United States

Department of 

Agriculture

Forest Service

Pacific Northwest

Research Station

General Technical

Report

PNW-GTR-555

October 2002

Adjusting for Radiotelemetry

Error to Improve Estimates 

of Habitat Use 

Scott L. Findholt, Bruce K. Johnson,

Lyman L. McDonald, John W. Kern, Alan Ager, 

Rosemary J. Stussy, and Larry D. Bryant
Scott L. Findholt, Bruce K. Johnson, and Rosemary J. Stussy are wildlife

research biologists, Oregon Department of Fish and Wildlife, 1401 Gekeler Lane, 

La Grande, OR 97850; Lyman L. McDonald is president and biometrician, Western

Ecosystems Technology, Inc., 2003 Central Avenue, Cheyenne, WY 82001; Alan

Ager is a research analyst, U.S. Department of Agriculture, Forest Service, Umatilla

National Forest, 2517 S.W. Hailey Avenue, Pendleton, OR 97801; John W. Kern is

a biometrician, Kern Statistical Services, Inc., 415 NW Robert, Pullman, WA 99163;

and Larry D. Bryant is a national range ecologist, U.S. Department of Agriculture,

Forest Service, P.O. Box 96090, Washington, DC 20090.

Authors
Findholt, Scott L.; Johnson, Bruce K.; McDonald, Lyman L.; Kern, John W.; 

Ager, Alan; Stussy, Rosemary J.; Bryant, Larry D. 2002. Adjusting for radiotelemetry error to improve estimates of habitat use. Gen. Tech. Rep. PNW-GTR555. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific

Northwest Research Station. 14 p.

Animal locations estimated from radiotelemetry have traditionally been treated as

error-free when analyzed in relation to habitat variables. Location error lowers the

power of statistical tests of habitat selection. We describe a method that incorporates the error surrounding point estimates into measures of environmental variables determined from a geographic information system. We estimated a bivariate

ellipsoidal probability density for errors surrounding radio collars placed at 20 random

sites. This probability density of errors was used to construct probability-weighted

estimates of environmental variables. Computer simulations indicated that slope,

sine and cosine of aspect, and canopy cover at radiotelemetry locations differed

from probability-weighted estimates of those variables (P ≤ 0.031). However, these

differences were based on large sample sizes (n ≥ 305) and were probably too

small to influence power of statistical tests of habitat selection. The frequency with

which soil, plant community, and canopy cover types were correctly classified with

simulated radiotelemetry point estimates increased with increasing patch sizes

(P ≤ 0.005). Our method could be used to assess how accurately environmental

variables can be determined across extremes of habitat and topography and the

spatial scale at which analyses retain adequate power. It also could be used with

other radiotelemetry systems, including those based on global positioning system

technology, if sufficient locations are obtained to describe their probability 

distribution. 

Keywords: Automated tracking, error neighborhood, habitat selection, LORAN-C,

Oregon, principal components analysis, radiotelemetry location error, Starkey. 

Abstract 
This space is intentionally left blank.
Habitat studies require accurate estimates of an animal’s location to correctly measure habitat variables (Nams 1989, White and Garrott 1990). Accurate estimates are

especially important when the study area contains a mosaic of small habitat patches.

Although errors have been recognized in both aerial (Garrott et al. 1987, Harrington

et al. 1987) and triangulation (Hupp and Ratti 1983, Lee et al. 1985, Springer 1979)

radiotelemetry methods, these errors are often ignored when determining environmental characteristics of estimated locations (Saltz 1994).

The main effect of error in the estimates of radiotelemetry locations is lower power

of statistical tests of habitat selection (White and Garrott 1986, 1990). Ad hoc solutions (Rotella and Ratti 1992) and statistical procedures (Samuel and Kenow 1992)

may improve estimates of habitat use when misclassification is probable for radio

location by triangulation. In this paper, we describe a new method to assess the

accuracy of measurements of environmental variables (e.g., elevation, slope, distance to roads) associated with automated animal telemetry system (AATS) location

estimates. Our objectives were to (1) develop an empirical method for calculating

the probability distribution of an animal’s location given a LORAN-C radiotelemetry

point estimate (hereafter point estimate), (2) describe how to use this probability

distribution to incorporate environmental variables in a geographical information

system (GIS) with radiotelemetry error neighborhoods (hereafter error neighborhood),

and (3) assess whether point or error neighborhood estimates provide more accurate

estimates of environmental variables, and therefore habitat use.

We conducted research on a portion of the Starkey Experimental Forest and Range

(Starkey) located on the Wallowa-Whitman National Forest, about 35 km southwest

of La Grande in Union County, Oregon. In 1989, an AATS was deployed at Starkey

that uses time differences (TDs) of retransmitted LORAN-C radio navigation signals

that are differentially corrected to compute locations of radio-collared animals (Dana

et al. 1989, Findholt et al. 1996, Johnson et al. 1998). A TD is the difference in time

of arrival of two LORAN-C signals, one from the master station, and one from a

secondary station. Estimated locations of Rocky Mountain elk (Cervus elaphus

nelsoni Bailey) and mule deer (Odocoileus hemionus Rafinesque) from the AATS,

when coupled with environmental variables and mapped in a GIS database, enable

researchers to analyze distributions of these species in relation to intensive timber

management, cattle grazing, vehicle traffic, and hunting (Bryant et al. 1991, Johnson

et al. 1991, Rowland et al. 1997). We enclosed the 10 102-ha study area with a

2.4-m fence to restrict movement of elk and deer. Elevation in this area ranges from

1120 to 1500 m. Vegetation is a mosaic of forest stands and grasslands, and soils

are derived from basalt and pumicite (Strickler 1965). Forest stands are dominated

by ponderosa pine (Pinus ponderosa Dougl. ex Laws.). Grand fir (Abies grandis

(Dougl.) Forbes) and Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) occur on

the northern aspects. Rowland et al. (1997) provide a detailed description of Starkey.

1

Introduction
We developed methods to estimate the probability density of LORAN-C radiotelemetry locations from experimental data. Forty radiotelemetry collars were tested

to ensure proper functioning. Differentially corrected global positioning system (DGPS)

locations were obtained in Starkey at 20 random sites with a Trimble Pathfinder

receiver.1 Two radio collars were placed in an upright position at each site to simulate the position of a standing animal. We used two radio collars per site to assess

whether radiotelemetry error varied among collars at the same sites. From 27

October through 3 November 1992, all 40 radio collars were located systematically

by using the AATS, once every 40 minutes, 24 hours each day; this provided about

300 attempted locations per radio collar. We determined the differences between

the DGPS location for each site and the point estimates to obtain estimates of error

in meters. One collar failed during this trial and was omitted from the analysis.

Radiotelemetry locations from stationary collars were treated similarly to locations

obtained during studies of animals at Starkey. Locations were corrected for mean

bias based on the DGPS locations of the sites (Findholt et al. 1996). We discarded

locations when they did not have the required number of TDs (three or four) or when

TDs did not meet minimum threshold values for signal strength, signal-to-noise ratios,

or geometric dilution of precision (Dana et al. 1989). Positions that contained cycle

slips also were discarded from the data set (Rowland et al. 1997). The number of

successful observation attempts from each collar varied from 26 to 152 (×

− =

107, SE = 5.2).

We estimated the probability that a particular pixel contained the true location of a

radio collar for each 30-m pixel near the home pixel. Each of the 39 radio collars

received equal weight because we did not want any unique environmental conditions that yielded acceptable TD conditions to have undue influence on the magnitude or direction of corrections. Consequently, when less than 152 successful

locations were obtained for a given collar, a simple random sample was drawn (with

replacement) from the locations for that collar to complete a set of 152 locations.

The sampling process generated 5,928 locations with balanced representation from

each collar. Relative errors of all 5,928 radiotelemetry locations from the 39 collars

were pooled.

We assumed that the bivariate probability density function was elliptical in shape

based on the observed pattern of LORAN-C location errors. The major and minor

axes of this ellipse were calculated from the eigenvalues and eigenvectors of the

covariance matrix of the observed error distribution (Mardia et al. 1979). The major

axis was in the direction of the eigenvector corresponding to the largest eigenvalue,

and the ratio of major:minor axis lengths was given by the ratio of the eigenvalues.

A (1-β)100 percent confidence ellipse was defined by the equation xTAx = c where

A is the covariance matrix of the location errors, xT is a bivariate vector of locational

errors, and c is a constant. A (1-β)100 percent confidence ellipse for the true location

is estimated by finding the smallest constant c, such that (1-β)100 percent of the

errors are contained by the ellipse. The calculations were performed by using 

MATLAB (Mathworks, Inc. 1995).

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.

2

Methods

Method Development
Probability weights for pixels in each error neighborhood were determined by counting the number of locations found in each pixel within the (1-β)100 percent confidence ellipse. We assumed that the shape of the ellipse would be similar for all

known locations, and therefore probability weights were estimated from the pooled

5,928 radiotelemetry locations.

We conducted a basic exploratory analysis to test the appropriateness of using a

single elliptical probability density to describe the radiotelemetry error polygon for

Starkey. We estimated the angle of orientation and the ratio of the major to minor

axis lengths for each radio collar by using only the observed locations without bootstrap resampling. All the axes were plotted on a single graph to allow visual assessment of variation among collars. We investigated any irregularities by comparing

estimates from both collars at the same location. These comparisons were displayed

graphically. We tested for differences among locations by using one-way analysis of

variance (ANOVA) with one or two observations per location. This analysis was

conducted with all radio collars except the one anomalous radio collar. We analyzed

directional data to estimate a 95 percent confidence interval for the mean angle of

orientation of the major axis (Mardia 1972).

We cross validated to further determine if using a single error neighborhood across

Starkey was valid. The test was conducted for nominal probabilities of 0.8, 0.9, 0.95,

and 0.99. An 80-percent error neighborhood is that set of pixels surrounding and

including the home pixel such that the sum of the probability weights equals 0.80.

Other error neighborhoods are defined similarly. Radiotelemetry locations associated

with one of the 39 radio collars were removed from the data set, and the error

neighborhood was estimated by using locations from the remaining 38 collars. This

confidence ellipse was tested against locations from the excluded collar by counting

the number of locations falling inside the new error neighborhood. We expected that

for a nominal 95-percent error neighborhood, about 95 percent of the locations for

each collar would fall inside the confidence ellipse. This procedure was repeated for

each collar giving an observed proportion of samples in the ellipse for each radiocollar and at each nominal probability level. A chi-square goodness-of-fit test (Zar

1974) was applied within each nominal probability level to test the null hypothesis

that the telemetry error distribution can be described by a single bivariate ellipsoidal

probability density.

The probability weight for a particular 30-m pixel was influenced by the precise

location of an observation within the home pixel. Consequently, the 30-m pixels were

divided into thirty-six 5- by 5-m pixels. Then, 80 and 95 percent weight matrices were

calculated for surrounding 30-m pixels conditioned on the subpixel in which an observation was recorded. Subunits (5 by 5 m) were selected because DGPS locations

were assumed to be within 5 m with 95 percent confidence (Findholt et al. 1996).

This technique resulted in 36 sets of probability weights for each confidence level. 

We generated 4,191 random universal transfer Mercator coordinates within Starkey

to determine whether point or error neighborhood estimates could more accurately

describe an animal’s habitat. We obtained, with GIS, the values for environmental

variables from the 30-m pixels containing the random points. A 30-m pixel was chosen

because most environmental variables could not be determined accurately in an

area less than 30 by 30 m. For a thorough discussion of environmental variables in

3

Method Testing
the Starkey habitat database, including how they were determined and their accuracy,

see Rowland et al. (1998). Continuous variables used were elevation, slope, sine

and cosine of aspect, and distance to nearest road. Discrete variables used included

canopy cover, plant community type, and soil type. The random sites were considered exact locations (i.e., true animal locations) when we were obtaining values of

environmental variables. We used the known probability distribution of radiotelemetry locations to obtain simulated locations of LORAN-C radiotelemetry point estimates at each random site. This was accomplished by randomly selecting points with

replacement from the 5,928 location errors that formed the probability distribution of

radiotelemetry locations and adding the location error to the true location. We determined the 80- and 95-percent error neighborhoods around the home pixel containing

the simulated LORAN-C point estimates. Next, we calculated values of environmental variables at the simulated radiotelemetry points and from the 80- and 95-percent

error neighborhoods. Finally, we subtracted the value of each continuous environmental variable at the “true animal location” (i.e., random site) from our simulated

point and error neighborhood estimates. We used mean absolute deviations as a

measure of accuracy for each method. For the discrete variables, the category

chosen for the point estimate was the one found in the home pixel, and for the 80-

and 95-percent error neighborhoods, we used the category most frequently represented as the estimate. We divided Starkey into three canopy cover classes (forage,

<40 percent canopy cover; marginal cover, 40 to 70 percent canopy cover; satisfactory cover, >70 percent canopy cover) based on Landsat classification; the resulting mean patch size was 2.9 ha. Mean patch size at Starkey for 15 plant community

types was 14.6 ha; mean patch size of 20 soil types was 20.4 ha.

Error neighborhoods for a simulated LORAN-C location may overlap the boundary

of Starkey when an animal location is adjacent to the fence and thus assign positive

probability to pixels that could not possibly contain the radio; i.e., an unadjusted

error neighborhood will contain pixels outside Starkey. To resolve this bias, error

neighborhoods were calculated by computing the weighted averages for only those

pixels inside the fence.

We used a general linear model (GLM) completely randomized block design ANOVA

to determine whether point estimates or error neighborhoods (80 and 95 percent)

provided the most accurate estimates of values of continuous environmental variables. This was accomplished by testing for differences by using all 4,191 random

sites throughout Starkey and from a subset of 332 sites in riparian areas (i.e., within

100 m of major streams) from the original 4,191. We evaluated riparian areas

because they were the most diverse topographically and contained a variety of

habitat types. In the ANOVA, the “treatments” were the three different methods

(point estimates, 80- and 95-percent error neighborhoods) and the “blocks” were

the individual random sites. When significant differences were detected, we used a

Student-Newman-Keuls multiple comparison range test. Chi-square tests of homogeneity were used to test whether the proportion of correctly classified categories

of discrete variables varied with radiotelemetry point or error neighborhood estimates for all random sites and sites in riparian areas. We used regression analysis

to test for relations between patch size and the proportion of correctly classified

canopy cover, soil, and plant community types at simulated radiotelemetry point

estimates. SAS (SAS 1985) was used for statistical analyses (level of significance,

α = 0.05). 

4

Statistical Analyses
We used the following equation to estimate weighted values of continuous environmental variables (Vw) for 80- and 95-percent error neighborhoods:

where 

Wi = relative probability weight of the 30- by 30-m pixel, 

Vi = value of the continuous environmental variable for the pixel, and

n = the number of pixels in the array that corresponds to error neighborhood size. 

We chose the category with the largest sum of relative probability weights to obtain

the estimate for a discrete variable with error neighborhoods. Programs used to estimate values of environmental variables from error neighborhood estimates and GIS

were written in Borland PASCAL (Borland International 1994). 

The spatial distribution of the combined radiotelemetry location errors was nearly

elliptical in shape with maximum frequency at the center of the ellipse (fig. 1). Major

and minor axes of the error ellipse for each radio collar are plotted in figure 2. Axis

orientation for all but one collar ranged from 0° to 34° north of east with one collar

(number 175) having its major axis oriented 72° north of east. The error distribution

for this anomalous collar and for collar 154, also at the same location, were plotted

5

Determining Values 

of Environmental

Variables from 

Radiotelemetry

Error Neighborhoods

Results

Statistics

n

Σ(Wi

×Vi)

VW = i=1 , n 

ΣWi

i=1

Figure 1—Error distribution of bias-corrected locations from 39 collars resulting

from the LORAN-C automated animal telemetry system at the Starkey

Experimental Forest and Range, northeast Oregon.
6

Figure 2—Plot of major and

minor axes of error distribution

estimated from each radio 

collar. Notice that collar 175

stands out anomalously from the

group, whereas the remaining

collars are consistent.

Figure 3—Comparison between

error distribution of collar 154

and collar 175. Both collars are

from the same location within 

the Starkey Experimental Forest

and Range in northeast Oregon.
7

Discussion

in figure 3 for comparison. The angle of orientation and ratio of major to minor axis

lengths were similar across all 20 locations (P > 0.7). We removed collar 154 from

the analysis to determine whether collar 175 biased results and found that angles 

of orientation and ratios of principal axes were still similar across all 20 locations

(P > 0.4). The average angle of orientation was 13.0° (95 percent confidence interval:

10.6° to 15.3°), and the average ratio of major to minor axis lengths was 3.7 (95

percent confidence interval: 3.2, 4.1).

The average observed coverage probabilities for each nominal probability level were

greater than the nominal level (table 1). The chi-square goodness-of-fit test did not

indicate a lack of fit for nominal probability levels of 90 percent or greater. The

observed coverage probabilities more closely matched the nominal levels as the

nominal level increased. The poorest fit was for the 80 percent nominal level, with an

average observed coverage of 90 percent, a minimum of 55 percent, and maximum

of 100 percent.

Estimates of sine and cosine of aspect were more accurate with radiotelemetry points

than with error neighborhood estimates at all random sites and the subsample of

sites from riparian areas (table 2). By contrast, estimates of slope were improved

with error neighborhood estimates (table 2). Canopy cover was correctly classified

more often with error neighborhood estimates than point estimates at all sites (table

3). No differences were found between point and error neighborhood estimates (P >

0.05) for elevation, distance to roads, plant community type, and soil type. As patch

size increased, the frequency that soil, plant community, and canopy cover type were

classified correctly also increased (fig. 4).

The error distribution of radiotelemetry locations is elliptically shaped and is similar

throughout Starkey for properly functioning radio collars. We found that with the

exception of radio collar 175, the distribution of the angle of orientation and the ratio

of major to minor axis lengths were similar for all 20 locations throughout Starkey.

Radio collar 175 appeared to generate an error distribution much different than the

other radio collars at the same location. We suspect that this particular collar may

have been damaged.

Results of cross-validation analyses and chi-square goodness-of-fit tests also provided

evidence that the error distribution was similar across Starkey and that a single error

neighborhood was appropriate, especially for nominal probability levels of 0.9 or

greater. The observed coverage probability of the error neighborhood tended to be

greater than or equal to the target nominal probability for each nominal level. A positive bias was associated with the technique, but the magnitude of the bias tended to

decrease with increasing nominal levels. For a given radiotelemetry location, some

pixels were given higher probability of inclusion in the sample than their actual probability. This resulted in more conservative inferences in resource selection studies. In

particular, when selection was observed with error neighborhood correction methods,

the statistical significance of effects was likely to be higher (lower probability values)

than the estimated significance level. When the nominal level of a test of significance

was set at 0.05, we may, in practice, have been testing at a lower probability level.
Table 1—Summary statistics for observed coverage probability based on crossvalidation analysis for nominal probability levels of 80, 90, 95, and 99 percent

Nominal probability

level Minimum Maximum Average Chi-square Pa

0.80 0.55 1.0 0.90 98.80 <0.001

.90 .74 1.0 .94 22.90 .97

.95 .80 1.0 .97 7.08 >.99

.99 .88 1.0 .99 1.41 >.99

a Based on chi-square goodness-of-fit tests.

Note: Frequency distribution = 38 for all analyses.

8

Table 2—Absolute mean differences between values of continuous environmental

variables at radiotelemetry points, 80- and 95-percent error neighborhoods (E.N.),

and true values at the Starkey Experimental Forest and Range, northeast Oregon

Variable n Point 80% E.N. 95% E.N. F Pa

All sites:

Elevation (m) 4,191 5.6 5.5 5.6 2.23 0.108

Aspect—

cosine 4,191 .21A 0.22A .22B 11.37 <.001

sine 4,191 .25A .26B .26C 20.30 <.001

Slope (%) 4,191 3.9A 3.5B 3.6B 47.29 <.001

Distance to roads (m) 4,191 40.6 40.9 41.1 1.93 .145

Sites < 100 m class 1 

streams:

Elevation (m) 332 8.9 8.8 8.9 .53 .591

Aspect—

cosine 332 .29A .33B .34B 11.28 <.001

sine 332 .29A .32B .33B 3.99 .019

Slope (%) 332 8.4A 7.3B 7.4B 8.25 <.001

Distance to roads (m) 332 40.7 41.9 42.1 1.92 .1480

Means in the same row with dissimilar letters are different (Student-Newman-Keuls multiple comparison

range test, P ≤ 0.05).

a P values are based on general linear model completely randomized block design analysis of variances.
9

Table 3—Proportion of canopy cover, plant community, and soil types correctly

classified using radiotelemetry points and 80- and 95-percent error neighborhoods (E.N.) at the Starkey Experimental Forest and Range, northeast Oregon

Variable n Point 80% E.N. 95% E.N. X2 P

All sites:

Canopy covera 2,742 74.2A 76.9B 76.7B 6.93 0.031

Plant community 2,720 77.2 78.6 78.8 2.25 .324

Soil type 2,742 76.7 76.8 76.9 .04 .981 

Sites < 100 m class 1 

streams:

Canopy cover 307 65.2 68.4 69.7 1.55 .461

Plant community 305 75.7 79.3 77.7 1.14 .564

Soil type 307 69.7 68.4 68.7 .13 .936

a Proportion of correctly classified sites with dissimilar letter is different (chi-square test of homogeneity).

Figure 4—Relation between patch size 

of canopy cover type, soil type, and plant

community type and proportion of correctly

classified patches with simulated LORANC radiotelemetry point estimates. Number

of classes used for each variable was

canopy cover (3), soil type (20), and plant

community type (15).
We recognize that selection of 80- and 95-percent error neighborhoods was arbitrary. For large error neighborhoods (> 80 percent), weighted averages and most

probable classes are expected to be similar. We could have used an error neighborhood of 100 percent although this may have allowed for significant influence from

outliers that may have been present. Further research should investigate development of selection criteria for error neighborhood size.

Our results indicated that values for environmental variables calculated from error

neighborhood estimates were the same as those from point estimates. Although

statistically significant differences existed between point and error neighborhood

estimates for some variables, we believe that these differences were an artifact of

large sample sizes (n > 305) and not biologically meaningful. Also, we believe differences found between point and error neighborhood estimates were too small to

influence power of statistical tests of habitat selection by elk, deer, and cattle. When

a point estimate is obtained at Starkey, we are 90-percent confident that it is within

a 3.1-ha area (Findholt et al. 1996). However, it is more likely that the location is

near the center of the area than the perimeter. Based on the error associated with

locations from the AATS at Starkey and the environmental heterogeneity existing

within the study area, overall point and error neighborhood estimates of environmental variables did not differ. Thus at Starkey, the power of statistical tests of

habitat selection is not influenced by point or error neighborhood estimates.

Our ability to estimate some continuous variables and correctly classify discrete

variables declined at sites within riparian areas. This probably was due to the

increased habitat heterogeneity and topographical variability of areas near streams.

Mean patch sizes of categorical variables in riparian areas were canopy cover (0.4

ha), plant community type (1.9 ha), and soil type (8.8 ha). Although patch size influenced whether the classes of discrete variables were classified correctly (fig. 4),

other factors (e.g., patch shape and juxtaposition) probably also affect classification

rates. This may explain some of the variation observed among variables where the

proportion of correctly classified categories differed with the same patch sizes. It

also may explain why differences between point and error neighborhood estimates

were not obtained at sites within riparian areas where mean patch sizes were smaller

than the radiotelemetry area estimate.

We assumed that measurement error did not exist in our GIS database for the

seven environmental variables examined. We estimated that error associated with

continuous environmental variables was less than 5 percent (Rowland et al. 1998).

Currently, we do not have estimates of measurement error for the discrete variables

except for canopy cover, which has a classification accuracy of 82 percent (Rowland

et al. 1998). Considering measurement error of continuous variables would not have

changed our conclusions because error was small. However, if we added the classification error associated with canopy cover to the error from our analysis, the proportion of correctly classified patches would have been 63 percent with the 80

percent error neighborhood.

We are uncertain whether error neighborhood estimates or point estimates are more

useful when environmental variables are incorporated with radiotelemetry locations.

Error neighborhoods, however, may provide more accurate environmental data in

highly heterogeneous landscapes with small patch sizes. Additional research is

10
needed, especially computer simulations, to determine the relation between radiotelemetry error, habitat heterogeneity (patch size), and sample size. For individuals

using radiotelemetry and a GIS, we recommend that our procedure or a similar

technique be used to determine whether more accurate values of environmental

variables are obtained from radiotelemetry point or error neighborhood estimates.

Samuel and Kenow (1992) describe another method that potentially provides

improved estimates of habitat use when misclassification is probable. Their analytical

technique involves obtaining random subsamples from the theoretical error distribution of an estimated animal location. Results of Monte Carlo simulations designed to

simulate triangulation errors and evaluate habitat misclassification suggest that the

subsampling method may improve estimates of habitat use. These adjustment techniques for misclassification should be compared to our error neighborhood approach.

Our model has utility beyond evaluating whether point or error neighborhood estimates more accurately describe an animal’s habitat. It may be used to assess how

accurately environmental variables can be determined with radiotelemetry points

and error neighborhood estimates across extremes of habitat and topographic variability within a study area. It also may be used to determine how many categories 

of a discrete variable are required to obtain a desired accuracy level. Our method

provides insight into whether a telemetry system is sufficiently accurate for habitat

analyses or to determine the spatial scale at which analysis is acceptable.

Methods described in this paper could be used with radiotelemetry systems other

than those based on LORAN-C, if sufficient locations are obtained to estimate probability weights for pixels surrounding estimated locations. The procedure we describe

could be accomplished with automated radiotelemetry systems such as those that

use satellites, or those that have fixed-tower receiving stations. Satellite telemetry

systems that seem well-suited for our approach include the Argos method (Keating

1994, Keating et al. 1991) and those based on GPS technology (Moen et al. 1996,

1997; Rempel and Rodgers 1997; Rempel et al. 1995). A variety of radiotelemetry

systems with fixed-tower receiving stations have been used to locate birds and

mammals (Flores and Eddleman 1995, Inglis et al. 1968, Lee et al. 1985). We believe

that our approach may be impractical with various types of conventional telemetry

such as aerial tracking, homing in on the animal when the animal is not actually seen,

and triangulation location techniques such as vehicle-mounted receiving systems or

hand-held antenna and receivers. In these instances, directional bearings could be

obtained from an unlimited number of locations. This would make it difficult to obtain

enough locations to estimate probability weights for pixels around estimated locations.

Our study was funded under provisions of the Federal Aid in Wildlife Restoration 

Act (Pittman-Robertson Act), administered by the Oregon Department of Fish and

Wildlife. Funding also was provided by the USDA Forest Service Pacific Northwest

Research Station and Pacific Northwest Region. We thank J.H. Noyes, M.M. Rowland,

and M.J. Wisdom for reviewing this paper. Research on elk and deer at Starkey is in

accordance with approved animal welfare protocol (Wisdom et al. 1993).

11

Acknowledgments
When you know: Multiply by: To find:

Meters (m) 3.28 Feet

Hectares (ha) 2.47 Acres

Kilometers (km) 0.62 Miles

Borland International. 1994. User’s guide Borland Paradox for Windows. Version 

5.0. Scotts Valley, CA: Borland International, Inc. 564 p. 

Bryant, L.D.; Thomas, J.W.; Johnson, B.K.; Noyes, J.H. 1991. Hunter and Rocky

Mountain elk (Cervus elaphus nelsoni) interactions in the Starkey Experimental

Forest and Range. In: Christensen, A.G.; Lyon, L.J.; Lonner, T.N., comps.

Proceedings: elk vulnerability symposium. Bozeman, MT: Montana State

University: 168-173.

Dana, P.H.; Fowler, W.; Hindman, D. 1989. Automated animal-tracking system: 

tracking elk with retransmitted Loran-C. In: Proceedings of the 18th annual technical symposium of the Wild Goose Association. Bedford, MA: The Wild Goose

Association. 18: 53-61.

Findholt, S.L.; Johnson, B.K.; Bryant, L.B.; Thomas, J.W. 1996. Corrections 

for position bias of a LORAN-C radio-telemetry system using DGPS. Northwest

Science. 70: 273-280.

Flores, R.E.; Eddleman, W.R. 1995. California black rail use of habitat in southwestern Arizona. Journal of Wildlife Management. 59: 357-363.

Garrott, R.A.; White, G.C.; Bartmann, R.M. [et al.]. 1987. Movements of 

female mule deer in northwest Colorado. Journal of Wildlife Management. 

51: 634-643.

Harrington, F.H.; Veitch, A.N.; Luttich, S.N. 1987. Tracking barren-ground and 

woodland caribou by satellite: the more the need for PTTs, the better they work. 

In: Proceedings, Argos users conference. Greenbelt, MD: Service Argos, USA: 

221-242.

Hupp, J.W.; Ratti, J.T. 1983. A test of radio telemetry triangulation accuracy in 

heterogeneous environments. In: Pincock, D.G., ed. Proceedings, 4th international wildlife biotelemetry conference. Halifax, NS: University of Nova Scotia:

31-41.

Inglis, J.M.; Sittler, O.D.; Kirby, J.D. 1968. A fixed station radio tracking system. 

Southwestern Naturalist. 13: 433-443.

Johnson, B.K.; Ager, A.A.; Findholt, S.L. [et al.]. 1998. Mitigating spatial 

differences in observation rate of automated telemetry systems. Journal of

Wildlife Management. 62: 958-967.

12

Literature Cited

English 

Equivalents
Johnson, B.K.; Noyes, J.H.; Thomas, J.W.; Bryant, L.D. 1991. Overview of the 

Starkey project: current measures of elk vulnerability. In: Christensen, A.G.; Lyon,

L.J.; Lonner, T.N., comps. Proceedings: elk vulnerability symposium. Bozeman,

MT: Montana State University: 225-228.

Keating, K.A. 1994. An alternative index of satellite telemetry location error. 

Journal of Wildlife Management. 58: 414-421.

Keating, K.A.; Brewster, W.G.; Key, C.H. 1991. Satellite telemetry: performance 

of animal-tracking systems. Journal of Wildlife Management. 55: 160-171.

Lee, J.E.; White, G.C.; Garrott, R.A. [et al.]. 1985. Assessing accuracy of 

a radiotelemetry system for estimating animal locations. Journal of Wildlife

Management. 49: 658-663.

Mardia, K.V. 1972. Statistics of directional data. London; New York: Academic 

Press. 351 p.

Mardia, K.V.; Kent, J.T.; Bibby, J.M. 1979. Multivariate analysis. New York: 

Academic Press. 407 p.

MathWorks. 1995. Matlab high-performance numeric computation and visualization software reference guide. Version 4.2.c.1. Natick, MA: The MathWorks, Inc.

231 p.

Moen, R.; Pastor, J.; Cohen, Y. 1997. Accuracy of GPS telemetry collar locations 

with differential correction. Journal of Wildlife Management. 61: 530-539.

Moen, R.; Pastor, J.; Cohen, Y.; Schwartz, C.C. 1996. Effects of moose movement and habitat use on GPS collar performance. Journal of Wildlife

Management. 60: 659-668.

Nams, V.O. 1989. Effects of radiotelemetry error on sample size and bias when 

testing for habitat selection. Canadian Journal of Zoology: 1631-1636.

Rempel, R.S.; Rodgers, A.R. 1997. Effects of differential correction on accuracy 

of a GPS animal location system. Journal of Wildlife Management. 61: 525-530.

Rempel, R.S.; Rodgers, A.R.; Abraham, K.F. 1995. Performance of a GPS animal 

location system under boreal forest canopy. Journal of Wildlife Management. 

59: 543-551.

Rotella, J.J.; Ratti, J.T. 1992. Mallard brood movements and wetland selection in 

southwestern Manitoba. Journal of Wildlife Management. 56: 508-515.

Rowland, M.M.; Bryant, L.D.; Johnson, B.K. [et al.]. 1997. The Starkey 

project: history, facilities, and data collection methods for ungulate research.

Gen. Tech. Rep. PNW-GTR-396. Portland, OR: U.S. Department of Agriculture,

Forest Service, Pacific Northwest Research Station. 62 p.

13
Rowland, M.M.; Coe, P.K.; Stussy, R.J. [et al.]. 1998. The Starkey habitat 

database for ungulate research: construction, documentation, and use. Gen.

Tech. Rep. PNW-GTR-430. Portland, OR: U.S. Department of Agriculture, Forest

Service, Pacific Northwest Research Station. 48 p.

Saltz, D. 1994. Reporting error measures in radio location by triangulation: a 

review. Journal of Wildlife Management. 58: 181-184.

Samuel, M.D.; Kenow, K.P. 1992. Evaluating habitat selection with radio-telemetry 

triangulation error. Journal of Wildlife Management. 56: 725-734.

SAS Institute. 1985. SAS/STAT guide for personal computers. Version 6. 

Cary, NC: SAS Institute, Inc. 378 p.

Springer, J.T. 1979. Some sources of bias and sampling error in radio triangulation.

Journal of Wildlife Management. 43: 926-935.

Strickler, G.S. 1965. Soil and vegetation on the Starkey Experimental Forest 

and Range. In: Proceedings of the Society of American Foresters. [Place of 

publication unknown]: Society of American Foresters: 27-30.

White, G.C.; Garrott, R.A. 1986. Effects of biotelemetry triangulation error on 

detecting habitat selection. Journal of Wildlife Management. 50: 509-513.

White, G.C.; Garrott, R.A. 1990. Analysis of wildlife radio-tracking data. San 

Diego, CA: Academic Press. 383 p.

Wisdom, M.J.; Cook, J.G.; Rowland, M.M.; Noyes, J.H. 1993. Protocols for care 

and handling of deer and elk at the Starkey Experimental Forest and Range.

Gen. Tech. Rep. PNW-GTR-311. Portland, OR: U.S. Department of Agriculture,

Forest Service, Pacific Northwest Research Station. 49 p.

Zar, J.H. 1974. Biostatistical analysis. Englewood Cliffs, NJ: Prentice-Hall, Inc. 

620 p.

14
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