand 

and stock tables by species and size 

classes are printed after each 5- 

year interval for the initial stand, 

thinned trees, residual stand, 

mortality trees, and projected stand 

(Table 1). A stand-level summary is 

printed for each stand after all 5- 

year projections have been 

completed (Table 2). This summary 

is useful for comparing overall 

thinning strategies. 

Program Applications 

OAKSIM can be applied to a wide 

range of stand, age, and site conditions. Like all simulators, however, 

OAKSIM has limitations, imposed 

primarily by the data bases used to 

construct the growth and yield 

models. Users must be cautious not 

to exceed these limitations because 

erroneous projections can occur. 

OAKSIM applications are limited to 

the following conditions: 

*Even-aged upland oak stands only 

*Oak component at least 75 percent of stand basal area 

*Stand age 30 to 120 years 

*Black oak site index 50 to 85 

.Percent stocking 20 to 120 percent 

*Tree d.b.h. 2.6 inches and larger 

*Maximum 50-year projection 

OAKSIM should be applied only to 

those stands composed primarily of 

oak species found on upland sites: 

white, black, scarlet, and chestnut. 

The simulator is not intended to be 

used on stands where northern red 

oak is the major oak component. It 

can, however, be used on stands 

where northern red oak is less than 

15 percent of the stand basal area. 

Stand structure should not differ 

radically from even-aged structures 

normally found on upland oak sites. 

Initial starting ages may range from 

30 to 100 years. If the simulator is 

started at age 100, then projections 

should only be made for 20 years to 

the maximum 120 years. The 

simulator should not be started 

over. For example, if projections 

are made from ages 30 to 80, 

resulting output should not be used 

as input for a projection from ages 

80 to 120. The program will 

terminate and error messages will 

be printed if a tree d.b.h. is less 

than 2.6 inches, or if stand age or 

site indexes fall outside their 

respective ranges of application. 

The user is responsible for meeting 

the other conditions. 
Input 

Control 

Instructtons 

4 

23 START 

Summarize 

lnltlal Conditlons 

Stand 

Calculate - Indiv~dual-Tree 

Diameter Growth 

for Tree 

Calculate Net 

Stand Basal I Area Growth I 

Diameter Growth 

Coefflclents 

Calculate 

Helght. Bark. 

& Volume 

for Each Tree 

Summarize 

New Stand 

Conditlons after 

5-year Projection 

YES 

Program Input and Output 

OAKSIM is designed to operate 

from a tree list containing the species and d.b.h. of each tree in the 

stand, but users may not always 

have access to a complete list of 

trees in a stand, except perhaps in 

research situations. A stand table 

input option, therefore, is included 

in OAKSIM to make the simulator 

more compatible with practical 

applications. Both the tree list and 

stand table options must be on a 

per-acre basis. The number of trees 

in each size and species (or species 

group) class must be specified with 

the stand table option. Size classes 

may be either 1- or 2-inch d.b.h. 

classes. A random number generator is called on to distribute the 

d.b.h.'s of trees in each species and 

d.b.h. class uniformly across the 

d.b.h. class. For example, if there 

are 25 white oak trees in the 6-inch 

d.b.h. class (a 1-inch class), the 

generated tree list will include 25 

white oak trees uniformly distributed from 5.55 to 6.54 inches. Initial 

growth projections are then based 

on this generated tree list. This 

approach provides a close approximation to the actual distribution of 

trees across d.b.h. classes. The age 

and site index (for black oak) must 

also be entered for each stand. 

OAKSIM's flexibility allows users 

to look at output for virtually any 

combination of species groups and 

product size classes. A maximum of 

five species groups may be specified 

by the user. Species identification 

codes in the tree-list or stand-table 

input will be assembled into groups 

according to user instructions. 

Product size classes may also be 

user-specified into three groups: 

sapling, pole, and sawtimber. Default values are 4.55 inches for 

poles and 11.55 inches for 

sawtimber. 

(Text continued on page 11) 

Figure 2.--Generalized flowchart 

of OAKSIM1s operation. 
TABLE I 

DATA TYPE AND STAND INFORMATION. 

TYPE OF INPUT DATA: STAND TABLE 

NUMBER OF STANDS: 1 

STAND SITE 

NUHBER A6 E INDEX 

------ --- ----- 

1 34.0 66.0 

HEIGHT AND BARK DATA. 

SPECIES 

GPOUP HTGRP RBAR B 0 B 1 

----- ----- ---- -- -A 

1 WO 0.910 0.881 0.056 

2 BO 0.900 0.832 0.103 

3 W0 0.530 0.919 -0.045 

4 WO 0.900 0,000 0.000 

PROJECTIONS. 

I NUMBER OF 5-YEAR PROJECTIONS: 10 

I 1ST & LAST STAND-STOCK TABLES ALWAYS PRINTED. 

ALL STAND TABLFS PRINTED: YES 

ALL STOCK TABLES PRINTED: NO 

VOLllFlES TO BE CALCULATED. 

TOP -- DIAMETERS - - 

--- 

CUBIC VOLUME 4.0 0.0 

BOARD FOOT VOLU!IE 8.0 6.0 

MINIMUM LENGTH FOR CUBIC VOLUMES IS 4.0 FEET, 

AND 8.0 FEET FOR BD FT VOLUMES. 

PRODUCT SIZE CLASSES ARE 4.55 INCHES FOR POLES, 

AND 8.55 INCHES FOR SAWLOGS. 

SPECIES CODES. 

SPECIES 

GROUP SPECIES CODES 

4 ALL OTHER CODES ARE IN THIS GROUP. 

THINNING OPTIONS. El 

NUMBER OF THINNINGS: 1 

THINNING METHOD: FREE THINNING 

THINNING INTENSITIES BY SPECIES 

GROUPS: 0 0 0 0 

AGE PERCENT 

THINNED STOCKING ------ -------- 

34 40.0 
TABLE I (continued) 

SIIMHARY STAND STATISTICS: INITIAL CONDITIONS FOR STAND AT AGE 34. 

N TREES: 

SAP 512.0 44.0 12.0 16.0 

POLE 110.0 48.0 2.0 6.0 

SAW 0.0 0.0 0.0 0.0 

TOTAL 622.0 92.0 14.0 22.0 

BA: 

SAP 34.1 3.0 0.8 1.2 39.1 

POLE 17.6 8.7 0.3 0.9 27.5 

SAW 0.0 0.0 0.0 0.0 0.0 

TOTAL 51.7 11.6 1.2 2.1 66.6 

PS: 

SAP 47.2 4.1 1.1 1.6 54.0 

POLE 19.7 9.4 0.3 1 .O L 30.5 

SAW 0.0 0.0 0.0 0.0 0.0 

TOTAL 66.9 13.5 1.5 2.6 84.5 

AVG DBH: 

SAP 3.4 3.5 3.5 3.6 

POLE 5.4 5.7 5.3 5.3 

SAG! 0.0 0.0 0.0 0.0 

CVOB 4.0: 

SAP 0.0 0.0 0.0 0.0 0.0 

POLE 225.7 126.0 3.0 12.7 367.4 

SAW 0.0 0.0 0.0 0.0 0.0 

TOTAL 225.7 126.0 3.0 12.7 367.4 

CVIR 4.0: 

SAP 0.0 0.0 0.0 0.0 0.0 

POLE 196.7 108.2 2.8 10.3 317.9 

SAW 0.0 0.0 0.0 0.0 0.0 

TOTAL 196.7 108.2 2.8 10.3 31 7.9 

CVOB 0.0: 

SAP 624.2 59.2 15.2 23.3 721.9 

POLE 388.5 199.2 5.9 22.0 615.5 

SAld 0.0 0.0 0.0 0.0 0.0 

TOTAL 1012.7 258.3 21.1 45.3 1337.4 

CVIB 0.0: 

SAP 537.1 49.7 13.9 18.9 619.6 

POLE 333.8 167.1 5.4 17.8 524.0 

SAW 0.0 0.0 0.0 0.0 0.0 

TOTAL 870.9 216.8 19.3 36.7 1143.7 

BFVOL 8.0: 

SAI.1 0.0 0.0 0.0 0.0 
TABLE I (ccntinued) 

STAND TABLE: INITIAL CONDITIONS FOR STAND AT AGE 34. STAND TABLE: MORTALITY FOR GROWTH PERIOD BEGINNING AT AGE 

DBH ---------- SPECIES GROUPS ----------- DBH ---------- SPECIES GROUPS ----------- 

CLASS 1 2 3 4 5 TOTALS CLASS 1 2 3 4 5 TOTALS 

750.0 ------ ------ ------ ------ ------ ------ ------- TOTALS 622.0 92.0 14.0 22.0 

TOTALS 5.0 1.0 0.0 0.0 6.0 

STAND TABLE: TREES REMOVED IN THINNING AT AGE 34. 

DBH -- - - - - - - - - SPECIES GROUPS ----------- STAND TABLE: INITIAL CONDITIONS FOR STAND AT AGE 39. 

CLASS 1 2 3 4 5 TOTALS 

----- ----- ----- ----- ----- ----- ------ DBH ---------- SPECIES GROUPS ----------- CLASS 1 2 3 4 5 TOTALS 

TOTALS 240.0 48.0 6.0 10.0 304.0 

STAND TABLE: RESIDUAL STAND AFTER THINNING AT AGE 34. 

DBH ---------- SPECIES GROUPS ----------- STAND TABLE: INITIAL CONDITIONS FOR STAND AT AGE 84. 

CLASS 1 2 3 4 DBH ---------- SPECIES GROUPS ----------- 

----- ----- ----- ----- ----- ----- ------ CLASS 1 2 3 4 5 TOTALS 

TOTALS 245.0 49.0 6.0 10.0 

TOTALS 164.0 32.0 5.0 5.0 206.0 
TABLE I (continued) 

SUMMARY STAND STATISTICS : INITIAL CONDITIONS FOR STAND AT AGE 84. 

SPECIES : 

----------- 

N TREES: 

SAP 

POLE 

SAW 

TOTAL 

BA: 

SAP 

POLE 

SAW 

TOTAL 

PS: 

SAP 

POLE 

SAW 

TOTAL 

AVG DBH: 

SAP 

POLE 

SAW 

CVOB 4.0: 

SAP 

POLE 

SAW 

TOTAL 

CVIB 4.0: 

SAP 

POLE 

SAW 

TOTAL 

CVOB 0.0: 

SAP 

POLE 

SAW 

TOTAL 

CVIB 0.0: 

SAP 

POLE 

SAW 

TOTAL 

BFVOL 8.0: 

SAW 

BFVOL 6.0: 

SAW 
N TREES: 

INITIAL 

CUT 

RESIDUAL 

MORTAL1 TY 

BA: 

INITI A1 

CUT 

RES IDUAL 

NRTALITY 

NET GROMTH 

GROSS GROWTH 

PSJ 

INITIAL 

CUT 

RESIDUAL 

MORTAL l TY 

NET GROWTH 

GROSS GROYTH 

QUADRAT IC DBF: 

INITIAL 

CUT 

RES I DUAL 

MORTAL 1 TY 

CVOB 4-02 

INITIAL 

CUT 

RESIDUAL 

MORTALITY 

NET GROWTH 

GROSS GROWIH 

CVIB 4.0: 

INITIAL 

CUT 

RESIDUAL 

MORTALITY 

NET GROWTH 

CROSS GROWTH 

CVOB 0- 0: 

INITIAL 

CUT 

RESIDUAL 

MORT AL ITY 

NET GROWTH 

GROSS GROWTH 283.3 
I0 l (rhh mms 1 cxi 

momo-ro 

*a**** 

utomcoutm 

m?)mry h h -rN N N 

0000 

*a** 

*o*o 

OD corn m m 

m 1;5 nui 

000000 .**** 9 

OUOOOO 
TABLE 2 (continued) 

ATTRI HUTE 34 

---- 

QUADRAT lC DBH: 

IN IT IAL 

CUT 

RESIDUAL 

NORTALlTY 

CVOB 4.0: 

INITIAL 

CUT 

RESIDUAL 

MORTALITY 

NET GROUrH 

CROSS GROWTH 

CVIB 4.0: 

INITIAL 

CUT 

RESIDUAL 

HORTALlrY 

NET GROYTH 

GROSS GROWTH 

CV08 010: 

INITIAL 

CUT 

RESIDUAL 

MORTALITY 

NET GROMTH 

GROSS GROWTH 

CVIB 0.0: 

INITIAL 

CUT 

-RESIDUAL 

WRTALITY 

NET GROYTH 

GROSS GROWTH 

BFVOL 8-02 

INXT lAL 

CUT 

RESIDUAL 

MORTAL I JY 

NET GROWTH 

CROSS GROWTH 

BFVOL 6.0: 

INITIAL 

CUT 

RESIDUAL 

MORTAL ITY 

NET GROWTH 

CROSS GROWTH 0.0 

TOTALS 
OAKSIM also allows considerable 

flexibility in calculating tree volumes. Merchantability standards 

may be specified. Two top d.i.b.'s 

for cubic volume and two top d.i.b.'s 

for board-foot volume calculations 

are specified by the user. Minimum 

lengths for both cubic and boardfoot volumes may also be specified. 

Default values are 4.0 and 8.0 feet, 

respectively. The appropriate 

height prediction equation (either 

white or black oak) and bark ratio 

equations for each species group are 

assign.ed by the user. 

The thinning option is initiated by 

user input. A list of the stand ages 

(initially or at any 5-year interval) 

and the desired percent stockings 

after thinning is all that is required. 

Program output is also controlled 

by user input. Stand and stock 

tables for initial and final conditions 

are always printed (Table 1). The 

user may, however, elect to have all 

intermediate stand tables, stock 

tables, or both printed. The final 

summary table is always printed. 

Growth Components 

Diameter Growth 

A distance-independent, individual-tree diameter growth model 

(Hilt 1983) is used in OAKSIM. The 

random variation of the model is 

used to allow trees within a given 

stand to change position over time. 

The mean 5-year basal area growth 

(BAG5YR) of an individual tree is 

predicted with the following equation: 

where BETA = (6.96762087 

*lo**(-6))*(SI* *l.5731724) 

* EXP(-.11839854*DBAR 

-.01198244*PS) (2) 

SI is the site index, DBAR is the 

quadratic mean stand diameter, PS 

is the percent stocking of the stand, 

and EXP is the base of the natural 

logarithms. All calculations in 

OAKSIM are made with double 

precision arithmetic. 

Percent Stocking 

4 8 12 16 20 

DBH (INCHES) 

Figure 3.--Predicted 5-vear basal-area growth rates (BAG5YR) for 

site index 70. 

Equations (1) and (2) are used to 

predict growth for all tree species 

in a stand. The tree size variable, 

DBH, also accounts for growth 

differences among species. In other 

words, big trees grow faster-- 

regardless of species. Trees in the 

black oak group (black, scarlet, and 

northern red) usually are larger, and 

therefore grow faster, than white 

and chestnut oaks in the same stand. 

The equations are applicable, however, only in stands where tree size 

differentiation has already 

occurred--stands at least 30 years 

old. Growth rates for other species 

that normally associate with upland 

oaks, such as dogwood, red maple, 

and yellow-poplar, can also be 

safely predicted with these 

equations as long as they are not the 

major component of the stand (see 

Program Applications). Bigtooth 

aspen, an unusually fast grower, 

would probably be slightly 

underestimated. Predicted growth 

rates for a range of stocking and 

mean stand diameter conditions are 

shown in Figure 3 for site index 70. 

The standard deviation (SIGMA) 

of the mean 5-year basal area 

growth for a given tree is calculated 

as follows: 

SIGMA = 0.00915129 

*~XP(0.12639572*DBH) (3) 
A random number generator is then 

used to generate a random number 

(Z) from a normal distribution with 

mean = 0 and variance = 1. The 

random growth rate (X) about the 

mean growth (BAG5YR) for a given 

tree is then calculated as: 

The random 5-year basal area 

growth rate is then converted with 

appropriate arithmetic to 5-year 

diameter growth. 

Equations 1 through 4 are used to 

predict diameter growth rates for 

the first 5-year projection. Diameter growth rates for successive 5- 

year projections are made with a 

random number draw from a conditional mean growth and a conditional standard deviation based on 

the bivariate normal distribution 

(see Hilt 1983). The conditional 

equations are based on values from 

equations 1 through 4 for both the 

5-year period of interest and the 

previous 5-year period. Use of the 

bivariate normal approach guarantees that fast-growing trees have a 

higher probability of remaining fast 

growers, and slow growers will remain slow growers. 

Mortality 

The probability of mortality 

(PMORT) for an individual tree is 

determined at the beginning of each 

5-year projection with the following 

logistic function: 

PMORT = l.O/(l.O+EXP(BO+Bl*DBH 

+B2*DGROW)) (5) 

where DGROW is the periodic 

annual diameter growth of the tree 

for the past 5 years. Variations in 

mortality due to site, age, and 

stocking for a given size tree are 

accounted for with the DGROW 

variable. If PMORT is calculated to 

be less than 0.001, then PMORT is 

assigned the value 0.001. This 

assignment of a small probability of 

mortality accounts for fast growing 

and very large trees that die 

occasionally at random times for no 

apparent reason. Predicted, rather 

than past, diameter growth rates 

are used for DGROW during the 

initial 5-year projection because 

past growth is hardly ever known 

initially. A random number between 

0 and 1, drawn from a uniform 

distribution, is used to decide 

whether the tree dies. If the 

random number is less than PMORT, 

the tree is considered dead and 

removed from the list. 

Only one diameter growth equation is required for all species, but 

several are required for mortality. 

For example, oak trees in the black 

oak group usually have a higher 

probability of mortality for a given 

d.b.h. than oak trees in the white 

oak group. Equation (5), therefore, 

was fitted to data from four species 

groups: (1) white oak, (2) black oak, 

(3) other trees (primarily hickory), 

and (4) understory species such as 

dogwood and sourwood. Coefficients in equation (5) for each group 

are listed in Table 3. PMORT is 

plotted over DGROW by DBH 

classes for the white oak group in 

Figure 4. 

Table 3.--Coefficients for mortality model (equation 5): 

PMORT = 1.O/(l,O+EXP(BO+Bl *DBH+B2 *DGROW)) 

Species Group B 0 B1 B 2 

White oaka -1.99 0.356 66.58 

Black oakb -2.48 .312 34.83 

Other treesc -.I83 .246 57.35 

understory .341 ,132 29.59 

aWhite and chestnut oaks 

b~lack, scarlet, and northern red oaks 

CHickory, red maple, yellow poplar 

d~ogw ood , sourwood, sassafras, serviceberry, shrubs 
0.0 .02 .04 .06 .08 .10 .12 .I4 

DGROW 

Figure 4.--Individual-tree probability of mortality (PMORT) for 

white oak group. DGROW is periodic annual diameter growth. 
Calibration 

Background 

Calibration is the act of adjusting 

the simulator to meet actual growth 

and yield situations. Theoretically, 

all one must do is combine the 

diameter growth and mortality 

equations 1 through 5, and the 

simulator will function for all age, 

site, and stand conditions. 

Unfortunately, this is seldom the 

case. Nearly all major simulators 

designed to handle a wide range of 

applications have required some 

modification. Modification is 

necessary with individual-tree simulators because the probability of 

mortality is dependent on growth, 

and growth in turn is dependent on 

the stocking after dead trees have 

been removed. Sometimes slight 

modelling errors become cumulative 

and cause longer projections to go 

astray. Modification is also necessary because not all variations in a 

growth and yield projection are 

completely accounted for by the 

growth models. 

OAKSIM was calibrated by comparing growth and yield projections 

with four sources of information: 

(1) actual growth and yield data 

from the managed stands discussed 

in the Data section, (2) upland oak 

yield tables for unmanaged stands 

prepared by Schnur (1937), (3) stand 

level projections made with GROAK 

(Dale 1972), and (4) personal experience. Although statistical validation tests have not yet been made, 

numerous comparisons with the 20- 

year managed stand data were performed. Longer projections of 50 

years for unmanaged stands were I compared with Schnur's tables up to 

age 80. Very few stands over age 80 

were included in Schnur's tables for 

the simple reason that they did not 

exist in 1937. GROAK, a standlevel growth and yield model developed from the same managed 

stands used for OAKSIM, provided 

excellent comparisons for overall 

stand growth to age 100. Personal 

experience provides the added element of "feel" for whether the 

projections are realistic. 

There are basically five components that need careful consideration 

for the calibration of an individualtree simulator: (1) stand basal area 

growth (net and gross), (2) number 

of trees (live and dead), (3) minimum and maximum diameters of 

trees in the projected stand, (4) 

distribution of trees over d.b.h., and 

(5) relative proportions of trees by 

species groups. Most other stand 

components, such as mean stand 

diameter and percent stocking, will 

follow accordingly if these five 

components are correct. Volume, 

which also should follow accordingly, was not considered during the 

calibration of OAKSIM because tree 

volumes, as discussed later, are 

assigned to trees after the projection has been made. 

Modifiers 

Net periodic annual basal area 

growth (BAG) for a given stand is 

first predicted with the following 

equation from GROAK; 

BAG = BA*AGE* *(-.8)*LOG(BA) 

+ .68521 *BA* AGE* *(-.75) 

+ .011383*BA*S1*AGE**(-1.05) (6) 

where BA is the stand basal area, 

and AGE is the stand age. This 

equation is incremented five times 

to arrive at the net 5-year basal 

area growth for the stand. Individual-tree basal area growth rates 

from (4) are then multiplied by a 

constant, k, until the net stand basal 

area growth is within 2 percent of 

the growth predicted with GROAK. 

The value of k must be determined 

iteratively because net growth is 

the difference between gross growth 

for the 5-year period (growth of all 

survivor trees; Husch et al. 1972) 

and trees removed from the list 

with the mortality model. Many 

simulators use stand-level modifiers 

to adjust individual-tree growth 

rates, and GROAK is a wise choice 

for upland oaks because it has been 

extensively and successfully applied 

over a wide geographic area of the 

upland oak timber type. 

After stand growth was calibrated, the total number of trees per 

acre and the relative number of 

trees in each species group required 

some adjustment, particularly over 

site index. This adjustment is made 

with a reassignment of PMORT 

from equation (5): 

PMORT = PMORT*0.8 (7) 

for the black oak group, and 

PMORT = PMORT*(0.5 + 0.025*SI) (8) 

for all other species groups. Equation (7) simply lowers the probability of mortality for black oak for all 

conditions, and equation (8) increases the probability of mortality with 

increasing values of site index for 

the other species groups. The probability of mortality for a black oak 

tree of a given d.b.h. still remains 

higher than other species for most 

circumstances. 

Minimum and maximum diameters, and also the distribution of 

trees in the projected stand, are 

adjusted with the reassignment of 

SIGMA from equation (3): 

SIGMA = SIGMA*(1.88945 

-.07837*SI + .00087*SI**2) (9) 

Variation in tree growth for a given 

d.b.h. was found to increase with 

increasing site index. Equations (1) 

through (5) and the appropriate 

modifiers in equations (6) to (9) 

expand OAKSIM1s application to a 

wider range of site index conditions 

than those available in the 20-year 

managed stand data base. 
Volume Computation 

Tree Height Bark Ratio 

Individual-tree volumes in 

OAKSIM are based on four components: (1) tree d.b.h. and species 

(available from the projected tree 

list), (2) height equations, (3) taper 

equations, and (4) bark ratio equations. Total tree heights (HT) are 

assigned to individual trees at each 

5-year interval with equations 

developed for upland oaks by Hilt 

and Dale (1982): 

where model coefficients BO and B1 

are based on stand age and site 

index. Height prediction equations 

are available only for trees in the 

white and black oak groups. Until 

height prediction equations for 

other species groups can be 

developed, either the white or black 

oak equation must be used. Errors 

that arise from this circumstance 

are not considered major because 

the tree size variable, DBH, again 

accounts for a considerable portion 

of the species effect. Equations for 

the black oak group for site index 60 

are shown in Figure 5. 

Taper Equations 

Diameters inside bark (DIB) up 

the stem are calculated for individual trees with the taper equation 

developed by Hilt (1980): 

where X = (HT-h)/(HT-4.5), and h = 

height at measurement point (feet). 

The same taper equation is used for 

all species. Trees must be at least 

2.6 inches in d.b.h. Sample tree 

profiles generated with (11) are 

shown in Figure 6. 

The ratio of DIB to DOB up the 

stem is estimated for each tree with 

the equation developed by Hilt et al. 

(1 98 3): 

Values of the model coefficients, BO 

and B1, for 10 species groups are 

listed in Table 4. The DIB/DOB 

ratio either remains constant or 

decreases up the stem for all 10 

groups. If a mean DIB/DOB ratio at 

breast height (RBAR) is available, 

then BO is set equal to the quantity 

(RBAR-B1) to adjust the ratios to 

local conditions. Equation (12) is 

plotted in Figure 7 for white oak, 

chestnut oak, and black cherry. 

Table 4. --Coefficients for bark 

ratio model (equation 12): 

DIBIDOB = BO+Bl*(DOB/DBH) 

Species BO B 1 

White oak 

Chestnut oak 

Black oak 

Northern red oak 

Southern red oak 

Black cherry 

Yellow -poplar 

Red maple 

Sugar maple 

American beech 

Program Execution for Volume 

Appropriate tree height and bark 

ratio equations are assigned to each 

species group by the user. Total 

height is then assigned to a tree 

based on the projected d.b.h., the 

age and site index of the stand, and 

the species group to which the tree 

belongs. Heights (h) to user-specified top d.i.b.'s are then calculated 

with a bisection algorithm. 

Minimum merchantable lengths 

specified by the user must be met, 

or no volumes will be calculated. 

Default values are 4.0 feet for cubic 

volume and 8.0 feet for board-foot 

volumes. The merchantable portion 

of the stem is then divided into 50 

equal segments, and the d.i.b. and 

d.0.b. at each section point are 

calculated with (11) and (12). Cubic 

volumes of each section are calculated as truncated cones and summed to obtain volumes inside and 

outside bark for the tree. A 1-foot 

cylindrical stump is also included in 

cubic volume values. Board-foot 

volumes are calculated from 16-foot 

logs with the International 1/4-inch 

rule. Fractions of logs are included 

if they are not exactly 16 feet. 

Thinning Rule 

The thinning rule used in OAKSIM 

is based on a mathematical model 

derived from the actual thinned 

plots discussed in the Data section. 

Complete development of the model 

will be documented in a forthcoming 

publication. The model has the 

following form: 

CUTFRQ (I) = 1.0 

-EXP(-~.~~~~~*CUMFRQ(I) 

+.019849*CUMFRQ (IlYTHINPS) (13) 

where CUTFRQ (I) is the cumulative 

frequency of the trees to be cut in 

the ith d.b.h. class divided by the 

tot3 number of live trees in the 

stand, CUMFRQ (I) is the cumulative relative frequency of the live 

trees in the ith d.b.h. class, and 

THINPS is tKe percent stocking 

desired after thinning. For example, if a thinning to the 40 percent residual stocking level were 

desired in a stand with 500 total 

stems and 100 stems in the 3-inch 

c8.b.h. class, CUMFRQ (3) would 

equal 0.20, CUTFRQ (3) would equal 

0.18, and the resulting number of 
90 

80 

60 

50 

40 AGE (YEARS) 

2 4 6 8 10 12 

DBH CINCHES) 

Figure 5.--Height-diameter-age curves for black oak, site index 60. 

trees to be removed in the 3-inch 

class would be equal to 0.18*500 = 

89. Age and site index did not have 

a significant effect on the thinning 

rule. Equation (13) is plotted in 

Figure 8 for a range of THINPS 

values. 

The thinning rule m a k e s e v e r y 

attempt to duplicate the actual 

thinning method applied by professional foresters in managed upland 

oak stands. OAKSIM is one of the 

few simulators that uses a thinning 

rule based on actual data, not artificial rules governed only by computer programming. Until additional 

plots can be established to study 

other thinning methods in upland 

oak stands, such as thinning strictly 

from above or below, this thinning 

rule should be used because the 

growth models are based on this 

thinning method. There is, however, 

some flexibility with OAKSIM. 

Three options are available for distributing cut trees across species 

groups Githin a d.b.h. class: (1) 

maintain t h e s a m e proportion of 

species as the unthinned stand, (2) 

double the allocated cut for specified species groups, and (3) eliminate specified species groups 

entirely. Only minor species groups 

such as understory species should be 

eliminated with the third option. 

Major species groups such as white 

oak or black oak should not be 

eliminated. 

OAKSIM uses an iterative 

application of the thinning rule to 

insure that all d.b.h. and species 

groups are thinned accordingly. 

Two or three passes through the 

tree list are generally required to 

reduce the stand to the desired 

TIIINPS. 

Random Number Generator 

A random number generator is 

used in OAKSIM to c o n v e r t s t a n d 

tables to tree lists and to calculate 

individual-tree diameter growth 

rates and probabilities of mortality. 

A random number (U) is drawn from 

a uniform distribution between 0 

and 1. This number is used unaltered to construct tree lists and calculate the probability of mortality, 

but is converted to a n o r m a l d e v i a t e 

(XNORRI) from a distribution with 

mean = 0 and variance = 1 with the 

following equation for diameter 

growth calculations: 
-- 20 inches 

15 inches 

--- 10 inches 

------ 2 inches 

12 3 4 5 6 7 8 9 101112 

RADIUS, ibCinches1 

Figure 6.-Sample stem profiles generated with taper equations 

used in OAKSIM. 

where U1 and U2 are random numbers drawn on successive occasions. 

The CALL statements in OAKSIM 

used to invoke the random number 

generator are based on local 

computing commands, and will 

require some modification by the 

user. The generator used in 

OAKSIM is almost identical to IBM's 

RANDOM Subroutine Package. If 

RANDOM or its local counterpart 

are not available, users are advised 

to use a well-tested random number 

generator. 

Use of random numbers makes 

OAKSIM a stochastic simulator. 

Output is somewhat dependent on 

the random numbers generated and 

can be altered by changing the seed 

used to initialize the generator 

(although this is not recommended). 

The seed statement in OAKSIM is IX 

= 111111. Testing has revealed that 

changing the seed, and hence the 

sequence of random numbers, 

changes the output only slightly, 

especially if long projections such as 

50 years are specified. Slight 

variations in output reflect only the 

natural variation inherent in the 

complex growth and yield of a 

forest stand. 

Example Using OAKSIM 

Bracketed numbers in this section 

refer to annotations on the OAKSIM 

output in Tables 1 and 2. Output for 

a young white oak stand in Kentucky 

that was thinned to 40 percent 

stocking with OAKSIM appears in 

Table 1. Only the final summary 

table of the unthinned OAKSIM run 

for the same stand is shown in Table 

2. 

Control cards supplied by the user 

indicate that stand table input is 

being used for a stand that is 34 

years old on site index 66 Dl. Tree 

volumes are desired for 4.0 and 0.0 

d.i.b. tops for cubic volumes, and 

8.0 and 6.0 d.i.b. tops for boardfoot volumes [21. Default values of 

4.0 and 8.0 feet are used for minimum merchantable lengths of logs. 

Trees between 4.6 and 8.6 will be 

classified as poles. A sawtimber 

threshold d.b.h. of 8.6 inches was 

used in this example only so readers 

can make comparisons with Schnur's 

(1937) yield tables and Dale's (1972) 

GROAK projections. A threshold 

d.b.h. of 11.6 inches for sawtimber 

would be more common. 

Volume computations and program output will also depend on the 

assignment of tree species codes to 

a species group, and the subsequent 

assignment of a height and bark 

ratio prediction equation to that 

species group [3,41 . Species group 1 

in this example consisted entirely of 

white oaks, group 2 was black and 

scarlet oak, group 3 was hickory and 

red maple, and group 4 was shrubs, 

such as dogwood and sourwood. 

A total of ten 5-year projections 

are to be made, with one initial 

thinning to 40 percent stocking 

[5,61. All intermediate stand tables 

are requested, but no intermediate 

stock tables are desired. 

The initial stock table for age 34 

[7] includes a comprehensive break- 
Figure 7.-DIBIDOB ratios for three species. 

down by species groups and size 

classes for all major stand 

characteristics. Average d.b.h. [81 

values listed in the stock tables are 

arithmetic means, not quadratic. 

The initial stock and stand 191 

tables are always printed. Since all 

intermediate stand tables were 

requested for this run of OAKSIM, 

stand tables for trees removed in 

thinning 1101, residual trees after 

thinning 1111, mortality trees [121 , and trees in the projected stand [131 

for all 5-year intervals are printed 

(only those to age 39 are listed in 

Table 1). Final stand [141 and stock 

tables 1151 are always printed. 

It is evident from [lo] that the 

majority of the 440 trees removed 

in the "free" thinning applied with 

the thinning rule (equation 13) were 

in the lower crown classes. Nearly 

80 percent of the trees in the 3-inch 

class were cut. Some of the largest 

trees, however, were also removed. 

These larger trees are representative of the larger cull and rough 

trees often found in most stands. 

The percentage of trees by species 

group in each d.b.h. class, as specified with the control cards 161, remained nearly the same after thinning. 

All of the detailed information 

available in the stand and stock 

tables must be utilized for a 

comprehensive evaluation of various 

thinning regimes. The size and 

species determine the value of a 

tree. For example, the changes that 

occurred in the white oak group 

should be examined closely because 

of the high value of this species 

relative to the other three groups. 

On the other hand, the final 

summary tables [16,Table 21 provide 

a good overall look at stand 

development over the projection 

period and is most useful for 

narrowing the choices of various 

thinning regimes. 
CUMFRQ 

Figure 8.-Thinning rule depends on cumulative frequencies of cut 

trees and live trees before cut. See text for definitions of CUTFRQ 

and CUMFRQ. 

Basal area, total cubic-foot volume inside bark, and board-foot 

volume growth and yield information extracted from 1161 and Table 2 

are plotted in Figure 9. Gross 

growth for the 50-year projection 

was reduced in the heavily thinned 

stand-88.7 square feet of basal 

area growth, compared to 104.7 for 

the unthinned stand, and 3017 cubic 

feet compared to 3389. Net growth, 

however, showed a marked increase 

in the thinned stand. Net basal area 

growth for the thinned stand was 

69.5 square feet; in the unthinned 

stand, it was only 45.7. Net cubic 

volume growth was 2544 cubic feet, 

compared to 2133. Mortality was 

sharply reduced with thinning, particularly for the first 25 years after 

thinning. Board-foot growth and 

yield increases from thinning are 

dramatic at age 84: the thinned 

stand had 32 percent more boardfoot volume in trees 8.6 inches 

d.b.h. and larger. This difference 

was due not only to the increased 

diameter of the thinned trees, but 

also to the fact that the thinned 

stand had 126 trees in the sawtimber size class compared to only 113 

trees for the unthinned stand. 

Even though gross growth rates 

are reduced somewhat by thinning 

this stand to 40 percent stocking, 

gains in net growth and board-foot 

yields indicate that a heavy thinning 

at age 34 is still a viable option. 

This run of OAKSIM also suggests 

another alternative: to thin initially 

to 40 percent and thin again at age 

59 to perhaps 60 percent, since 

mortality started to increase at that 

age. 
AGE 

0 i I I I I I I I 

30 40 50 60 70 80 90 

AGE 

AGE 

Figure 9.--Basal areas, cubic volumes (total stem inside 

bark), and board-foot volumes (all trees 8.6 inches and 

larger to a 6 inch top) per acre for sample run of OAKSIM. 

Discussion 

This initial version of OAKSIM is 

applicable to a wide range of age, 

site, and stocking conditions for a 

large portion of the upland oak timber type. The ultimate goal is to 

produce a complete simulator capable of generating the entire growth 

cycle--not only growth of the present stand, but also ingrowth and 

regeneration. Ingrowth can be substantial in heavily thinned upland 

oak stands. And stump sprouts from 

ingrowth trees will most likely 

determine the species composition 

of the next stand after the rotation 

harvest cut. Timber management 

planning for the current rotation, 

however, should be based primarily 

on those trees already covered by 

this version of OAKSIM, not on 

ingrowth trees. 

Future enhancements planned for 

OAKSIM should also encourage 

application of the simulator. Computer programming statements will 

be added to allow input from variable-plot (prism) timber cruises. This 

will eliminate the need for users to 

construct their own stand tables for 

input into OAKSIM. A mierocomputer version of OAKSIM will also give 

more users access to the simulator. 

This version of OAKSIM has been 

rigorously tested. Its net stand 

basal area growth is compatible 

with that of the previously developed stand growth and yield simulator, 

GROAK. However, a complete 

statistical validation of OAKSIM is 

also planned, primarily for the purpose of placing error limits on the 

growth and yield projections. Some 

measure of accuracy of the simulator is essential for large-scale 

applications. 
Literature Cited 

OAKSIM is available from the 

author upon request. The program 

consists of approximately 1700 

statements, and should be compiled 

to save computing costs. Control 

statements and data can be stored 

in a separate data file and read 

during execution. Use of a CRT 

screen and a text editor language 

package maximizes the program's 

flexibility. The ages and intensities 

of thinning can be changed easily to 

test a variety of management 

alternatives. Execution time on the 

AMDAHL 470 V/6 computer is 

approximately 10 seconds for a 50- 

year projection for one stand. 

Complete operating instructions for 

OAKSIM will be published in a user's 

guide. 

Dale, M. E. Growth and yield predictions for upland oak stands 10 

years after initial thinning. Res. 

Pap. NE-241. Upper Darby, PA: 

U.S. Department of Agriculture, 

Forest Service, Northeastern 

Forest Experiment Station; 1972. 

21 p. 

Gingrich, S. F. Measuring and evaluating stocking and stand density 

in upland hardwood forests in the 

central states. Forest Science 

13:38-53; 1967. 

Hilt, D. E. Taper-based system for 

estimating stem volumes of upland oaks. Res. Pap. NE-458. 

Broomall, PA: U.S. Department of 

Agriculture, Forest Service, 

Northeastern Forest Experiment 

Station; 1980. 12 p. 

Hilt, D. E. Individual-tree diameter 

growth model for managed, evenaged, upland oak stands. Res. 

Pap. NE-533. Broomall, PA: U.S. 

Department of Agriculture, 

Forest Service, Northeastern 

Forest Experiment Station; 1983. 

15 p. 

Hilt, D. E.; Dale, M. E. Height 

prediction equations for evenaged upland oak stands. Res. Pap. 

NE-493. Broomall, PA: U.S. Department of Agriculture, Forest 

Service, Northeastern Forest 

Experiment Station; 1982. 9 p. 

Hilt, D. E.; Rast, E. D.; Bailey, H. J. 

Predicting diameters inside bark 

for 10 important hardwood 

species. Res. Pap. NE-531. 

Broomall, PA: U.S. Department 

of Agriculture, Forest Service, 

Northeastern Forest Experiment 

Station; 1983. 7 p. 

Husch, Bertram; Miller, C. I.; Beers, 

T. W. Forest mensuration, 2nd ed. 

New York: Ronald Press; 1972. 

410 p. 

Little, Elbert L. Important forest 

trees of the United States. Agric. 

Handb. 519. Washington, DC: 

U.S. Department of Agriculture; 

1978. 70 p. 

Schnur, L. G. Yield, stand, and volume tables for even-aged upland 

oak forests. Tech. Bull. 560. 

Washington, DC: U.S. 

Department of Agriculture; 1937. 

Hilt, Donald E. OAKSIM: An individual-tree growth and yield simulator 

for managed, even-aged, upland oak stands. Res. Pap. NE-562. 

Broomall, PA: U.S. Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station; 1985. 21 p. 

OAKSIM is an individual-tree growth and yield simulator for managed, 

even-aged, upland oak stands. Growth and yield projections for various 

thinning alternatives c a n b e made with OAKSIM for a period of up to 50 

years. Simulator components include an individual-tree diameter growth 

model, a mortality model, height prediction equations, bark ratio 

equations, a taper-based volume system, and a mathematical thinning rule 

based on actual data. OAKSIM c a n b e applied to a wide range of age, site, 

and stand conditions to develop management (thinning) guidelines. 

I ODC: 242 : 561 : 562 : 564: 567 : 568 : 612 

Keywords: Increment; thinning. 

*U.S. GOVERNMENT PRINTING OFFICE:1985-505-028:20026 
Headquarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

0 Berea, Kentucky, in cooperation with krea College. 

0 Burlington, Vermont, in cooperation with the University of 

Vermont. 

0 Delaware, Ohio. 

0 Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

0 Hamden, Connecticut, in cooperation with Yale University. 

0 Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

0 Orono, Maine, in cooperation with the University of Maine, 

Orono. . 0 Parsons, West Virginia. 

0 Princeton, West Virginia. 

0 Syracuse, New York, in cooperation with the State University of 

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

0 University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. 

0 Warren, Pennsylvania.