United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

General Technical

Report RMRS-GTR-57

August 2000

Reliability of Confidence

Intervals Calculated by

Bootstrap and Classical

Methods Using the FIA 1-ha

Plot Design

H. T. Schreuder

M. S. Williams

0 

μˆ ˆ − t σn 5,000 

μˆ 10,000 

μˆ ˆ + t σn

Bootstrap or Classical?
Abstract

Schreuder, H. T.; Williams, M. S. 2000. Reliability of confidence intervals calculated by

bootstrap and classical methods using the FIA 1-ha plot design. Gen. Tech. Rep. RMRSGTR-57. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain

Research Station. 6 p.

In simulation sampling from forest populations using sample sizes of 20, 40, and 60 plots

respectively, confidence intervals based on the bootstrap (accelerated, percentile, and t-distribution

based) were calculated and compared with those based on the classical t confidence intervals for

mapped populations and subdomains within those populations. A 68.1 ha mapped population,

constructed out of 0.081 ha (1/5 acre) Forest Inventory and Analysis of the USDA Forest Service

(FIA) plot measurements at 2 points of time in Maine, United States and a 64 ha mapped population

from Surinam, South America with only one measurement, were used. The plot designs used were

the FIA plot consisting of a 1-ha circular plot subsampled by four 0.0169 ha (1/24 acre) subplots, a

0.081 ha plot that was used in the north east by FIA, and a 10-point cluster of VRP plots that was used

in the north central by FIA.

The confidence intervals of all estimates, even those from a sample of size 60, failed to meet the

nominal 95% standard. Of the 4 methods used to derive the intervals, the classical method was

consistently best in terms of achieved confidence level. This was followed by the three bootstrap

methods: t-distribution based, accelerated, and percentile.

We recommend use of the classical t confidence intervals even for small sample sizes and less

common attributes. If the classical standard error cannot be computed easily, the t-distribution based

bootstrap should be used since it gives only slightly less reliable confidence levels. Also, the

bootstrap standard error can often be computed in situations where the classical standard error

cannot be.

Keywords: FIA plot, subdomains, simulation study, mapped populations, fixed-area sampling

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Telephone (970) 498-1392

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E-mail rschneider@fs.fed.us

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240 West Prospect Road

Fort Collins, CO 80526

The Authors

H. T. Schreuder and M. S. Williams are Mathematical Statisticians, Rocky Mountain Research

Station, USDA Forest Service, located at the Natural Resources Research Center, 2150 Centre

Avenue, Building A, Fort Collins, CO 80526.
Reliability of Confidence Intervals Calculated

by Bootstrap and Classical Methods Using

the Fia 1-Ha Plot Design

H. T. Schreuder

M. S. Williams

Contents

Introduction ...................................................................................................................... 1

Literature Review ............................................................................................................. 1

Methods ............................................................................................................... 3

Materials and Methods ..................................................................................................... 3

Results and Discussion .................................................................................................... 3

Summary .......................................................................................................................... 6

Literature Cited ................................................................................................................ 6

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-57. 2000 1

Introduction

Dale Robertson (1993), Chief of the USDA Forest

Service (FS) ordered mapped designs (ground plots

mapped for the forest conditions and ecotones

within them) be used by all Forest Inventory and

Analysis (FIA) units in their inventories and on

National Forest System lands.

In the Forest Health Monitoring program (FHM) of

the FS, a cluster of 4 fixed-area circular subplots are

used to sample a circular 1-ha plot1

. These subplots (

radius of 7.32 m = 24 ft) are mapped for forest conditions (Messer et al. 1991, Scott et al. 1993). This official

FIA plot design is favored over a similar one involving

variable radius plot (VRP) sampling (Hahn et al. 1995)

that was considered earlier. Estimation theory for the

design is given in Williams and Schreuder (1995) and

Scott and Bechtold (1995).

Previously, the northeastern FIA unit of the FS (NE

FIA) used a 0.081 ha (1/5-acre) circular plot (radius =

57.2 ft) at each location. The other FIA units used a 5 or

10-point cluster of VRP plots.

Little or no work has been done to evaluate the

reliability of confidence intervals for estimating forest

parameters as conducted by FIA. The primary objective of the FIA program is to produce estimates of

forest attributes such as total volume and number of

trees and change in such attributes over time for large

regions of the United States. For these common attributes, the assumption of normality approximated

by the t-distribution should be reasonable and the

nominal coverage rates will generally be achieved

even for fairly small sample sizes. But, often users are

interested in generating estimates for subpopulations

or for subdomains, where the latter are subpopulations known for the sampled but not for the unsampled

units of the original data set.

An excellent example of this is the subdomain represented by the screened plots used to establish a possible growth decline in Georgia and Alabama. This

situation occurred in the mid 1980s. A series of studies

(Gadbury et al. 1998, Ueng et al. 1997, Zeide 1992, and

references therein) debated whether the growth of

naturally occurring, undisturbed stands of various

pine species had declined from the period of 1962-1972

to the period of 1972-82. As noted in Casady et al.

(1998), confidence intervals for subdomains constructed

along traditional (classical) lines can lead to serious

undercoverage; a fact not always appreciated in the

literature. In forestry, confidence intervals for

subdomain estimates constructed from traditional asymptotic theory can be subject to serious undercoverage

because the assumption of normality is not even remotely satisfied by the distribution of subdomain estimates. This is particularly true for those that are a

mixture of 0 estimates with extremely skewed continuous distribution (e.g. plot mortality estimates).

The objective of this study was to compare the classical and 3 types of bootstrap methods for estimating

confidence intervals at a given nominal (95%) level for

the standard FIA, the north east (NE) 0.081 ha and the

north central (NC) 5-point VRP plots. We evaluated

the reliability by coverage rate since we wanted high

confidence that the statements made were correct. A

68.1 ha mapped population constructed for 2 points of

time from original FIA 1/5 acre plots in Maine and a 60

ha Surinam population mapped at one point of time

were used. The bootstrap methods are the percentile

bootstrap, the t-distribution based bootstrap, and the

accelerated bootstrap methods, which are described

later.

Literature Review

Current objectives for FIA are to generate descriptive statistics, detect changes in such statistics, and

analyze the data to identify, and possibly establish,

cause-effect relationships (Schreuder and McClure

1991). Analytical inference using forest-survey data is

becoming more important and requires examination

of confidence intervals, which is the common way of

testing significance of hypotheses with survey data.

Use of survey data to establish cause-effect relationships is controversial (Schreuder and Thomas 1991),

but such data have been used to identify possible

cause-effect relationships in epidemiology (Feinstein

1988). Schreuder and McClure (1991) suggest modifications of the FIM designs to improve change detection and identify possible causes of change.

Such change in objectives to analytical inference

forces more reliable estimation of confidence intervals

and confidence levels for hypotheses testing. At the

same time, new methods, such as the bootstrapping

methods described below, offer exciting new possible

solutions to reliable confidence interval estimation.

Efron and Tibshirani (1993) define the bootstrap as a

computer-based method to assign measures of accuracy to statistical estimates. They note (p.160) that with

the bootstrap method accurate confidence intervals

1

FIA units now often consider the 4 subplots to be the actual plot. can be constructed without making normal theory
2 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-57. 2000

assumptions. Bootstrapping also does not have symmetric confidence intervals when the distribution of

possible estimates may not be symmetric, as is often

the case with subdomain estimates. This is especially

important when the goal of the inference is to determine the sustainability of a resource. In this case, the

test of hypothesis determines whether 0 is included in

the confidence interval (see for example Williams 1998

for subdomain change estimates).

The bootstrap t-method from Efron and Tibshirani,

1993 builds a table of bootstrap t-values. B bootstrap

samples are generated and used to compute the

bootstrap version of t for each. The bootstrap table

consists of the percentiles of these B values with the

lower 

α / 2 and upper α / 2percentage of the values

eliminated. Efron and Tibshirani recommend against

this method because it can give erratic results, can be

heavily influenced by a few outliers, and better

bootstrap methods are available.

In the percentile interval method of bootstrapping

(Efron and Tibshirani 1993), B bootstrap estimates

 

ˆ * θ are generated. If 

G(ˆ )

* θ is the cumulative distribution function of 

ˆ * θ , then the percentile interval is:

 

(ˆ , ˆ ) (ˆ , ˆ ) [ ˆ ( / ), ˆ ( / )] *( / ) *( / ) θθ θ θ α α α α

lo up = = G G − 2 12 1 1 −−− 2 12

for coverage 

1− α where 

ˆ *( / ) θ α 2 indicates the

 

100 2 . / α th percentile of B bootstrap replications.

 

ˆ ( ), ˆ ( ), , ˆ ( ) ** * θθ θ 1 2 ... B ⋅

Efron and Tibshirani note that the bootstrap-t intervals have good theoretical coverage probabilities but

tend to be erratic in practice. The percentile intervals

are less erratic but have less desirable coverage properties. We eliminated the bootstrap-t procedure from

consideration after some preliminary simulations

showed it to perform quite poorly.

A method that corrects for bias due to non-normality and accelerates convergence to a solution by correcting for the rate of change of the normalized standard error of 

ˆ

θ relative to the true parameter θ in

constructing the confidence limits of the percentile

interval method is called BCa. This method yields

substantially improved limits in both theory and

practice although the accuracy of the actual confidence level can still be erratic for small sample sizes

(Efron and Tibshirani 1992). This method is accurate

and unaffected by transformations. The BCa interval

with desired coverage 

1− α is:

 

(ˆ , ˆ ) (ˆ , ˆ θθ θ θ ), α α

lo hi = 1 2 where

 

α φ α α 1 1 0 0

2

0

2 = ++ {ˆ (ˆ ) /( − ˆ(ˆ + ))} (/) (/) z z z az z

and

 

α φ α α 2 1 0 0

1 2

0

1 2 = ++ − + − − {ˆ (ˆ ) /( ˆ(ˆ ))} ( /) ( /) z z z az z

where z(.)is the (.) percentile of the standard normal.

The bias correction term 

zˆ0 is obtained by computing

the proportion of bootstrap estimates less than the

original estimate 

ˆ

θ, say pB, and then computing:

 

z pB ˆ ( ) 0

1 = − φ

where 

φ−1 is the inverse function of a standard normal cumulative distribution function. The acceleration is:

 

ˆ [ (ˆ ˆ ) ]/ [ (ˆ ˆ ) ] (.) ( ) (.) ( )

/ a i i

i

n

i

n

= − −

= =

∑ θθ θθ ∑ 3 232

1 1

6

where the 

ˆ

θ( )i and 

ˆ

θ(.) are the ith and average jackknife estimates of the parameter, and 

αˆ is the acceleration because it measures the change of the standard error of 

ˆ

θ relative to the value θ. This method

has two advantages. One advantage is that this method

is unaffected by transformations so that the BCa

endpoints transform correctly if the parameter of

interest θ is changed to some function of θ. A second

advantage to this method is that the BCa intervals are

second order accurate (i.e., their errors in matching

the true confidence levels go to 0 as a function of 

1/ n

as opposed to the bootstrap-t and percentile methods

which are of order 

1/ n ). This means that BCa gives

better approximations of exact endpoints if they

exist. Efron and Tibshirani do not discuss the use of

the standard t-distribution with the bootstrap estimator of standard error considered here, called the

t-distribution based bootstrap. This method uses the

classical estimator for θ with the bootstrap standard

error.

Efron and Tibshirani also discuss what they call the

ABC bootstrap method, which eliminates the problem

of excessive computations as required in the BCa

method. The ABC method uses Taylor series expansions for approximations so that the estimates may

break down occasionally, principally for non-smooth

statistics such as the sample median. Since we want a

robust procedure not subject to occasionally dubious

results, and since the number of computations generally should not be a concern for our applications, we do

not consider the ABC procedure here.

Smith (1997) evaluates the use of bootstrap confidence limits for groundfish trawl survey estimates of

average abundance. In such surveys, stratified sampling is often used to monitor groundfish populations.

The small sample sizes used and the skewed data

characteristics of the variable of interest may be appropriate for the classical large sample properties of such
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-57. 2000 3

estimates. Simulation results show that the percentile

bootstrap limits were close to the expected values and

that the bias, corrected and accelerated bootstrap confidence limits, can overcorrect for the data.

Methods

Random samples were drawn from mapped populations using a random number generator described

in Kahaner et al. (1988), and the confidence limits at

the nominal 95% confidence level were determined

for the classical and 3 bootstrap methods in estimating a series of parameters. We focused on small

sample sizes because all methods considered should

work well for large sample sizes where asymptotic

results are relevant and because FIM and similar

surveys often have sample sizes of 30 or less due to

considerable post-stratification.

Materials and Methods

The following populations were used in the

simulations:

Maine: this consists of 841 mapped circular 0.081

ha (1/5 acre) plots for which tree measurements

were recorded at 2 time periods. These plots were

combined judiciously to give a square population of

68.1 ha using the transformation described by Williams et al. (2000). The population was divided into 3

distinct forest types, softwood, hardwood, and mixed

softwood-hardwood. A plot was classified as either

hardwood or softwood if 75% or more of the trees in

it fell into one of the 2 categories, otherwise it was

classified as mixed hardwood-softwood. The mix of

hardwoods and softwood trees changed in the interval between measurements resulting in change in

forest type. Plots were arranged within the 68.1 ha

square to separate the population into 6 stands (2

each of hardwood, softwood, and mixed hardwoodsoftwood).

Surinam: this comprised a 60-ha (1500 x 400 m)

section of a forest in Surinam, South America mapped

by a group of students of S.G.Banyard (Schreuder et al.

1987) at the International Institute for Aerial Survey

and Earth Sciences ITC in Enschede, Netherlands. The

coordinates of all 6806 trees were digitized with a

mechanical digitizer to the nearest 0.1 m and recorded

on a computer-compatible tape along with tree diameters and species.

For the simulation, we drew a series of 4000 samples

of size 20, 40, and 60 using randomly selected point

centers as a starting point for all 3 plot designs. For

Maine, we focused on the parameter estimates of the

initial number of trees (N1), change in number of trees

(∆N), basal area (BA), basal area growth (S) as estimated by the Van Deusen estimator (Schreuder et al.

1993, p.145) , mortality (M), and removals (R) using

Horvitz-Thompson type estimators as described in

Williams and Schreuder (1995). This was done for the

population and also for subdomains of seedlingsaplings, pole timber, and sawtimber-size trees. For

Surinam, estimates were generated for number of

trees and basal area for the population and for 3 species

groups selected such that groups 1 and 2 were common and group 3 was rare.

The methods are denoted by Cl for classical, Bt for

bootstrapping using the standard t distribution, Bp for

the percentile bootstrap, and BCa for the accelerated

bootstrap.

Results and Discussion

We show only the results for the FIA plot design

since the other plot designs add little to the results. On

average these plot designs provide slightly worse results than the FIA plot in terms of confidence-level

cover rates. We show the results for one subdomain

and for the overall population. The width of the standard bootstrap confidence intervals are almost always

the shortest, those for the accelerated bootstrap next,

with those for the classical t confidence intervals being

almost always the widest. This is why the actual confidence levels for the classical estimation are usually

the most reliable.

Maine results (table 1 and figures 1 through 4):

1. The 95% nominal confidence level is almost never

reached by any of the 4 estimation techniques.

2. The classical confidence levels are almost always

better than for the t-distribution based bootstrap, which

is almost always better than the accelerated bootstrap,

which is usually better than the percentile bootstrap.

3. The actual coverage rate approaches the nominal value generally, as one goes from n=20 to n=40

to n=60 (except for Cl, Bt, and Bp with S). But even

for n=60, the actual is still often below the nominal

level and this is particularly true for the more rare

variables (mortality, removals, and other attributes

not shown).
4 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-57. 2000

Table1—Actual and 95% nominal confidence levels for 3 sample sizes and 4 estimation methods for 1 domain and for the

entire population for Maine and Surinam South America; 4000 samples, 4000 bootstrap samples.

Maine sample size

20 20 40 40 60 60

Parameter Method Hardwood All Hardwood All Hardwood All

 Nˆ Cl-*2 92.9 94.3 93.7 94.6 94.8 94.8

Bt 92.5 93.6 93.3 94.3 94.7 94.6

Bp 92.4 92.4 91.9 93.7 94.6 94.1

Bca 93.8 92.6 93.7 94.0 94.8 94.6

 

∆Nˆ Cl 93.4 94.2 94.8 94.0 95.0 94.2

Bt 93.0 93.4 94.5 93.7 94.8 93.9

Bp 91.2 91.9 93.7 93.1 94.3 93.8

BCa 91.3 92.7 93.8 93.4 93.9 93.9

 BAˆ Cl 93.8 94.8 94.9 94.4 94.7 94.5

Bt 93.2 94.2 94.7 94.1 94.6 94.2

Bp 92.7 92.5 94.5 93.4 94.7 94.0

BCa 93.5 92.9 94.7 93.6 95.1 94.1

 

∆ ˆS Cl 92.7 95.1 94.7 94.6 94.8 94.4

Bt 92.5 94.6 94.7 94.2 94.7 94.2

Bp 90.4 94.6 93.1 93.5 93.8 93.8

BCa 90.7 93.3 93.1 93.6 93.4 93.9

 Mˆ Cl 88.3 93.4 91.6 93.9 92.0 93.9

Bt 87.7 92.7 91.2 93.9 91.8 93.8

Bp 87.9 91.2 91.6 93.3 92.0 93.3

BCa 89.7 91.9 92.6 93.6 93.5 93.7

 

Cˆ Cl 85.4 91.5 90.0 93.0 91.8 93.0

Bt 85.0 91.0 89.7 92.9 91.7 93.8

Bp 85.3 90.2 90.4 92.5 92.2 93.6

BCa 86.6 91.4 91.7 93.2 93.1 94.1

Surinam sample size

20 20 40 40 60 60

Rare All Rare All Rare All

 Nˆ Cl 92.3 95.4 93.8 94.6 92.4 94.9

Bt 92.0 94.8 93.1 94.3 92.4 94.9

Bp 91.2 93.5 93.3 93.9 92.3 94.4

BCa 90.7 93.6 90.7 94.0 91.3 94.5

 BAˆ Cl 90.0 93.8 92.6 94.4 92.6 94.2

Bt 89.4 93.3 92.2 93.9 92.5 94.1

Bp 89.5 91.9 92.3 93.1 92.4 93.6

BCa 89.6 92.1 93.1 93.6 93.3 93.7

*2 Cl=classical,Bt=standard bootstrap, Bp=percentile bootstrap, Bca=accelerated bootstrap.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-57. 2000 5

Cl

Bt

Bp BCa

n= 20

n= 40

89 n= 60

90

91

92

93

94

Cl

Bt

Bp BCa

n= 20

n= 40

88 n= 60

90

92

94

96

Cl

Bt

Bp

BCa

n=20

n=40

n=60 89

90

91

92

93

94

Cl

Bt

Bp BCa

n= 20

n= 60 92

93

94

95

96

n= 40

Surinam results (table 1):

1. The classical confidence intervals are consistently

best in terms of the closeness of the actual achieved

confidence level to the nominal ones. This is true for all

3 sample sizes. The actual and nominal levels are

generally very close but the actual improves only

slightly, with increasing sample size; the actual is

rarely above 95%.

2. The accelerated bootstrap method has better

attained confidence levels than the percentile

method. Specifically, the accelerated bootstrap is

Figure 2—Percent coverage rates for mortaity, Mˆ .

Figure 3—Percent coverage rates for number of trees Nˆ .

Figure 4—Percent coverage rates for removals, 

Cˆ .

better in 55 cases, worse in 31, and tied 22 times

relative to the percentile method.

3. The bootstrap actual confidence levels show a

consistent improvement going from n=20 to n=40 to

n=60. Even for n=60, the actual does not reach the

nominal 95% level.

4. The confidence interval widths for the bootstrap

methods are almost always narrower than for the

classical method (not shown).

5. There is little difference between the 3 designs, but

the FIM plot yields slightly higher actual confidence

levels (not shown).

Figure 1—Percent coverage rates for survivor growth, 

∆ ˆS .

Cl

Bt

Bp

BCa
6 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-57. 2000

After reading the papers of DiCiccio and Efron

(1996) and Efron and Tibshirani (1993), we had

expected the accelerated bootstrap method of

calculating confidence intervals to be superior to

the other methods tested. But as these authors

concede, this method can be erratic for small sample

sizes where asymptotic results do not apply. Yet,

such sample sizes are quite prevalent for many

applications of FIA type data. Population Maine, as

constructed, is extremely variable since these are

FIA plots from across the entire state. But population Surinam is a real population and yielded basically the same results.

The great advantage of bootstrapping is that confidence intervals can be generated easily no matter

how complex the actual sampling design is and the

standard errors can be computed when it is difficult

or impossible to compute classical standard errors.

A further important advantage is that bootstrap

confidence intervals tend to reflect the true nature of

the sample distribution. Thus, the interval estimate

will contain negative values only when the data give

some indication that it is a real possibility, unlike the

classical methods. Therefore, we feel that inference

based on bootstrap methods is potentially more

meaningful in spite of the inferior coverage rates.

Given the advantages of bootstrapping, it is disappointing that these methods did not perform well

with small sample sizes.

Summary

For the sample sizes considered, the results show

rather conclusively that classical confidence intervals

are more reliable than those for the bootstrap using the

standard t-distribution, the accelerated bootstrap and

the percentile bootstrap, in that order. If the classical

standard error cannot be computed, the bootstrap

with standard t-distribution is the method of choice.

Actual coverage probabilities are close to the nominal

95% confidence levels for n=60 but clearly, improved

methods are needed to attain it with a high degree of

confidence. Bayesian methods (Cassidy et al. 1998) or

saddle-point approximations, as successfully implemented in Li et al. (1995), may be the answer ultimately

but, at present, they are difficult to implement.

Literature Cited

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for domain parameters when the domain size is random. Survey

Meth. 24:57-67.

DiCiccio, T.J. and Efron, B. 1996. Bootstrap confidence intervals. Stat.

Sci 11:189-228.

Efron, B and Tibshirani, R.J. 1993. An Introduction to the Bootstrap.

Chapman and Hall, NY. 436 p.

Feinstein, A. R. 1988. Scientific standards in epidemiologic studies of

the menace of daily life. Science 242: 1257-1263.

Gadbury, G.L., Iyer, H.K., Schreuder, H.T. and Ueng, C.Y. 1998. A

nonparametric analysis of plot basal area growth using tree based

models. USDA Forest Service Rocky Mountain Res. Paper RMRSRP-2.

Hahn, J. T., MacLean, C. D., Arner, S. L., and Bechtold, W. A. 1995.

Procedures to handle FIA cluster plots that stradle two or more

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Kahaner, D, Moler, C and Nash, S. 1988. Numerical methods and

software. Prentice Hall, NY.

Li, J, Chen, M-C, Schreuder, H.T. and Gregoire, T.G. 1995. Forestry

applications of saddle-point approximations to construct confidence intervals for population means. Biometrics 51: 61-72.

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A., Poso, S., Rautala, J., eds. Proc. Ilvessalo Symposium on National

Forest Inventories. Helsinki, Finland, August 17-21, 1993. Finnish

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Shao, J and Tu, D. 1995. The jackknife and bootstrap. Springer Series

in Stat 516 p.

Smith, S.J. 1997. Bootstrap confidence limits for groundfish trawl survey

estimates of mean abundance. Can J Fish Aquat Sci 54:616-630.

Ueng,C.Y., Gadbury, G.L. and Schreuder, H.T. 1997. Robust regression analysis of growth in basal area of natural pine stands in

Georgia and Alabama, 1962-72 and 1972-82. USDA Forest Service

RM Forest and Range Exp Station Res Paper RM-RP-331.

Williams, M.S. 1998. Distinguishing between change and growth in

forest surveys. Can. J. For. Res 28:1099-1106.

Williams, M. S. and Schreuder, H. T. 1995. Documentation and

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used by FIA: A simulation study. For. Sci. 31, 41:26-45.

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correcting for off-plot influences on circular fixed-area plots in

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Statistics.

Zeide, B.1992. Has pine growth declined in the Southeastern United

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range, forests, water, recreation, fire, resource inventory, land reclamation, community sustainability, forest engineering technology,

multiple use economics, wildlife and fish habitat, and forest insects

and diseases. Studies are conducted cooperatively, and applications

may be found worldwide.

Research Locations

Flagstaff, Arizona Reno, Nevada

Fort Collins, Colorado* Albuquerque, New Mexico

Boise, Idaho Rapid City, South Dakota

Moscow, Idaho Logan, Utah

Bozeman, Montana Ogden, Utah

Missoula, Montana Provo, Utah

Lincoln, Nebraska Laramie, Wyoming

*Station Headquarters, Natural Resources Research Center,

2150 Centre Avenue, Building A, Fort Collins, CO 80526