Efficiency and Bias in Strip and Line Transect Sampling

Abstract

Efficiency and relative bias of strip and line (Fourier series estimator) survey methods were compared. Comparisons involved the negative exponential and half-normal detection functions for expected sample sizes of 40, 60, and 100 and three levels of spatial aggregation. Efficiency and bias were computed as functions of strip width, w. Final comparisons were based on mean square errors (MSE), also as a function of w. The line estimator always had a smaller MSE than the strip estimator when the detection function was a negative exponential. Therefore, line sampling is preferred when detectability drops off rapidly with increasing distance from the line. The line estimator had a smaller MSE for most combinations of spatial aggregation and strip width, w, for the halfnormal detection function. In general, the results indicate a preference for the line method over strip on the basis of bias and efficiency. J. WILDL. MANAGE. 49(4):1012-1018 Applied ecologists faced with the problem of estimating the size (N) or density (D) of a population frequently consider the use of strip or line sampling (see Burnham and Anderson 1984 for a comparison of these two methods). Strip transects are merely long narrow plots or quadrats and elementary sampling theory applies; this theory has existed for several decades (see Gates 1979 and Seber 1982 for reviews). In contrast, with perhaps one exception (Hayne 1949), serious attempts toward a rigorous theory for line sampling and analysis began much later with papers by Eberhardt (1968) and Gates et al. (1968). Reviews and examples of the present state of the theory and application are found in Gates (1979), Burnham et al. (1980), Ralph and Scott (1981), and Hayes and Buckland (1983). Eberhardt (1980:34) raised the issue, there is also a more fundamental question whether any [line transect] technique is actually more effective than using a relatively narrow strip transect (also see Eberhardt et al. 1979: 24). One faces a series of trade-offs or compromises between statistical bias and efficiency in attempting to answer the question posed by Eberhardt. For example, consider the survey of waterfowl nests reported by Anderson and Pospahala (1970). Narrow (2.46 m on each side of the observer) strip transects were searched, and This content downloaded from 157.55.39.25 on Tue, 02 Aug 2016 04:10:05 UTC All use subject to http://about.jstor.org/terms J. Wildl. Manage. 49(4):1985 EFFICIENCY AND BIAS IN TRANSECT SAMPLING * Burnham et al. 1013 the total number of observed nests (n = sample size) was expanded to an estimate of N and D for the area of interest. Fortunately, perpendicular distance data were also taken to allow an estimate of N and D based on line theory. The analysis of the distance data also allowed a test of the critical assumption required in strip sampling that no nests had gone undetected. Approximately 13% of the nests had gone undetected, representing a significant bias in the strip estimate (see Eberhardt 1978b:16-17 and Pollock 1978 for further analyses of these data). Burnham and Anderson (1984) estimated that the width would have to be reduced to 1.54 m on each side of the observer to assure that essentially all nests would have been detected. This extremely narrow would be inefficient and impractical (Eberhardt et al. 1979:25). A narrow strip may allow all objects to be detected, hence, counted. This will produce an unbiased estimator of density, D. However, it may not be a reliable technique because sample size could be small, which means the estimator would have a large variance. As the strip width increases, two opposing phenomena occur: variance decreases, but bias increases and can become severe. By contrast a line may avoid, or reduce, bias because estimators employ the perpendicular distance data to adjust for decreasing detection probability as a function of distance. Therefore, line width may be large (effectively unbounded) and the number counted (sample size, n), typically much greater than on a narrow strip transect. An additional parameter must be estimated in line transects. Therefore, one wonders about efficiency (defined here as the ratio of the standard errors of the estimators) of the line vs. strip sampling schemes. In strip sampling, only the var(n) is involved in the sampling variance of D, which is usually estimated from counts on replicate strips. In line sampling, one also must consider var( f(0)), the variance of the estimated probability density function of the perpendicular distances, evaluated at zero. The purpose of this paper is to examine efficiency and bias in line vs. strip sampling as a function of strip width. From these theoretical results, we suggest some guidelines useful in the design and conduct of field