The design effects of cluster sampling on the estimation of mean lengths and total mortality of reef fish

Abstract

Cluster sampling is commonly used in fishery-dependent and -independent surveys. However, the impact of the design effect of cluster sampling on stock assessments has often been overlooked. This study used vermilion snapper ( Rhomboplites aurorubens) samples collected from commercial fisheries in the Gulf of Mexico as an example to illustrate how cluster sampling may influence the precision of estimated mean lengths and total mortality. First, the within-cluster correlations in fish lengths among cluster samples collected from commercial fisheries or simulated based on different sampling designs were evaluated. Second, the effects of different cluster sampling designs on the precision of mean lengths were estimated using the bootstrap method. Finally, the impact of different sampling designs on the confidence intervals of total mortality, a key parameter for assessing a fish stock, was evaluated. A strong correlation in fish length among vermilion snapper cluster samples was found, which significantly decreased the precision in mean lengths and caused a several fold increase in the confidence interval for total mortality. The design effects of cluster sampling had a significant impact on (1) sampling design, (2) hypothesis testing, and (3) stock assessment. The large design effects of cluster sampling are quite common for reef fish. Systematic studies of design effects on different types of population parameters (means, ratios, frequency distributions, etc.) based on historical data may be needed for different species.