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

A mathematical model was used to examine the effects of choosingvarious units of sampling distance of a zigzag survey on the adequacy of reconstructing patchy distribution fields. The modelsimulates fish or plankton patches (or gaps) of different shapesand 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 (R_s) and perpendiculardirection (R_p) allows optimisation of the survey design andthe algorithm of data analysis. A field can be reconstructed properly (r² > 0.70) if the distance between transects D < (1.0–1.5)R_s and the unit of sampling distance d < (1.0–1.5)R_p. A posteriori determination of patchorientation allows reconstruction of the best field attainable onthe basis of the survey data. In cases of field movement, if thedimension of patches in the direction of movement exceeds that ofa surveyed area, a survey in the opposite direction gives bestresults; in contrast, if the dimension of moving patches is smaller than that of a surveyed area, it is reasonable to carryout a survey in the same direction. The criterion remains validwhen a survey is carried out by zigzag transects and a unit ofsampling 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 allowsless adequate reconstruction of an original distribution field (in cases of both immovable and movable fields) than corresponding parallel pattern.