Unbiased Estimation in Line-Intercept Sampling

SUMMARY A theory for unbiased estimation of the total of arbitrary particle characteristics in line-intercept sampling, for transects of fixed and of random length, is presented. This theory unifies present lineintercept sampling results. Examples are given and variance estimation is discussed. 1. Introduction and Literature Review Line-intercept sampling (LIS) is a method of sampling particles in a region whereby, roughly, a particle is sampled if a chosen line segment, called a 'transect', intersects the particle. It has the advantage over 'quadrat sampling' in that there is no need to delineate the quadrats and determine which objects are in each quadrat. Examples of the economics of LIS versus quadrat sampling can be found in Canfield (1941), Bauer (1943), Warren and Olsen (1964), and Bailey (1970). The particles may represent plants, shrubs, tree crowns, nearly stationary animals, animal dens or signs, roads, logs, forest debris, particles on a microscope slide, particles in a plane section of a rock or metal sample, etc. In early biological applications, sampling with a transect appears to have been a purposivesampling technique for studying how vegetation varies with changing environment, with the transect running perpendicular to the zonation (Weaver and Clements, 1929). In the study of range vegetation, Canfield (1941) incorporated random placement of the transect and, by taking the proportion of the sampled transect intercepted by the vegetation, obtained an unbiased estimator of coverage that is, the ratio of the area covered by the vegetation to the area of the region of interest. However, he did not prove the unbiasedness of this estimator. Canfield called this method the 'line-interception method'. He also discussed such design questions as how many lines of what length are required and whether or not the area of interest should be stratified. Bauer (1943) compared transect sampling to quadrat sampling in an area of dense chapparal vegetation and in a laboratory experiment. He concluded that '. . . transect sampling deserves much wider use. . .'. McIntyre (1953) investigated the possibility of using data on intercept lengths in order to estimate not only coverage, but also density-that is, the ratio of the number of particles to the area of the region of interest. He was able to do this for populations which consisted of particles that were all magnifications of a known shape. Lucas and Seber (1977) presented and proved the unbiasedness of estimators of particle density and coverage for arbitrarily shaped and located particles when the transect is randomly placed. Their estimator of coverage is the same as that of Canfield (1941). Eberhardt (1978) reviewed three transect methods for use in ecological sampling: LIS, and two methods, 'line-transect sampling' and 'strip-transect sampling', in which the particles are points and the probability of observing a particle is a function of its perpendicular distance