Notes on the Precision of Numerical and Volumetric Plankton Estimates from Small‐sample Concentrates1

Abstract

Standard enumeration and volumetric determination techniques were employed to measure littoral plankton in a shallow prairie lake. Numerical and volumetric estimates were obtained from two‐liter water samples which had their plankton (and tripton) content concentrated by means of a continuous‐flow centrifuge.Microplankton were enumerated, and their volumes were calculated on a species and total basis employing a two‐stage sampling scheme. Distributions of various species in Sedgwick‐Rafter cell mounts from four representative samples (containing at least 73 species) were examined. Occurrences of certain forms in the “fields” of Sedgwick‐Rafter cell mounts conformed very closely to the Poisson series while others departed significantly. A majority of the latter were adequately fitted by the negative binomial distribution. For illustrative purposes, totals of selected species distributed as Poisson and negative binomial were estimated and assigned confidence limits. The value of the contagion or over‐dispersion factor, 1/k̂, in constructing confidence limits was pointed out. In addition, the sample size required to yield an estimate having a specified precision was computed for a selected species distributed as Poisson. It was generally concluded that the error of estimated individual species totals usually greatly exceeds the desired level. Hence the size of subsample necessary to secure reasonably precise estimates for the numbers of each microplankton species in a given sample concentrate would be, as a rule, quite unwieldy.Total microplankton counts per subsample were assumed to be normally distributed. Applications of standard statistical techniques indicated that efficiency in the two‐stage sampling scheme is most effectively increased by including counts from additional primary sampling units (Sedgwick‐Rafter cell mounts). The most practical subsampling ratio from the standpoint of increasing the precision of over‐all numerical estimates without expending additional time and labor appeared to be four cell mounts and ten micrometer “fields” per mount.Microplankton volumetric determinations were made employing a “calculated” volume method. The precision of volumetric unit counts for individual species was indeterminable because of the unknown distribution of the volumetric units. A lack of knowledge concerning such contagious distributions precludes a rigorous assessment of the “calculated” volume’s utility.Macroplankton were counted and had their volume calculated in a manner similar to that described for the microplankton except that the elementary sampling unit constituted an entire Sedgwick‐Rafter cell mount. Very adequate numerical and volumetric estimates of individual macroplankton species and total macroplankton were secured from counts and measurements in only three cell mounts per sample concentrate. It was determined that had the allowable error of estimate been relaxed to 20 per cent (±) of the true value, on the average, a sample size of only one cell mount would have sufficed for estimating total macroplankton.