Design unbiased estimation in line intersect sampling using segmented transects

In many applications of line intersect sampling, transects consist of multiple, connected segments in a prescribed configuration. The relationship between the transect configuration and the selection probability of a population element is illustrated and a consistent sampling protocol, applicable to populations composed of arbitrarily shaped elements, is proposed. It is shown that this protocol obviates the arbitrary practice of treating multiple intersections of a single particle as independent probabilistic events and preserves the design-unbiasedness of Kaiser's ( 1983, Biometrics 39, 965-976) conditional and unconditional estimators, suitably generalized to segmented transect designs. The relative efficiency and utility of segmented transect designs are also discussed from a fixed population perspective.