Aggregation, Transformation, and the Design of Benthos Sampling Programs

Abstract

Solutions are offered to the problems of data transformation and the design of efficient programs for sampling the benthos of lakes and large rivers. All types of benthic animals from many types of substrate, sampled with diverse sampling gear, are aggregated in a similar fashion. Aggregation can be indexed by the unbiased exponent of the power relationship between density and variance. A single variance stabilizing transformation can be used for all macrobenthos population data since the relationship of sample variance to mean density is similar in all taxa of benthic animals. Stabilized variance in population data satisfies one of the main assumptions of the analysis of variance and allows use of normal statistics provided that the other assumptions are met. The fourth-root transformation stabilized the variance in all macrobenthos samples while either the commonly used square root or logarithmic transformations did not. Sampling programs can be optimized empirically. Standard deviation (s) is predictable from mean density (M; m−2) and sampler size (A; cm2) from the equation: log10s = 0.581 + 0.696 log10M − 2.82 × 10−4 A. The data show that it is easier to obtain a precise estimate of macrobenthos density at high densities. Small diameter samplers are most efficient in obtaining high levels of precision. Data were taken from the literature. Key words: aggregation, benthos, freshwater, regression, sampling, transformation