Variability of Density Estimates and the Optimization of Sampling Programs for Stream Benthos

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Abstract
Several sets of published data were analyzed to examine the effect of mean density, size and type of sampler, and functional group of the collected organisms on the variance in estimates of stream benthos density. The logarithm of variance (log s2) is a quadratic function of the logarithm of mean density (log .hivin.X, individuals .cntdot. m-2). Because of the curvilinear relationship between the logarithm of variance and the logarithm of mean density, I suggest that none of the commonly used transformations (square root, fourth root or logarithmic) will stabilize the variance at all the densities encountered. Information about sampler size (Q, square metres) further improves the prediction of the logarithm of sampling variance, which increases with an increase in mean density and decreases with an increase in the size of the sampler. On average, density estimates obtained with artificial substrates were as variable as those from natural substrates, although some artificial substrates (baskets of rocks) yielded less variable density estimates than average. The number of replicates necessary to obtain a given precision decreases with increasing mean density and sampler size, whereas the total area to be sampled increases with sampler size. Although I suggest that the use of small samplers reduces the cost of estimates of density, the sampler size that minimizes the sum of the sampling and processing effort can depend on the mean density.