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Speed and accuracy of methods for obtaining measurements of forests.

Ecological studies in forests often require determination of identity, density, diameter, and size class of trees. Making a complete count and inventory of trees in a study area is most accurate, but usually is too time consuming and impractical. Therefore, various sampling methods have been employed (Tanner, 1942; Cottam and Curtis, 1949, 1955; Grosenbaugh, 1952; Lindsey et al., 1958; Cantana, 1963) and accuracy and time-wise efficiency of methods have been evaluated (Shanks, 1954; Rice and Penfound, 1955; Cottam and Curtis, 1956; Penfound and Rice, 1957; James and Shugart, 1970). The present study improves on these evaluations for four methods by performing replicate trials to investigate repeatability in the field, which were lacking in previous studies. Point-quarter, random-pairs, 0.004-ha-arm-length-rectangle, and 0.04-ha-circle methods were investigated.

MATERIALS AND METHODS--The study area was a small woods ca. 5 ha in size consisting primarily of oaks and hickories; in order of greatest abundance were post oak (Quercus stellata), black hickory (Carga texana), and shagbark hickory (Carga ovata). The woodlot was a small city park, Gregory Park, in Fayetteville, Washington County, Arkansas, and the study was conducted in late winter and spring 2000. All trees [greater than or equal to]16 cm diameter at breast height were counted, identified, and diameters measured in a 1-ha (100 by 100 m) section of the woods. This hectare contained 226 trees and its boundaries became boundaries of the study area where sampling methods were tested.

In the study area, we tested four sampling methods for determining species, density, diameter, and size class of trees. Two were plotless procedures, point quarter technique (Cottam et al., 1953) and random-pairs technique (Cottam and Curds, 1949, 1955), and two methods used plots, 0.004-ha, arm-length rectangles (Penfound and Rice, 1957) and 0.04-ha circular plots (Lindsey et al., 1958). Positions of sampling points for the plotless methods and beginning points for the rectangles and center points for centers of circular plots were selected from random-number draws designating coordinates on a grid superimposed over a map of the study area. Arm-length rectangles were 20 by 2 m equaling 0.004 ha, circular plots were 11.28 m in radius equaling 0.04 ha.

Relative efficiency of the various sampling methods was rated based on how many samples for each method was required to approximate the true density of trees in the study area, combined with how long it took to obtain the requisite number of samples. Successive samples for a method were summed and after each summation overall density was calculated and degree of agreement with the real value for density was noted. Length of time to sample was recorded.

Three trials were conducted with each method to evaluate repeatability in estimating true density. Two people worked cooperatively with each sampling technique. They identified species, measured all diameters, and depending on the method, distances to trees or size of plots. Diameters were measured using a Biltmore reach stick (James and Shugart, 1970), distances to or between centers of tree trunks were determined with a tape measure for the two plotless methods. Relative desirability of each method was based on the total sampling time for obtaining successive measurements that converged on overall true density rather than true density of each species encountered. Analysis of separate species was not performed because of possible errors in identification during the part of the study conducted before leafing. Because there were three trials for each method used in analyzing density, a coefficient of variation could be calculated for successive samples within each method. Also, after each sample within a method, an estimate of total number of trees per hectare was calculated. The mean of these three estimates of density within a method was evaluated with respect to how close it was to the known density. Determining when these two factors stabilize is crucial in designating the number of samples required for a particular sampling method. In this study, stabilization was achieved for a particular sampling method on the first sample of three successive samples in which the coefficient of variation rounded off to <5% across the three trials, and also the mean of the estimated density for the corresponding three samples rounded off to within [less than or equal to]5% of the true 226 trees/ha in the study area.

Field workers doing one sampling trial at a time did not know when the requisite number of samples was reached, which was based on three trials. Therefore, they obtained an inordinate number of samples to be certain sampling was sufficient. This explains the extension of trials beyond the number needed in the figures that follow. The Bonferroni t-test (Miller, 1981) was used in statistical testing.

RESULTS AND DISCUSSION--We recognize that most studies involving sampling of forests require appraisals of density, diameters, diameter-class categories, and identifications of trees. In this study, we collected data for all of the above to make time devoted to sampling realistic, but used only overall density as the target for evaluating degree of accuracy. Efficiency of each method, therefore, is based on the time involved for all measurements plus number of samples needed to stabilize with respect to true density in the study area.

The point-quarter, random-pairs, and arm-length-rectangle methods all required ca. 30 samples to stabilize (Table 1, Figs. 1a, 1b, and 1c). According to Cottam and Curtis (1955), when using the random-pairs method with a 180&deg; exclusion angle, average distance between trees is multiplied by a 0.80 before calculating density. When we used this coefficient, all three trials with continued sampling consistently overestimated density, estimating ca. 260 rather than the actual 226/ha. By substituting several different coefficients, a new one (0.86) was discovered that corrected this error (Fig. 1b). Nevertheless, uncertainty concerning the coefficient diminishes the usefulness of the random-pairs method.

An average of only five samples was needed using the 0.04-ha circles (Table 1, Fig. Id), far fewer samples than with other methods, although one of the trials, after initially stabilizing, did not perform as well as the other two in continuing to represent true density (Fig. Id). Total number of samples for the combined three trials to stabilize shown in Figs. 1a-1d, were 110 for the point-quarter, 139 for the random-pairs, 140 for arm-length-rectangles, and 35 for the 0.04-ha-circles methods. A total of 1,410, 675, 825, and 280 min transpired, respectively, in performing the three trials per method. Dividing total number of samples by total time consumed for each method produced the average-time-per-sample column in Table 1.


The product of time per sample and required number of samples yields an efficiency value for each method (Table 1). The efficiency rating for the 0.04-ha, circular-plot method was much better (lower value; thus, less time required) than the other three methods. This rating for the circular-plot method was significantly better ([alpha] = 0.05) than all other methods except the random-pairs method, a technique that was discredited above because of uncertainty concerning the value of the required correction coefficient.

Although relative usefulness of the various sampling techniques was based on estimating density only, as described in methods, time required for sampling (Table 1) involved not only counting trees but also recording species and diameter of each tree. Therefore, data for analyzing species and size class were included in calculation of time per sample. In this study, time for sampling by the various methods was based on two people acting as a team. Having one person would take longer for all methods. Circular plots also were determined to be the best of several methods by Lindsey et al. (1958) and James and Shugart (1970). Lindsey et al. (1958) performed sampling simulations with replications on floors of large rooms indoors, and James and Shugart (1970) conducted one field trial on each method considered. The benefit of our study is that there were replications performed in the field. In comparing methods, various authors indicated that rectangular plots were the next best to circular plots, that plotless methods were less desirable, and that random-pairs and wandering-quarter methods were at the bottom of the ranking (Rice and Penfound, 1955; Cottam and Curtis, 1956; Lindsey et al., 1958; James and Shugart, 1970). The time-to-accuracy arrangement of methods tested in our study (Table 1) showed a different sequence: 0.04-ha-circle best, then random-pairs, next 0.004-ha-arm-length-rectangles, finally point-quarter, but reliability of the random-pairs method was diminished by uncertainties in the required correction coefficient. Methods analyzed here were developed in the 1950s and were subject to some evaluation then. Nevertheless, these methods subsequently have been and are still being proposed and used in various forms (e.g., Willson, 1974; Mudappa and Kannan, 1997; Cox, 2002; Camamero and Gulierrez, 2002; Arevalo and Fernandez-Palacios, 2003). Our study not only considered time efficiency in using each method, but for the first time, investigated their repeatability (accuracy) as performed in the field.

E. E. Dale provided useful advice and needed equipment, C. L. Sagers made helpful comments on the manuscript, J. E. Dunn provided suggestions concerning statistical analysis, and D. W. Ouellette gave valuable assistance in the field. P. Barringa translated the abstract into Spanish. Credit for comments that substantially improved the quality of the manuscript is due to two anonymous reviewers

Submitted 2, January 2003. Accepted 29 November 2008.


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Department of Biological Sciences, University of Arkansas, Fayetteville, AR 72701

Associate Editor was David B. Wester.

* Correspondent.
TABLE 1--Required number of samples for values obtained
by each method of sampling to stabilize. Also listed
are average time to obtain each sample and overall efficiency of each

 Required number Average time per
Sampling method of samples sample (a) (min)

0.04-ha circles 5 8.0 (ab)
Random pairs 28 4.9 (a)
0.004-ha, arm-length 29 5.9 (a)
Point-quarter 31 12.8 (b)

Sampling method Overall efficiency (a,b)

0.04-ha circles 40 (a)
Random pairs 137 (ab)
0.004-ha, arm-length 171 (b)
Point-quarter 397 (c)

(a) Average times and overall efficiencies followed by the
same letter are not significantly different (Bonferroni test,
P < 0.05).

(b) Required number of samples times average time per sample.
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Author:Patterson, C. Joan; James, Douglas A.
Publication:Southwestern Naturalist
Article Type:Report
Geographic Code:1USA
Date:Sep 1, 2009
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