Patchy distribution fields: sampling distance unit of a zigzag survey and reconstruction adequacy.

A mathematical model was used to examine the effects of choosing various units of sampling distance of a zigzag survey on the adequacy of reconstructing patchy distribution fields. The model simulates fish or plankton patches (or gaps) of different shapes and spatial orientations, and an acoustic survey by zigzag or parallel transects along which a unit of sampling distance is set. Adequacy of the reconstructed fields to those originally generated is evaluated by calculating their correlations (r). A priori information on the autocorrelation radii for the field in the directions of the survey (Rs) and perpendicular direction (Rp) allows optimisation of the survey design and the algorithm of data analysis. A field can be reconstructed properly (r2 > 0.70) if the distance between transects D < (1.0-1.5)Rs and the unit of sampling distance d < (1.0-1.5)Rp. A posteriori determination of patch orientation allows reconstruction of the best field attainable on the basis of the survey data. In cases of field movement, if the dimension of patches in the direction of movement exceeds that of a surveyed area, a survey in the opposite direction gives best results; in contrast, if the dimension of moving patches is smaller than that of a surveyed area, it is reasonable to carry out a survey in the same direction. The criterion remains valid when a survey is carried out by zigzag transects and a unit of sampling distance is set along them. The results obtained indicate that, for a fixed transect spacing and a given number of sampling points on each full transect, zigzag pattern allows less adequate reconstruction of an original distribution field (in cases of both immovable and movable fields) than corresponding parallel pattern.