Patchy distribution fields: a spiral survey design and reconstruction adequacy.

A mathematical model was used to examine the effects of a spiral survey design on the adequacy of reconstructing patchy distribution fields. The model simulates fish or plankton patches (or gaps) of different shapes and spatial orientations, and acoustic surveys by a spiral of Archimedes; for comparison, surveys by parallel or zigzag transects are imitated. Adequacy of the reconstructed fields to those originally generated was evaluated by calculating their correlations (r). The mathematical experiments conducted showed that spiral surveys ensure, practically speaking, the same adequacy of field reconstruction (both in cases of immovable or movable patches) as do surveys by parallel or zigzag transects with greater sampling effort (overall path). In the case of a spiral survey, a patchy field can be reconstructed properly (r(2) = 0.70) if the overall survey path is not less than S/R(av) = 20-30, where R(av) is the autocorrelation radius averaged for various directions. Thus, the results obtained allow us to conclude that a spiral survey design is expedient in cases that the minimal duration of a survey is a decisive factor for its conduction and there is a priori information that no onshore-offshore gradients of fish density exist in a region under study.