Further topics in distance sampling
K P Burnham, Stephen T. Buckland, Jon Henrik Laake, David Louis Borchers, Tiago André Marques, Jonathan R. B. Bishop, Len Thomas · 2004
Abstract Conceptually, line transects can be considered as one-dimensional distance sampling, because only distances perpendicular to the line of travel are used, even though objects are distributed in two dimensions. Point transects sample distances in those two dimensions because radial detection distances are taken at any angle in what could be represented as an x y coordinate system. In principle, distance sampling can be conducted in three dimensions, such as underwater for fish, where objects can be located anywhere in three dimensions relative to the observer. The observer might traverse a ‘line’, and record detection distance in two dimensions perpendicular to the line of travel, or remain at a point, recording data in three dimensions within the sphere centred at the point. Given the assumption of random line or point placement with respect to the three-dimensional distribution of objects, the mathematical theory is easily developed for the three-dimensional case. In practice, the third dimension may pose a problem: there may only be a thin layer in three dimensions, and in the vertical dimension, objects may exhibit strong density gradients (e.g. birds in a forest canopy, or fish near the sea surface).