SPATIAL-DISTRIBUTION FUNCTIONS AND ABUNDANCES INFERRED FROM SPARSE NOISY PLANKTON DATA - AN APPLICATION OF CONSTRAINED THIN-PLATE SPLINES

As plankton biologists ask more detailed questions of necessarily spar se and noisy spatial data, the need for well founded methods for stati stical analysis of such data grows. This note examines the utility of constrained thin-plate smoothing splines as a tool for inferring under lying spatial distribution functions from sparse noisy data. Constrain ed thin-plate splines are described in a straightforward manner. An ec onomical method of calculation is suggested, which sacrifices mathemat ical optimality for ease of computation. Using simulated data several methods for choosing the complexity of the inferred distribution funct ion are compared and robustness to large amplitude noise is examined. Confidence intervals are calculated and tested. The method is applied to egg data from Dover sole (Solea solea) in the Bristol Channel.