WestProPlus: A Stochastic 

Spreadsheet Program for 

the Management of All-Aged 

Douglas-Fir–Hemlock Forests 

in the Pacific Northwest

Jingjing Liang, Joseph Buongiorno, and Robert A. Monserud

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

General Technical 

Report

PNW-GTR-674

June 2006
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, cooperation with the 

States and private forest owners, and management of the National Forests and National 

Grasslands, it strives—as directed by Congress—to provide increasingly greater service to a 

growing Nation.

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and 

activities on the basis of race, color, national origin, age, disability, and where applicable, sex, 

marital status, familial status, parental status, religion, sexual orientation, genetic information, 

political beliefs, reprisal, or because all or part of an individual’s income is derived from any 

public assistance program. (Not all prohibited bases apply to all programs.) Persons with 

disabilities who require alternative means for communication of program information (Braille, 

large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 720-2600 (voice 

and TDD). To file a complaint of discrimination, write USDA, Director, Office of Civil Rights, 

1400 Independence Avenue, SW, Washington, DC 20250-9410 or call (800) 795-3272 (voice) 

or (202) 720-6382 (TDD). USDA is an equal opportunity provider and employer.

Authors 

Jingjing Liang is a post-doctoral researcher, U.S. Department of Agriculture, 

Forest Service, Rocky Mountain Research Station, Forestry Sciences Laboratory, 800 E Beckwith Ave., Missoula, MT 59801; Joseph Buongiorno is the Class 

of 1933 Bascom Professor and John N. McGovern WARF Professor, Department of Forest Ecology and Management, University of Wisconsin-Madison, 

1630 Linden Drive, Madison, WI 53706; Robert A. Monserud is a supervisory 

research forester, U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Research Station, 620 SW Main St., Suite 400, Portland, OR 97205.

Cover photograph by Tom Iraci.
Abstract

Liang, Jingjing; Buongiorno, Joseph; Monserud, Robert A. 2006. WestProPlus: 

a stochastic spreadsheet program for the management of all-aged Douglasfir–western hemlock forests in the Pacific Northwest. Gen. Tech. Rep. PNWGTR-674. Portland, OR: U.S. Department of Agriculture, Forest Service, 

Pacific Northwest Research Station. 42 p.

WestProPlus is an add-in program developed to work with Microsoft Excel to 

simulate the growth and management of all-aged Douglas-fir–western hemlock 

(Pseudotsuga menziesii (Mirb.) Franco–Tsuga heterophylla (Raf.) Sarg.) stands 

in Oregon and Washington. Its built-in growth model was calibrated from 2,706 

permanent plots in the Douglas-fir–western hemlock forest type in Oregon and 

Washington. Stands are described by the number of trees per acre in each of 

nineteen 2-in diameter classes in four species groups: Douglas-fir, other shadeintolerant species, western hemlock, and other shade-tolerant species. 

WestProPlus allows managers to predict stand development by year and 

for many decades from a specific initial state. The simulations can be stochastic 

or deterministic. The stochastic simulations are based on bootstrapping of the 

observed errors in models of stand growth, timber prices, and interest rate. 

When used in stochastic simulations, this bootstrap technique simulates random 

variables by sampling randomly (with replacement) from actual observations 

of the variable, rather than from an assumed distribution. Users can choose 

cutting regimes by specifying the interval between harvests (cutting cycle) and a 

target distribution of trees remaining after harvest. A target distribution can 

be a reverse-J-shaped distribution or any other desired distribution. Diameterlimit cuts can also be simulated. Tabulated and graphic results show diameter 

distributions, basal area, volumes by log grade, income, net present value, and 

indices of stand diversity by species and size. 

This manual documents the program installation and activation, provides 

suggestions for working with Excel, and gives background information on WestProPlus’s models. It offers a comprehensive tutorial in the form of two practical 

examples that explain how to start the program, enter simulation data, execute a 

simulation, compare simulations, and plot summary statistics. 

Keywords: WestProPlus, simulation, growth model, Douglas-fir, western 

hemlock, management, economics, ecology, diversity, wood quality, risk, 

stochastic, deterministic.
Contents

	 1	 1. Introduction

	 1	 What Is WestProPlus?

	 2	 Why Simulate This Type of Stand?

	 2	 How Does WestProPlus Work?

	 3	 What Is in This Manual?

	 3	 2. Getting Started

	 3	 System Requirements

	 3	 Loading WestProPlus

	 5	 Unloading WestProPlus

	 5	 3. Using WestProPlus

	 5	 WestProPlus Input

	 7	 BDq Calculator

	 7	 Storing Data and Retrieving Stored Data

	 8	 Running Simulations

	 8	 4. Example: Simulating BDq Management Regimes

	 9	 Simulation Parameters

	11	 Running Simulations

	12	 Simulation Output

	21	 Comparison of BDq Selection Regimes Under a Stochastic Environment

	23	 Troubleshooting WestProPlus

	25	 Acknowledgments

	25	 Metric Equivalents

	25	 Literature Cited

	28	 Appendix 1—WestProPlus Plot Data

	32	 Appendix 2—Growth-and-Yield Model

	35	 Appendix 3—Log Grade Equations

	37	 Appendix 4—Stochastic Stumpage Price and Interest Rate Models

	39	 Appendix 5—Definition of Diversity of Tree Species and Size

	40	 Glossary


WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

1. Introduction

WestProPlus is a program intended to help forest managers predict the effects of 

management, or lack thereof, on stand growth, productivity, income, wood quality, diversity of species, and diversity of tree size. The WestProPlus user’s manual 

documents background, instruction, and additional suggestions for using the 

WestProPlus program. The next section explains how to install WestProPlus on 

your computer and provides a description of the input data, as well as instructions 

for loading and saving these data, running simulations, and saving the results. 

Examples of applications in simulating management regimes are given. If you 

are new to WestProPlus, it will be useful to run these examples while reading the 

manual. We included answers to some common questions. Appendixes cover the 

growth equations, volume equations, and log grade equations of WestProPlus, 

and the data used to calibrate these equations. 

The WestProPlus software and all the sample spreadsheets can be 

downloaded from http://www.forest.wisc.edu/facstaff/buongiorno/. 

What Is WestProPlus?

WestProPlus is a computer program to predict the development of all-aged 

Douglas-fir–western hemlock (Pseudotsuga menziesii (Mirb.) Franco–Tsuga 

heterophylla (Raf.) Sarg.) forests in the Pacific Northwest. With this program, 

various management regimes can be considered, and their outcomes can be 

quickly predicted. WestProPlus is a successor of WestPro (Ralston et al. 2003). 

WestProPlus has the following features compared to WestPro:

• Extensions of the database from 66 uneven-aged plots to 2,706 all-aged 

plots, covering most of the Douglas-fir–western hemlock type in Oregon 

and Washington (app. 1). 

• Expansion of species groups from two (softwoods, hardwoods) to four 

(Douglas-fir, other shade-intolerant, western hemlock, other shadetolerant).

• Calibration of an improved growth model, with particular attention 

to the effect of stand diversity on growth, mortality, and recruitment 

(Liang et al. 2005).

• Introduction of log grade equations to predict the effects of management 

on wood quality.

• Recognition of risk and uncertainty in stand growth, timber prices, and 

interest rates. 


GENERAL TECHNICAL REPORT PNW-GTR-674 

Three other deterministic relatives of WestProPlus (CalPro, NorthPro, and 

SouthPro) already exist for California mixed-conifer forests (Liang et al. 2004b), 

northern hardwoods in Wisconsin and Michigan (Liang et al. 2004a), and for 

loblolly pine (Pinus taeda L.) in the Southern United States (Schulte et al. 1998), 

respectively. We have used our experience with these programs to further simplify 

the data input and the program output to increase WestProPlus’ usefulness for 

practitioners.

Why Simulate This Type of Stand?

Douglas-fir–western hemlock forests in the Pacific Northwest are very productive. 

They were harvested heavily during the late 1800s and early 1900s, at an unsustainable rate (Curtis and Carey 1996). Consequently, although they vary highly 

in composition and structure, Douglas-fir–western hemlock forests are mostly in 

early seral stages (Barbour and Billings 1988). 

Douglas-fir wood is valued for its superior mechanical properties, making it 

most useful in building and construction (Barbour and Kellogg 1990). Western 

hemlock is another important commercial species. It is shade tolerant yet fast 

growing, deer and elk browse it, and hemlock trees are a part of the aesthetics 

of Western forests (Burns and Honkala 1990). 

Even-age silviculture is prevalent in managed Douglas-fir forests. There has 

been little tendency to adopt uneven-age (selection) management (Emmingham 

1998) despite its attractive features (Guldin 1996, Hansen et al. 1991). This seems 

to be due to a lack of experience with uneven-age management, and scarcity of 

data regarding its effects compared to even-age systems. 

WestProPlus helps predict the development of Douglas-fir–western hemlock 

stands with various types of silviculture. Some of the examples in this manual 

suggest that effective uneven-age management of Douglas-fir–western hemlock 

forests can be profitable while maintaining stands with high diversity of tree species and size. 

How Does WestProPlus Work?

WestProPlus predictions are based on a stochastic version of a multispecies, siteand density-dependent matrix growth model (Liang et al. 2005, app. 2) coupled 

with a log grade model (app. 3) and stochastic stumpage price and interest rate 

models (app. 4). To run WestProPlus, you specify an initial stand state and define 

a management policy by target stand state and cutting cycle. The program predicts economic and ecological effects of the policy. You may use a deterministic 

model of stand growth with fixed timber prices and interest rate, or stochastic 
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

models of stand growth, timber prices, and interest rate. The stochastic simulation 

reflects the random disturbances that were observed in developing each model.

If you do stochastic simulations, as you change policy, WestProPlus repeats 

the same sequence of random numbers to simulate stochastic stand growth, timber prices, and interest rates. Using the same string of random numbers facilitates 

comparison of management policies. A new string of random numbers may also 

be generated by quitting WestProPlus and loading it again (see section 2).

What Is in This Manual?

The next section explains how to install WestProPlus on your computer and 

provides a description of the input data, as well as instructions for loading and 

saving these data, running simulations, and saving the results. Examples of 

applications in simulating uneven-age management regimes are given. We 

included answers to some common questions. Appendixes cover the equations 

involved in WestProPlus, and the data used to calibrate these equations. The 

manual assumes that you are familiar with the basics of Microsoft Excel®.

1

 All 

the spreadsheets shown in this manual are screenshots from the Excel 2002. 

2. Getting Started

System Requirements

You need the following hardware and software to operate WestProPlus:

• A personal computer with at least 128 megabytes of random access 

memory (RAM)

• Microsoft Windows 98, 2000, Me, XP, or Windows NTTM 4

• Microsoft Excel 97 or above

• A free copy of the WestProPlus software downloaded from 

http://www.forest.wisc.edu/facstaff/buongiorno/, or from the 

authors through jbuongio@wisc.edu.

Loading WestProPlus

To install the program for the first time:

1. Insert the diskette containing WestProPlus.xla into your computer, or 

download it from the Web site to your local disk and go to step 3.

2. Select the WestProPlus.xla icon and copy it onto your hard disk. For your 

convenience, you may save it in a new folder named WestProPlus, e.g., 

C:\WestProPlus\WestProPlus.xla. 

1

The use of trade or firm names in this publication is for reader information and does not 

imply endorsement by the U.S. Department of Agriculture of any product or service.
GENERAL TECHNICAL REPORT PNW-GTR-674 

3. Open Microsoft Excel and START A NEW WORKBOOK.

4. Under the Tools menu, select Add-ins. In the add-ins dialogue box, select 

Browse and choose WestProPlus.xla from its location on your hard disk. 

Click OK.

5. Return to the Tools menu. WestProPlus is now the last item in the menu. 

Select WestProPlus and click OK in the title box.

6. The WestProPlus menu should now be in the Excel menu bar.

Until you uninstall it, WestProPlus will be a permanent option in the Tools 

menu of Excel. You can load the program by selecting WestProPlus in the Tools

menu. This will add WestProPlus to the Excel menu, and the Input Data worksheet (fig. 1) will appear.

There are three sample workbooks at http://www.forest.wisc.edu/facstaff/

buongiorno/ with the Input Data worksheets corresponding to the “Examples” 

section of this paper. By copying the data from these worksheets into your Input 

Data worksheet you will be able to run these examples with WestProPlus.

Figure 1—Input Data worksheet.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

Unloading WestProPlus

To finish working with WestProPlus, choose the command Quit under the 

WestProPlus menu (fig. 2). The WestProPlus menu will disappear, but the 

current worksheets will stay in the Excel window until you close them.

Figure 2—The WestProPlus menu.

To remove the WestProPlus menu and uninstall the program:

1. Quit WestProPlus. 

2. Under the Tools menu, select Add-ins. Deselect WestProPlus to remove 

the title from the add-ins list.

3. Close the Excel window. 

3. Using WestProPlus

WestProPlus Input

The Input Data worksheet (fig. 1) contains all the information needed by the 

program. Cells with question marks require numeric entries, except that initial 

timber prices are optional. WestProPlus rounds off numeric entries to one or 

two decimal places. Before running a simulation, WestProPlus checks all your 

entries and will prompt you to fix any improper input data. 

In figure 1, the four rows labeled “Initial state” contain the initial number of 

trees per acre in the stand (at time zero), by species groups and by 2-in diameter 

classes. WestProPlus recognizes four species groups: Douglas-fir, other shadeintolerant species, western hemlock, and other shade-tolerant species (app. 1, 

table 3). 

The four rows labeled “Target state” contain the number of trees per acre 

that should remain after harvest, by species group and diameter class. A target 

entry of zero instructs WestProPlus to harvest all trees in that category. When 
GENERAL TECHNICAL REPORT PNW-GTR-674 

the number of trees in the stand exceeds the target value, the harvest is the difference between the available trees and the target; otherwise the harvest is zero. You 

can avoid harvesting in a particular species group and size class by entering a very 

high target, e.g., 10,000. You can enter the initial and target states by hand or 

with the BDq calculator described below.

WestProPlus measures time in years. All simulations start at time zero and 

last for the “Length of simulation.” The “Year of first harvest” may be set at any 

nonnegative integer value. The “Length of cutting cycle,” i.e., the interval between 

harvests, must be at least 1 year. To simulate stand growth without harvest, set 

the “Year of first harvest” to a value greater than the “Length of simulation.” 

The “Re-entry Cost” represents cost of doing a harvest, in dollars per acre, 

beyond the harvesting cost already reflected in the stumpage price. The cost of 

timber sale preparation and administration would be part of a typical re-entry 

cost. 

The “Site Productivity” measured by mean annual increment, describes the 

wood-growing capacity of a site. It is defined as the increment in volume of a 

timber stand averaged over the period between age zero and the age at which 

mean annual increment reaches its maximum value (Hanson et al. 2002). If you 

do not enter any value for Site Productivity, WestProPlus assumes that the site 

productivity is 150 ft3 • ac

-1 • yr-1, the average site productivity in the 2,706 permanent plots in Washington and Oregon used to calibrate the growth equations of 

WestProPlus. The site productivity should be between 10 to 300 ft3 • ac

-1 • yr-1, the 

range of the data. 

The “Site Index” was measured by the average total height of the dominant 

and codominant trees at 50 years of age (Hanson et al. 2002). WestProPlus uses 

site index to predict log grade. The site index should be between 30 and 99 ft, 

the range of the data.

The “Interest Rate” represents the initial interest rate. Starting from this 

initial value, WestProPlus generates a sequence of yearly stochastic interest rates. 

These interest rates are used to calculate the net present value (NPV) of each 

harvest, and the cumulative NPV.

The “Initial Timber Prices” are the initial stumpage prices in dollars per thousand board feet (mbf) by log grade and species group. These entries are optional. 

If you leave these cells blank, WestProPlus will generate random initial prices. 

Starting from these initial values, WestProPlus generates a sequence of stochastic 

prices (app. 4). 
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

BDq Calculator 

A BDq distribution is a tree distribution, by diameter class, defined by a stand 

basal area (B), a maximum and minimum tree diameter (D), and a q-ratio (q), the 

ratio of the number of trees in a given diameter class to the number of trees in the 

next larger class. You can use the BDq calculator (Schulte et al. 1998) to define the 

target state or the initial state with a BDq distribution.

To use the BDq calculator, click on the BDq Calculator icon in the Input Data 

worksheet. Use the arrow buttons to set the stand basal area (ft2 • ac

-1), the q-ratio, 

the minimum and the maximum diameters (in); click the Calculate button (fig. 3). 

The example in figure 3 shows the number of trees by diameter class that 

would give a basal area of 120 ft2 • ac

-1 with trees of diameters from 3 to 33 in and 

a q-ratio of 1.3 for the Douglas-fir trees in the initial stand state. You can copy the 

resulting stand distribution to the Input Data worksheet as the initial distribution 

or as the target distribution for a species group by selecting the destination and 

clicking the Copy button on the BDq calculator (fig. 3). 

Figure 3—The BDq Distribution Calculator window.

Storing Data and Retrieving Stored Data 

After entering data in the Input Data worksheet, you can save this worksheet 

for later use. You should save your work frequently to avoid losing data. It is 

advisable to save the work in a particular folder to facilitate locating the file in 

the future. 

To run several simulations (e.g., to examine the effects of changing some of 

the parameters), you may find it efficient to work with previously saved input data. 

To retrieve the data, choose the File  Open command in Excel to open your 

saved file or double click on the file icon.
GENERAL TECHNICAL REPORT PNW-GTR-674 

Running Simulations

After completing the Input Data worksheet or retrieving a previously saved one, 

you are ready to run a simulation. To run WestProPlus, make sure that the WestProPlus menu is in the Excel menu bar. If not, click WestProPlus under the Tools

menu to activate WestProPlus. You can then choose to run stochastic simulation 

or deterministic simulation by clicking Run Stochastic or Run Deterministic in the 

WestProPlus menu, respectively (fig. 2). 

Each WestProPlus simulation generates the following worksheets and charts:

• TreesPerAcre worksheet: The number of trees by species and diameter 

class for each simulated year.

• Basal Area worksheet: The basal area by species and timber size, 

for each simulated year.

• Volume worksheet: The volume in stock by log grade, for each 

simulated year. 

• Products worksheet: The physical output and the financial return 

from the harvests throughout the simulation.

• Diversity worksheet: Shannon’s species diversity indices and size 

diversity indices for each year of the simulation.

• Diversity chart: A plot of Shannon’s indices of species and size 

diversity over time.

• Species BA chart: A stacked area chart showing the development of stand 

basal area by species group over time.

• Size BA chart: A stacked area chart showing the development of 

stand basal area by timber size over time.

• Volume chart: A stacked area chart showing the development of 

volume in stock by log grade over time.

To compare various management regimes, save the output worksheets immediately after running a simulation. Otherwise WestProPlus will overwrite the 

previous results every time you run a new simulation.

All the data in the output worksheets are protected and you cannot change 

them. To see how results change with different input data, change the Input Data 

worksheet and rerun the simulation. 

4. Example: Simulating BDq Management Regimes

In this example, we performed stochastic simulations of selection regimes based 

on the BDq principle. For a given initial state, we changed the q-ratio of the target 

stand state and interpreted the results in terms of effects on economic returns, 
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

productivity, tree diversity, wood quality, and stand structure. We concentrate on 

the q-ratio because it is the main effect in most uneven-age management criteria 

(Liang et al., in press).

Simulation Parameters

The simulations were for 200 years, with cutting cycles of 10 years. The initial 

stand state was the average distribution of the 2,706 permanent plots used in 

calibrating the growth equations of WestProPlus (fig. 4). Composition by number 

of trees was 34 percent Douglas-fir, 30 percent other shade-intolerant species, 

20 percent western hemlock, and 16 percent other shade-tolerant species. The 

average site productivity was 150 ft3 • ac

-1 • yr-1 and the average 50-year site index 

was 90 ft. The first harvest occurred at year 1. The fixed cost of re-entry was set 

at $254 • ac

-1, the estimated cost of preparing and administering timber sales in 

the state of Washington (Ralston et al. 2003). The initial interest rate was set at 

3.8 percent per year, the yield of AAA bonds net of inflation, from 1970 to 2004 

(US GPO 2005). The stumpage prices were approximated as the average delivered log prices (pond value) over four quarters in 2005 (Oregon Department of 

Forestry (2005) minus an estimated average cost of $1.13 ft-3 for getting logs from 

the woods to the mill pond. 

Figure 4—Initial stand state.

0

20

40

60

80

4 8 12 16 20 24 28 32 36 40

Diameter (in)

Trees • ac-1

Douglas-fir

Other shade-intolerant species

Western hemlock

Other shade-tolerant species

The three alternative target distributions are shown in figure 5. They all 

assumed a maximum diameter of 40 in for all species. The basal area was kept 

the same in the three alternatives, 87 ft2 • ac

-1 in total (Miller and Emmingham 

2001), consisting of 30 ft2 • ac

-1 of Douglas-fir, 26 ft2

 • ac

-1 of other shade-intolerant 
10

GENERAL TECHNICAL REPORT PNW-GTR-674 

species, 17 ft2 • ac

-1 of western hemlock, and 14 ft2

 • ac

-1 of other shade-tolerant 

species. The q-ratio was set at 1.2, 1.4, or 1.8. Higher q values kept more trees in 

the smaller diameter classes relative to the large (fig. 5). 

Figure 5—Target distribution of trees by species groups and diameter class for the BDq regime used here.

Figure 6 shows the BDq calculator set to produce the target state for Douglasfir trees with basal area of 30 ft2

 • ac

-1, maximum diameter of 40 in, and q-ratio of 

1.2. Clicking on the Calculate button produces the number of trees by size class. 

Figure 6—BDq Distribution Calculation dialog box.

To copy the distribution of Douglas-fir to the Input Data worksheet, select the 

option box corresponding to Douglas-fir Target Distribution and click on the Copy

button. Figure 7 shows the Input Data worksheet for the above BDq selection 

regime with q = 1.2. 
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

11

Figure 7—Input Data worksheet for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.

Running Simulations 

Upon running a simulation, WestProPlus will replace any old tables and charts 

with new ones. For this reason, you should save the workbook after each simulation. To run a series of simulations, load the input data for the first management 

regime, run the simulation, save your outcome, and proceed to load and run the 

second management regime. You can then compare the data on economic return, 

various ecological criteria, and wood quality for different regimes. To that end, 

comparative charts and tables can be built with Excel from the WestProPlus 

output worksheets. 
12

GENERAL TECHNICAL REPORT PNW-GTR-674 

Simulation Output 

The simulation outcomes of the preceding BDq selection are displayed in tables 

and charts. They are located in the same workbook as the Input Data worksheet. 

The following results are for the stochastic simulation with the initial condition 

and BDq management specified by the input data in figure 7.

TreesPerAcre worksheet—

This worksheet (fig. 8) shows the number of trees per acre, by species and diameter 

class, for each year of simulation. Scrolling to the right reveals the tree distribution for other species. The underlined numbers are the year of harvest, and the 

number of trees per acre after the harvest.

Figure 8—TreePerAcre worksheet for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

13

Basal Area worksheet—

This worksheet (fig. 9) shows, for each simulated year, the total stand basal area, 

the stand basal area by species group, and the stand basal area for three timber 

size categories: small timber (trees from 5 to 15 in diameter at breast height 

(d.b.h.), medium timber for trees from 15 to 21 in d.b.h., and large timber for trees 

21 in d.b.h. and larger. Underlined numbers show the year of harvest and the basal 

areas just after harvest, and the first row represents the average basal area over the 

whole simulation period. 

Figure 9—Basal Area worksheet for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
14

GENERAL TECHNICAL REPORT PNW-GTR-674 

Volume worksheet—

This worksheet (fig. 10) shows the volume in stock by log grade. The log grade 

equations used by WestProPlus are described in appendix 3. The underlined numbers represent the year of harvest and the volume per acre just after the harvest, 

and the first row represents the average volume over the whole simulation period.

Products worksheet—

The upper part of the products worksheet (fig. 11) shows data for each harvest: 

basal area cut, volume harvested by log grade, gross income, predicted NPV of 

the current harvest, the total (cumulative) NPV, and the initial stock value. The 

log grade equations, and the stochastic stumpage price model and interest rate 

model used by WestProPlus are described in appendixes 3 and 4. 

Figure 10—Volume worksheet for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

15

Figure 11—Products worksheet for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.

The lower part of the products worksheet shows the average annual cut and 

the average stock in terms of basal area and volume by log grade. It also displays 

the average species diversity and size diversity over the whole simulation period. 

The results show that with this particular BDq selection and a 10-year cutting 

cycle, the average yield over 200 years would be 63.97 ft3 • ac

-1 • yr-1, for a NPV of 

$11,395.87 • ac

-1. This is the value of the land and initial trees, under this management. It suggests that this regime would be economically efficient. Because the 

value of the initial trees was $5,692.05 • ac

-1, the present value of the return from 

land and initial trees would exceed the initial investment in trees. 
16

GENERAL TECHNICAL REPORT PNW-GTR-674 

Diversity worksheet—

The diversity worksheet (fig. 12) shows Shannon’s indices of species group diversity and tree size diversity for each simulated year (see app. 5 for the definitions of 

Shannon’s diversity). The underlined data show the year of harvest and the values 

of the diversity indices just after harvest. The average of the diversity indices over 

all years is displayed above the annual values.

Figure 12—Diversity worksheet for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

17

Diversity chart—

The Diversity chart (fig. 13) displays the evolution of Shannon’s indices over time. 

The results show that the effect of stochasticity in forest growth is greater than the 

effect of harvests on the species and size diversity.

Figure 13—Diversity chart for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
18

GENERAL TECHNICAL REPORT PNW-GTR-674 

Figure 14—Species basal area by species chart for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum 

diameter, q = 1.2, and 10 years cutting cycle.

Species BA chart—

This chart (fig. 14) shows the development of basal area by species throughout the 

simulation period. The chart shows the sharp decrease of total basal area is due to 

the periodic harvests. It also suggests that in the long run, this management would 

sustain all four species groups in the stand. 
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

19

Timber Size BA chart—

This chart (fig. 15) shows the development of basal area by timber size throughout 

the simulation. It excludes the basal area of trees less than 5 in d.b.h. The results 

suggest that all three size groups would remain present in the stand for 200 years. 

The basal area of the largest trees would tend to increase over time with this 

management.

Figure 15—Timber Size BA chart for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
20

GENERAL TECHNICAL REPORT PNW-GTR-674 

Volume chart—

This chart (fig. 16) shows the development of volume in stock by log grade 

throughout the simulation period. The chart suggests that all log grades would 

continue to be present in the stand. The stock of peeler, and No. 1 Sawmill logs 

tended to increase slightly over time under this management.

Figure 16—Volume chart for the BDq selection regime with 87 ft2 • ac-1 residual basal area, 40 in maximum diameter, 

q = 1.2, and 10 years cutting cycle.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

21

Comparison of BDq Selection Regimes Under a 

Stochastic Environment

As an example of how WestProPlus can be used to compare management under a 

stochastic environment, follow the steps below to compare BDq selection regimes 

with a 10-year cutting cycle, 87 ft2 • ac

-1 residual basal area, 40 in maximum 

diameter, and a q-ratio of 1.2, 1.4, or 1.8:

• Load WestProPlus, fill in, and save three Input Data worksheets corresponding to the three q-ratios.

• Run a stochastic simulation for each Input Data worksheet and record the 

total NPV ($ • ac

-1), productivity (ft3

 • ac

-1 • yr-1), average stand diversity of 

tree species and size, average basal area, and average percentage of peeler 

logs from the products worksheet (fig. 11).

• Keep the three Input Data worksheets active on the desktop and Quit

WestProPlus (see section 2).

• Reload WestProPlus (see section 2) and go to step 2 to start a new 

replication.

WestProPlus simulations are run three times in step 2 (once for each regime) 

with the same string of random numbers to compare the regimes efficiently, while 

steps 3 and 4 generate a new string of random numbers for another replication. 

An example of 10 replications is in table 1. There was a strong positive effect 

of q-ratio on the productivity (fig. 17), because more large trees were cut with 

higher q-ratios. As smaller trees were left on the stand, higher q-ratio led to significantly lower percentage of peelers, and lower tree size diversity (fig. 17). Here, 

we have detected little or no effect of q-ratio on the other criteria with only 10 

replications. More replications with more initial states suggest that as the q-ratio 

increases, NPV increases, species diversity decreases, and basal area increases 

(Liang et al., in press). 
22

GENERAL TECHNICAL REPORT PNW-GTR-674 

Table 1—Simulation results of the three BDq selection regimes with different 

q-ratios

NPV Productivity

Replication q = 1.2 q = 1.4 q = 1.8 q = 1.2 q = 1.4 q = 1.8

$ • ac

-1 ft3 • ac-1 • yr-1

1 11,396 16,239 13,312 63.97 68.56 99.99

2 17,078 9,414 9,360 59.46 64.21 95.85

3 12,136 6,104 13,744 59.69 72.42 98.97

4 7,558 13,222 11,978 55.79 72.90 112.46

5 7,618 8,250 10,666 47.92 64.91 116.16

6 12,574 11,496 10,425 55.93 64.31 98.00

7 8,298 17,314 14,390 61.82 85.62 126.88

8 14,790 5,022 22,120 57.26 75.92 108.32

9 7,366 12,456 11,038 53.14 68.75 111.96

10 15,062 11,316 8,054 49.35 70.98 99.25

Species diversity Size diversity

q = 1.2 q = 1.4 q = 1.8 q = 1.2 q = 1.4 q = 1.8

1 1.31 1.33 1.31 2.84 2.78 2.38

2 1.31 1.32 1.33 2.85 2.79 2.38

3 1.32 1.32 1.28 2.83 2.78 2.39

4 1.32 1.33 1.34 2.85 2.79 2.41

5 1.30 1.31 1.30 2.83 2.78 2.36

6 1.32 1.34 1.31 2.85 2.78 2.38

7 1.33 1.33 1.32 2.85 2.77 2.37

8 1.33 1.34 1.33 2.85 2.77 2.38

9 1.34 1.34 1.32 2.86 2.79 2.38

10 1.31 1.31 1.34 2.85 2.79 2.42

Percentage of peeler Average basal area

q = 1.2 q = 1.4 q = 1.8 q = 1.2 q = 1.4 q = 1.8

Percent ft2 • ac

-1

1 0.31 0.23 0.17 70.7 81.8 76.9

2 0.30 0.22 0.17 73.8 72.7 73.6

3 0.30 0.22 0.16 70.6 83.4 77.5

4 0.31 0.22 0.16 73.5 82.5 80.8

5 0.29 0.22 0.16 65.2 74.7 86.1

6 0.32 0.23 0.16 73.7 77.5 78.2

7 0.29 0.22 0.16 76.5 88.0 89.1

8 0.31 0.22 0.17 71.5 85.9 75.5

9 0.29 0.22 0.16 71.7 80.0 81.1

10 0.30 0.22 0.16 68.4 81.7 74.0

Note: Except for net present value (NPV), all data are averages over 200 years.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

23

Troubleshooting WestProPlus

Why can’t I open WestProPlus?

First, make sure you have the latest version of WestProPlus (2005). Check our 

Web site: http://www.forest.wisc.edu/facstaff/buongiorno/ for updates. 

Set your Excel macro security level to Medium. You can change the level at 

Tools  Macro  Security. After setting the macro security level to Medium, each 

time you load WestProPlus, a security warning message window will pop up, and 

you should select Enable Macros (fig. 18).

Figure 17—Mean and standard error of the management criteria over 10 replications for different q-ratios, other things being 

held constant.
24

GENERAL TECHNICAL REPORT PNW-GTR-674 

WestProPlus does not insert a new Input Data worksheet. What can I do?

Before inserting a new Input Data worksheet, WestProPlus checks to see if there is 

a worksheet named Input Data already open. If there is one, WestProPlus will not 

generate a new Input Data worksheet. To get a new Input Data worksheet, close 

all Excel windows and reopen WestProPlus.

Why is there no BDq calculator in the example worksheets?

The example workbooks contain only the input data. After you have installed 

WestProPlus, the BDq calculator icon will appear in the new Input Data worksheet. At that point, you can copy data from the example workbooks into the 

Input Data worksheet.

Why is the BDq calculator not working?

WestProPlus must be open to use the BDq calculator. To use the BDq calculator 

on a previously saved Input Data worksheet, WestProPlus must be in the Excel 

menu bar.

Why can’t I copy all the content from the example worksheet to the 

Input Data worksheet?

All the cells of the Input Data worksheet are protected except those that need 

entries (marked with ? marks). Copy only the data from the example worksheet 

and paste them to the corresponding locations in the Input Data worksheet.

For further assistance, or to send us your comments, please contact us 

through jbuongio@wisc.edu. 

Figure 18—Microsoft Excel Security Warning Window against Macro viruses.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

25

Acknowledgments

We thank Dean Parry, Karen Waddell, and Susan Stevens Hummel for 

assistance with the data. The research leading to this program was supported, 

in part, by the USDA Forest Service, Pacific Northwest Research Station, 

by USDA-CSREES grant 2001-35108-10673, and by the School of Natural 

Resources, University of Wisconsin-Madison. The authors take sole 

responsibility for any error or omission.

Metric Equivalents

When you know: Multiply by: To find:

Inches (in) 2.54 Centimeters 

Feet (ft) .3048 Meters

Square feet (ft2) .0929 Square meters

Square feet per acre (ft2 • ac

-1) .229 Square meters per hectare 

Cubic feet (ft3) .0283 Cubic meters 

Cubic feet per acre (ft3 • ac

-1) .070 Cubic meters per hectare 

Literature Cited

Barbour, M.G.; Billings, W.D. 1988. North American terrestrial vegetation. 

Cambridge, United Kingdom: Cambridge University Press. 421 p.

Barbour, R.J.; Kellogg, R.M. 1990. Forest management and end-product 

quality: a Canadian perspective. Canadian Journal of Forest Research.

 20: 405–414.

Barbour, R.J.; Parry, D.L. 2001. Log and lumber grades as indicators of wood 

quality in 20- to 100-year-old Douglas-fir trees from thinned and unthinned 

stands. Gen. Tech. Rep. PNW-GTR-510. Portland, OR: U.S. Department of 

Agriculture, Forest Service, Pacific Northwest Research Station. 22 p. 

Burns, R.M.; Honkala, B.H., tech. coords. 1990. Silvics of North America: 

1. Conifers. Agric. Handb. 654. Washington, DC: U.S. Department of 

Agriculture. 675 p.

Curtis, R.O.; Carey, A.B. 1996. Managing economic and ecological values in 

Douglas-fir forests. Journal of Forestry. 94: 1–7, 35–37. 

Efron, B.; Tibshirani, R.J. 1994. An introduction to the bootstrap. Boca Raton, 

FL: CRC Press. 456 p.
26

GENERAL TECHNICAL REPORT PNW-GTR-674 

Emmingham, W. 1998. Uneven-aged management in the Pacific Northwest. 

Journal of Forestry. 96(7): 37–39.

Guldin, J.M. 1996. The role of uneven-aged silviculture in the context of 

ecosystem management. Western Journal of Applied Forestry. 11(1): 4–12.

Hansen, A.J.; Spies, T.A.; Swanson, F.J.; Ohmann, J.L. 1991. Conserving 

biodiversity in managed forests: lessons from natural forests. BioScience. 

41(6): 382–392.

Hanson, E.J.; Azuma, D.L.; Hiserote, B.A. 2002. Site index equations and 

mean annual increment equations for the Pacific Northwest Research 

Station Forest Inventory and Analysis, 1985–2001. Res. Note PNW-RN533. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Research Station. 24 p.

Hiserote, B.; Waddell, K. 2003. The PNW-FIA integrated database user guide. 

A database of forest inventory information for California, Oregon and 

Washington, V 1.3. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 10 p.

Liang, J.; Buongiorno, J.; Monserud, R.A. [In press]. Bootstrap simulation 

and response surface optimization of management regimes for Douglas-fir/

western hemlock stands. Forest Science.

Liang, J.; Buongiorno, J.; Kolbe, A.; Schulte, B. 2004a. NorthPro: a spreadsheet 

program for the management of uneven-aged northern hardwood stands. 

Madison, WI: University of Wisconsin-Madison, Department of Forest 

Ecology and Management. 36 p.

Liang, J.; Buongiorno, J.; Monserud R.A. 2004b. CalPro: A spreadsheet program 

for the management of California mixed-conifer stands. Gen. Tech. Rep. 

PNW-GTR-619. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 32 p.

Liang, J.; Buongiorno, J.; Monserud R.A. 2005. Growth and yield of all-aged 

Douglas-fir/western hemlock forest stands: a matrix model with stand 

diversity effects. Canadian Journal of Forest Research. 35(10): 2369–2382.

Miller, M.; Emmingham, B. 2001. Can selection thinning convert even-aged 

Douglas-fir stands to uneven-aged structures? Western Journal of Applied 

Forestry. 16(1): 35–43. 
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

27

Northwest Log Rules Advisory Group. 1998. Official log scaling and grading 

rules. 8th ed. Eugene, OR. 48 p.

Oregon Department of Forestry. 2005. Quarterly Douglas-fir stumpage prices. 

http://egov.oregon.gov/ODF/STATE_FORESTS/TIMBER_SALES/logpage.

shtml. (20 March 2006).

Ralston, R.; Buongiorno, J.; Schulte, B.; Fried, J. 2003. WestPro: a computer 

program for simulating uneven-aged Douglas-fir stand growth and yield in 

the Pacific Northwest. Gen. Tech. Rep. PNW-GTR-574. Portland, OR: U.S. 

Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 25 p.

Schulte, B.; Buongiorno, J.; Lin, C.R.; Skog, K. 1998. SouthPro: a computer 

program for managing uneven-aged loblolly pine stands. Gen. Tech. Rep. 

FPL-GTR-112. Madison, WI: U.S. Department of Agriculture, Forest 

Service, Forest Products Laboratory. 47 p.

Spelter, H. 2004. Converting among log scaling methods. Journal of Forestry 

102(4): 33–39.

Stevens, J.A.; Barbour, R.J. 2000. Managing the stands of the future based on 

the lessons of the past: estimating western timber species product recovery 

by using historical data. Res. Note PNW-RN-528. Portland, OR: U.S. 

Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 9 p.

U.S. Government Printing Office [US GPO]. 2005. Economic report of the 

President. Washington, DC. 335 p.
28

GENERAL TECHNICAL REPORT PNW-GTR-674 

Appendix 1—WestProPlus Plot Data

The data to calibrate the stand growth model used by WestProPlus came from 

the PNW-FIA Integrated Database (Version 1.3) (Hiserote and Waddell 2003), 

specifically, the part of the database that combines information from four forest 

inventories (eastern Oregon, western Oregon, eastern Washington, and western 

Washington) conducted by the USDA Forest Service between 1988 and 2000. 

The 2,706 plots used in calibrating WestProPlus had all been classified in the 

Douglas-fir–western hemlock forest type, they had been measured at two successive inventories, and they were located in Oregon and Washington west of 120° in 

longitude (fig. 19). This area includes the Coast Range and the Cascade Range of 

western Washington and Oregon, as well as the Klamath region of southwestern 

Oregon. About 80 percent of the plots were on private land, and most of the 

remaining 20 percent were on lands belonging to the states of Oregon or Washington (table 2). United States federal lands (e.g., national forests, national parks, and 

Bureau of Land Management land) comprise only 2.4 percent of the land in this 

database.

Figure 19—Geographic distribution of the Forest Inventory and 

Analysis plots used to calibrate the growth and yield model.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

29

Table 2—Distribution of plots by ownership

Ownership Number of plots Percent

Private 2,136 78.9

Public

State 438 16.2

Local government 67 2.5

Bureau of Land Management 20 0.7

National Park Service 16 0.6

Other federal owner 29 1.1

Total 2,706 100.0

The trees were categorized into four species classes (table 3): Douglas-fir, 

other shade-intolerant species, western hemlock, and other shade-tolerant 

species (Barbour and Billings 1988). Red alder (Alnus rubra Bong.) and ponderosa 

pine (Pinus ponderosa Dougl. ex Laws.) were the most abundant shade-intolerant 

species other than Douglas-fir. Western redcedar (Thuja plicata Donn ex D. 

Don) and bigleaf maple (Acer macrophyllum Pursh) were the most abundant 

shade-tolerant species other than western hemlock (table 3). Within each species, 

trees were grouped into nineteen 2-in diameter classes, from 3 to 5 in up to 40 in 

and above. 

The plot characteristics are summarized in table 4. The theoretical maximum 

species diversity is ln(4) = 1.39, and the maximum size diversity is ln(19) = 2.94, 

occurring when all the basal area is equally distributed in all 4 species classes and 

19 size classes, respectively. There was a 0.90 correlation between the diversity 

by species group, used here, and the diversity by individual species. The average 

recruitment was highest for Douglas-fir and other shade-intolerant trees (table 4).

The individual tree data (table 5) show that, on average, Douglas-fir trees 

had the highest diameter growth rate, and lowest mortality rate. Other shadetolerant species had the highest single tree gross volume. Although the time 

between measurements was short, averaging a decade, there was much difference 

in trees and stand conditions between plots. It is this cross-sectional variation 

that allows inferring how stands would grow in very different conditions that 

might arise in space and over long periods.
30

GENERAL TECHNICAL REPORT PNW-GTR-674 

Table 3—Frequency of tree species in all sample plots, for each of our four 

species groups

Percentage

Common name Scientific name of plots

Douglas-fir Pseudotsuga menzeisii (Mirb.) Franco 41.27

Other shade-intolerant species 24.07

Red alder Alnus rubra Bong. 10.85

Ponderosa pine Pinus ponderosa Dougl. ex Laws. 7.10

Lodgepole pine Pinus contorta Dougl. ex Loud. 1.94

Western larch Larix occidentalis Nutt. 0.92

Black cottonwood Populus trichocarpa (Torr. & Gray) 0.72

Pacific madrone Arbutus menziesii Pursh 0.63

Incense-cedar Calocedrus decurrens Torr. 0.44

Oregon white oak Quercus garryana Dougl. ex Hook 0.42

Western juniper Juniperus occidentalis Hook. 0.26

Oregon ash Fraxinus latifolia Benth. 0.25

Noble fir Abies procera Rehd. 0.18

Quaking aspen Populus tremuloides Michx. 0.15

Western white pine Pinus monticola Dougl. ex D. Don 0.14

Sugar pine Pinus lambertiana Dougl. 0.05

Jeffrey pine Pinus jeffreyi Grev. & Balf. 0.01

Western hemlock Tsuga heterophylla (Raf.) Sarg.) 18.80

Other shade-tolerant species 15.86

Western redcedar Thuja plicata Donn ex D. Don 5.88

Bigleaf maple Acer macrophyllum Pursh 3.09

Grand fir Abies grandis (Dougl. ex D. Don) Lindl. 2.09

Sitka spruce Picea sitchensis (Bong.) Carr. 1.44

Pacific silver fir Abies amabilis Dougl. ex Forbes 1.32

White fir Abies concolor (Gord. & Glend.) Lindl. 0.94

 ex Hildebr.

Mountain hemlock Tsuga mertensiana (Bong.) Carr. 0.42

Engelmann spruce Picea engelmannii Parry ex Engelm. 0.34

Subalpine fir Abies lasiocarpa (Hook.) Nutt. 0.17

Port-Orford-cedar Chamaecyparis lawsoniana (A Murr.) Parl. 0.12

Pacific yew Taxus brevifolia Nutt. 0.03

Alaska yellowcedar Chamaecyparis nootkatensis (D. Don) Spach 0.02

Redwood Sequoia sempervirens (D. Don) Endl. 0.01

 All the species 100.00
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

31

Table 4—Summary statistics for plot data (2,706 plots)

First inventory

Other shade Western Other shade Site Inter-inventory Basal

Douglas-fir intolerants hemlock tolerants productivity period area

- - - - - - - - - - - - - - - Trees • ac

-1 - - - - - - - - - - - - - - - Ft3 • ac-1 • yr-1 Year Ft2 • ac-1

Mean 86.38 62.42 56.79 41.24 149.59 10.53 119.01

Standard deviation 121.74 105.75 119.63 87.59 72.17 0.90 74.23

Maximum 1,246.45 1,982.99 1,223.36 1,056.16 300.00 23.00 418.66

Minimum 0 0 0 0 10.00 9.00 2.40

Number of plots 2,706 2,706 2,706 2,706 2,706 2,706 2,706

Recruitment

Other shade Western Other shade Species Size Total

Douglas-fir intolerants hemlock tolerants diversity diversity volume

- - - - - - - - - - - - - Trees • ac

-1 - - - - - - - - - - - - - Ft3 • ac-1

Mean 2.22 1.55 1.34 1.01 0.54 1.65 4,733.54

Standard deviation 7.32 6.35 5.67 4.48 0.39 0.63 3,588.06

Maximum 103.87 165.25 96.76 96.37 1.38 2.76 22,122.76

Minimum 0 0 0 0 0 0 28.15

Number of plots 2,706 2,706 2,706 2,706 2,706 2,706 2,706

Note: Recruitment is change between the two inventories.

Table 5—Summary statistics for individual tree data

Douglas- Other shade- Western Other shade-

 fir intolerant species hemlock tolerant species

Diameter (in)

Mean 15.28 12.01 12.97 16.06

Standard deviation 8.39 6.33 7.69 10.69

Maximum 81.81 51.42 68.37 119.90

Minimum 1.57 1.57 1.57 1.57

Number of trees 23,161 11,831 11,612 8,900

Diameter growth (in yr-1)

Mean 0.28 0.18 0.23 0.23

Standard deviation 0.17 0.14 0.15 0.17

Maximum 5.50 6.47 3.77 3.33

Minimum 0 -0.11 0 -0.45

Number of trees 23,161 11,831 11,612 8,900

Mortality rate (y-1)

Mean 0.003 0.006 0.003 0.004

Standard deviation 0.016 0.023 0.017 0.019

Maximum 0.111 0.111 0.111 0.111

Minimum 0 0 0 0

Number of trees 23,838 12,650 12,007 9,295

Volume (ft3 tree-1)

Mean 77.69 39.55 61.09 83.34

Standard deviation 99.59 51.91 90.41 154.33

Maximum 1,986.80 790.70 1,353.26 5,826.92

Minimum 0.35 0.35 0.35 0

Number of trees 23,161 11,831 11,612 8,900

Note: Diameter and volume are at the time of the first inventory, diameter growth and mortality rate are 

between the two inventories.
32

GENERAL TECHNICAL REPORT PNW-GTR-674 

Appendix 2—Growth-and-Yield Model

The growth model of WestProPlus has the following form (Liang et al. 2005):

 yt + 1 = Gyt

 + r + ut + 1 (1)

where yt = [yijt] is the number of trees per unit area of species group i, and 

diameter class j, at time t, and i = 1 for Douglas-fir, i = 2 for other shade-intolerant 

species, i = 3 for western hemlock, and i = 4 for other shade-tolerant species. The 

matrix G and the vector r are defined as: 

G =

G1

 

G2

 G3  

G4 

, Gi = 

ai1 

ai2 

bi,17 ai,18

ai,19 bi,18

bi1 .

 . . .

 . .

r = 

r1 

, ri = 

ri

r2

r3

r4

0

0. . .

where aij is the probability that a tree of species i and diameter class j stays alive 

and in the same diameter class between t and t+1, bij is the probability that a tree 

of species i and diameter class j stays alive and grows into diameter class j+1, and 

ri is the number of trees of species group i recruited in the smallest diameter 

class between t and t+1, with a period of 1 year. The vector ut+1 represents the 

stochastic part of growth. ut+1 is bootstrapped each year from the set of vector 

differences between the observed and the deterministically predicted stand state, 

for each of the 2,706 plots in Oregon and Washington (Liang et al., in press). The 

bij probability is equal to the annual tree diameter growth, gij (in • yr

-1), divided 

by the width of the diameter class. Diameter growth is a function of tree diameter 

Dj (in), stand basal area B (ft2 • ac

-1), site productivity Q (ft3

 • ac

-1 • yr-1), tree species 

diversity Hs, and tree size diversity Hd.

g1j = 0.3094 + 0.0124Dj - 0.0001Dj - 0.0010B + 0.0007Q + 0.0259Hs - 0.0955Hd

g2j = 0.2403 + 0.0038Dj - 0.0001Dj - 0.0007B + 0.0005Q + 0.0278Hs - 0.0273Hd

g3j = 0.3553 + 0.0148Dj - 0.0003Dj - 0.0010B + 0.0002Q + 0.0098Hs - 0.0689Hd

g4j = 0.2304 + 0.0081Dj - 0.0001Dj - 0.0008B + 0.0005Q + 0.0506Hs - 0.0568Hd

2

2

2

2
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

33

The expected recruitment ri (trees • ac

-1 • yr-1) of species i is represented by a 

Tobit model:

with:

ri = &BixiSi	BixiSiFBixiSi	

B1x1 = -8.8824 - 0.1211B + 0.0971N1 + 0.0227Q + 4.5033Hs - 2.7500Hd

B2x2 = -9.5715 - 0.0773B + 0.0975N2 + 0.0058Q + 3.4070Hs - 2.4200Hd

B3x3 = -12.508 - 0.0872B + 0.0926N3 + 0.0190Q + 5.9506Hs - 4.0100Hd

B4x4 = -13.987 - 0.0700B + 0.0924N4 + 0.0209Q + 3.2546Hs - 0.9200Hd

where Ni is the number of trees per acre in species group i; F and f are respectively the standard normal cumulative and density functions, and the standard 

deviations of the residuals are, s1 = 9.5366, s2 = 9.0863, s3 = 11.0664, s4 = 9.3270.

The probability of tree mortality per year, mij , is a species-dependent probit 

function of tree size and stand state:

m1 = 10.5&-2.1103 - 0.0905Dj + 0.0012Dj + 0.0019B - 0.0014Q + 0.0059Hs + 0.5110Hd 	

m2 = 10.5&-1.4063 - 0.0519Dj + 0.0010Dj + 0.0012B - 0.0010Q + 0.0022Hs + 0.1411Hd 	

m3 = 10.5&-3.1746 - 0.1057Dj + 0.0019Dj + 0.0036B - 0.0016Q + 0.3252Hs + 0.4192Hd 	

m4 = 10.5&-1.5188 - 0.0236Dj + 0.0002Dj + 0.0010B - 0.0021Q + 0.2721Hs + 0.3528Hd 	

1

1

1

1

2

2

2

2

The probability that a tree stays alive and in the same size class from 

t to t+1 is, then:

aij = 1 - bij - mij

The expected single-tree volume vij (ft3) is a species-dependent function of tree 

and stand characteristics:

v1j = -0.01712 - 0.00013Dj + 0.00001Dj + 0.00161B + 0.01174Q + 0.00350Hs + 0.00092Hd

v2j = -0.01536 - 0.00004Dj + 0.00000Dj + 0.00054B + 0.00691Q + 0.00038Hs + 0.00100Hd

v3j = -0.01294 - 0.00016Dj + 0.00001Dj + 0.00087B + 0.00416Q + 0.00185Hs + 0.00145Hd

v4j = -0.00392 - 0.00019Dj + 0.00000Dj + 0.00105B + 0.00584Q + 0.00692Hs + 0.00035Hd

2

2

2

2
34

GENERAL TECHNICAL REPORT PNW-GTR-674 

Table 6—Effect of log diameter at 

20 ft log length on cubic volume to 

board foot conversion (no defects, 

no trim, taper 0.125 in • ft-1) 

 Cubic feet per thousand

Diameter Scribner board feet

Inches ft3 • mbf- -1

5–7 221.4

7–9 303.6

9–11 242.9

11–13 200.0

13–15 189.3

15–17 182.1

17–19 164.3

19–21 157.1

21–23 142.9

23–25 139.3

27+ 142.9

Source: Spelter (2004).

Total stand volume in cubic feet has to be converted to total stand volume in 

thousand board feet (mbf) in order to calculate the value of stocking and harvest. 

The conversion ratios for different log sizes are shown in table 6.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

35

Appendix 3—Log Grade Model

The equations to predict log grade were calibrated with data from 3,378 logs in 

the USFS Product Recovery Database (Stevens and Barbour 2000). The logs 

are classified into five grade categories, according to their diameter, branch size, 

growth rate, and minimum length (Barbour and Parry 2001, Northwest Log Rules 

Advisory Group 1998). For WestProPlus, the logs were divided into the four species groups recognized by the growth model (app. 2). 

In addition to the log grade, the diameter of the logs was known for all species 

groups. The database also contains information on the stands from which the logs 

were taken. However, for Douglas-fir and western hemlock, only the tree diameter 

D (in) and the site index S (ft) influenced log grade significantly (Liang et al., in 

press). 

The log grade was predicted with a logistic regression and a nominal response 

variable:

where πijl /πijm was the ratio between the probability of log grade l (l = 1, 2, ..., m-1), 

and log grade m, for species i and diameter class j. The parameters, bil, of the log 

grade equation for Douglas-fir and western hemlock are in table 7. For both species, log grade was higher for larger trees on sites with lower site index.

There were no data on stand characteristics for other shade-tolerant and 

shade-intolerant species, and no systematic relation was observed between grade 

and diameter for these species groups. WestProPlus uses the observed percentages 

of total volume by log grade for each diameter class, and assumes that they are 

constant (table 8). 
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GENERAL TECHNICAL REPORT PNW-GTR-674 

Table 7—Estimation results of the nominal-logistic equations of log grade

Dependent Independent Standard Probability P

variable variable Coefficient error (a = 0.05)

Douglas-fir

π1/ π4 Constant 2.91 1.20 0.02

 D 0.02 0 0

 S -0.33 0.10 0

π3/ π4 Constant 1.66 1.43 0.25

 D 0.02 0 0

 S -0.33 0.13 0.03

Western hemlock

π1/ π4 Constant -8.94 4.28 0.04

 D 0.16 0.02 0

 S -1.33 0.50 0.03

π2/ π4 Constant -8.37 4.04 0.04

 D 0.14 0.02 0

 S -1.00 0.43 0.07

π3/ π4 Constant -5.90 1.59 0

 D 0.10 0.01 0

 S -0.43 0.13 0

πl = probability of log grade l (no Douglas-fir logs were observed for grade 2; grade 5 was not observed for 

either species).

D = tree diameter.

S = site index.

P = level at which the effect of the control variable would be just significant.

Table 8—Percentage of timber volume by log grade (1 through 5) and size for 

the shade-intolerant species except Douglas-fir, and the shade-tolerant species 

except western hemlock

Other shade-intolerant species Other shade-tolerant species 

Diameter 1 2 3 4 5 1 2 3 4 5

in - - - - - - - - - - - - - - - - - - - - - - - Percent - - - - - - - - - - - - - - - - - - - - - - -

4 0 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 30 0 58 12

8 0 0 0 100 0 0 30 0 66 4

10 0 20 0 80 0 0 37 0 61 1

12 0 24 0 76 0 0 35 0 64 1

14 0 23 10 66 0 0 33 12 55 0

16 0 16 59 25 0 0 28 50 20 2

18 0 20 69 7 4 0 36 47 16 1

20 0 16 78 6 0 0 36 48 11 4

22 0 21 79 0 0 0 29 60 9 2

24 0 14 77 4 5 0 37 50 11 2

26 6 27 64 3 0 1 26 66 6 1

28 7 33 58 2 0 1 40 52 6 1

30 19 43 36 2 0 1 32 56 7 4

32 21 43 29 0 7 3 42 50 5 0

34 13 69 13 0 6 0 44 52 4 0

36 0 70 20 0 10 0 44 48 8 0

38 0 40 60 0 0 8 62 31 0 0

40 0 75 25 0 0 0 43 50 0 7
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

37

Table 9—Stumpage prices ($ • mbf-1) in Oregon by log grade and species group 

in 2005 

Log Other shade- Other shadegrade Douglas-fir intolerant species Western hemlock tolerant species

- - - - - - - - - - - - - - - - - - - - - - $ • mbf -1 - - - - - - - - - - - - - - - - - - - - - -

1 765 550 275 650

2 465 540 270 625

3 435 440 245 625

4 390 375 205 625

5 50 50 50 65

Price source: Oregon Department of Forestry (2005), and an assumed logging and hauling cost of $180 mbf -1.

Appendix 4—Stochastic Stumpage Price and 

Interest Rate Models

The stumpage price model in WestProPlus (Liang et al., in press) was calibrated 

with quarterly stumpage prices of Douglas-fir grade 1 logs from 1977 to 2003 in 

Oregon (Oregon Department of Forestry 2005). The following autoregressivemoving average model was used to represent quarterly price changes:

DPt+1 = -0.60DPt + 0.05et + et+1 (3) 

where Pt and Pt+1 were stumpage prices ($ • mbf -1) at quarter t and quarter 

t+1, respectively, and et was a white-noise residual error. The parameters were 

estimated from the data with the Box-Jenkins method. WestProPlus simulates 

stochastic price series with this model by bootstrapping, i.e., by drawing randomly 

with replacement at each step t a pair of shocks et and et+1 from the residuals 

obtained by fitting model (3) to the data. 

The initial price of Douglas-fir grade 1 logs is equal to that entered by the 

user (fig. 1), or lacking this, it is bootstrapped from the prices observed from 1977 

to 2003. With bootstrapped initial prices, the mean predicted stumpage prices 

of Douglas-fir grade 1 logs and the standard error over 500 replications of 100-

year simulations had a slight positive trend over time, but it was not statistically 

significant.

The prices of logs of grades other than grade 1 is calculated according to the 

relative prices entered by the user (fig. 1), or lacking this, according to the relative 

prices in table 9. In either case, the relative prices are assumed to be constant over 

time. 
38

GENERAL TECHNICAL REPORT PNW-GTR-674 

The annual rate of return of AAA bonds from 1970 to 2004 (US GPO 2005) 

was used as the interest rate. WestProPlus uses an autoregressive model of interest 

rates:

rt+1 = 0.72 + 0.81rt + et (4)

where rt was the interest rate at year t, and et was the white-noise residual. 

WestProPlus simulates stochastic interest rates by bootstrapping: at each step t, 

a shock was drawn randomly with replacement from the sample of the residuals 

obtained by fitting the model to the data. With bootstrapped initial interest rate, 

the mean predicted interest rate over 500 simulations showed no trend over time.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

39

Appendix 5—Definition of Diversity of Tree Species 

and Size

WestProPlus uses Shannon’s index to measure the stand diversity in terms of tree 

species (how uniformly trees are distributed across species groups), and timber 

size classes. WestProPlus measures the presence of trees in a class by their basal 

area, which gives more weight to larger trees. 

The tree species diversity is defined in WestProPlus as:

where yi is the basal area of trees of species group i per acre, and y is total basal 

area. In WestProPlus, m = 4 (there are four species groups). The tree species diversity has a maximum value of ln(4) = 1.39, when basal area is equally distributed 

in the four species groups, and a minimum value of zero when all trees are in the 

same species group.

Similarly, tree size diversity is:

where yj is the basal area of trees in diameter class j per acre. In WestProPlus, 

n = 19 diameter classes. The tree size diversity has a maximum ln(19) = 2.94 

when basal area is equally distributed in all 19 diameter classes, and a minimum 

of zero when all trees are the same diameter class.
40

GENERAL TECHNICAL REPORT PNW-GTR-674 

Glossary

BA chart—A WestProPlus-generated chart showing, for a selected range of years, 

the per-acre basal area of softwoods, hardwoods, and the whole stand.

BDq distribution—A tree distribution, by diameter class, defined by a stand basal 

area (B), a maximum and minimum tree diameter (D), and a q-ratio (q), the ratio 

of the number of trees in a given diameter class to the number of trees in the next 

larger class.

bootstrap method—When used in stochastic simulations, this technique simulates 

random variables by sampling randomly (with replacement) from actual observations of the variable, rather than from an assumed distribution. See Efron and 

Tibshirani 1994 for the details. 

cutting cycle—The number of years between successive harvests. For two-cut 

silvicultural systems, this is the number of years between the two harvests.

diameter class—One of nineteen 2-in diameter at breast height (d.b.h.) categories 

used by WestProPlus to classify trees by size. Diameter classes range from 4 to 

40+ in, with each class denoted by its midpoint diameter. Diameter class 4 is 

for trees with diameters from 3 to less than 5 in. The 40+ in class is for all trees 

with 39 in diameter and larger.

diversity chart—A WestProPlus-generated chart showing changes in the 

Shannon index of species or size diversity over a selected range of years.

initial stand state—The number of live trees per acre, by species and size, at the 

start of a simulation.

input data worksheet—A worksheet to enter the data for running a WestProPlus 

simulation.

log grade— An estimate of the type and quality of lumber recovered when the 

log is sawed.

Microsoft Excel add-in—A command, function, or software program that runs 

within Microsoft Excel and adds special capabilities. WestProPlus is an add-in.

net present value (NPV)—The net revenue discounted to the present.

preharvest stand state—The number of live trees per acre, by species and size, 

immediately before a harvest.

products worksheet—A WestProPlus output worksheet that shows, for each 

harvest, the basal area cut, the volume removed by grade, the gross income 

generated, and the net present value of the harvest, as well as the total net 

present value of the stand and its mean annual production in terms of basal 

area cut and volume harvested, on a per acre basis.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

41

re-entry costs—Costs per acre associated with each harvest that are not reflected 

in the stumpage prices. These may include, e.g., the added expense of marking 

the stand for single-tree selection or for controlling hardwood competition.

setup file worksheet—A worksheet to store WestProPlus setup files. It is typically 

hidden.

setup files—Collections of related input data that are stored together on a Setup 

File worksheet. Setup files may contain data for initial stand states, target stand 

states, cutting cycle parameters, stumpage prices, or fixed costs, and may be used 

in varying combinations as input for WestProPlus simulations.

site index—The average height of a stand’s dominant and codominant trees at 

age 50 years.

size diversity—The diversity of tree diameter classes as measured by the Shannon 

index. With 19 diameter classes, size diversity reaches its maximum value of 2.94 

when the basal area or number of trees is distributed evenly among the diameter 

classes.

species diversity—The diversity of species groups as measured by the Shannon 

index. With four species classes, species diversity reaches its maximum value 

of 1.39 when the basal area or number of trees is distributed evenly among the 

species groups.

species groups—The four categories used by WestProPlus to classify trees by 

species. For a complete list of species, see table 3.

Douglas-fir—Pseudotsuga menziesii.

Other shade-intolerant species—Including Alnus rubra, Pinus ponderosa, 

Pinus contorta, etc. 

Western hemlock—Tsuga heterophylla.

Other shade-tolerant species—Including Thuja plicata, Acer macrophyllum, 

Abies grandis, etc. 

stumpage prices—Prices paid to a landowner for standing timber.

target stand state—The desired number of live trees per acre in each species 

group and diameter class after a harvest.

total net present value—The sum of all discounted revenues minus the sum of 

all discounted costs.

workbook—The workbook is the normal document or file type in Microsoft 

Excel. A workbook is the electronic equivalent of a three-ring binder. Inside 

workbooks you will find sheets, such as worksheets and chart sheets.
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GENERAL TECHNICAL REPORT PNW-GTR-674 

worksheet—Most of the work you do in Excel will be on a worksheet. A worksheet 

is a grid of rows and columns. Each cell is the intersection of a row and a column 

and has a unique address, or reference.
WestProPlus: A Stochastic Spreadsheet Program for the Management of All-Aged Douglas-Fir–Western Hemlock Forests

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