Sequential analysis and design of fixed-precision sampling of Lake Kariba fishes using Taylor’s power law

Abstract

Taylor’s power law (TPL), which states that the variance of abundance is a power function of mean abundance, has been used to design sampling of agricultural pests and fish species. We show that TPL holds for means and variances of abundance of accumulated fish samples in the fished and unfished areas separately of Lake Kariba (between Zambia and Zimbabwe), measuring abundance indices by number and weight separately. We use TPL parameters estimated from sequentially accumulated samples to update a stopping line of fixed precision 0.1 after each new sample from a sampling day. In these Lake Kariba data, depending on the sampling area and abundance measure, our updated stopping-line method requires 21% to 41% of the number of sampling days and 19% to 40% of the number of samples that are planned a priori and performed under systematic sampling. Our novel method yields mean abundance estimates similar to those from systematic sampling and provides a conservative approach to reaching a fixed sampling precision level with reduced sampling labor and time. Using mixed-effect modeling for cumulative means and variances with either number or weight from both fished and unfished areas, we find that fishing increases the slope of TPL. This study provides the conceptual framework and an empirical case study for implementing a sequential sampling method for fish assemblages of an inland lake. The possible limitations and applications of our method for sampling in other environments are discussed.