Multistage Sampling Designs in Fisheries Research: Applications in Small Streams

Abstract

A common, although generally unrecognized, use of multistage sampling designs in freshwater fisheries research is for estimation of the total number of fish in small streams. Here there are two stages of sampling. At the first stage one selects a sample of stream sections, usually of equal length, and at the second stage one estimates the total number of fish present in each selected section. This paper argues that the conventional practice of selecting stream sections of equal length is ill-advised on both biological and statistical grounds, and that errors of estimation of fish numbers within selected sections will usually be small compared with errors of estimation resulting from expansion of sampled sections to an entire stream. If stream sections are instead allowed to vary in size according to natural habitat units, then alternative two-stage sampling designs may take advantage of the probable strong correlation between habitat unit sizes and fish numbers. When stream sections of unequal sizes are selected with probabilities proportional to their size (PPS), or measures of the sizes of selected sections are incorporated into estimators, one may substantially increase precision of estimation of the total number of fish in small streams. Relative performances of four alternative two-stage designs are contrasted in terms of precision, relative cost, and overall cost-effectiveness. Choice among alternative designs depends primarily on the correlation between fish numbers and habitat unit sizes, on the total number of stream sections, and on sample size. Recommendations for choices among the designs are presented based on these criteria.