Evaluation of Sampling Designs for Red Sea Urchins Strongylocentrotus franciscanus in British Columbia

Abstract Estimates of the total stock biomass of marine invertebrates that aggregate, such as red sea urchins Strongylocentrotus franciscanus, are often highly uncertain, partly because it is difficult to estimate their density. To improve estimates, we used 200 simulated red sea urchin populations with spatial and numerical properties based on field data to evaluate various simulated survey designs for a given number of transects in terms of the precision, bias, and efficiency (relative variance) of their estimates. We considered a random transect sampling method that is currently used in British Columbia for red sea urchins, which samples every other quadrat within each transect, as well as a complete version of that transect method, which samples every quadrat. We also evaluated more complex random transect sampling designs, including restricted adaptive cluster sampling and a design stratified by type of substrate within each transect. The complete transect method produced essentially unbiased estimates of red sea urchin density (as did the currently used sampling design) and had lower variance than the current method, but the complete method used twice as many quadrat samples per transect to do so (incurring higher costs of sampling by divers). In contrast, the design stratified by substrate required 33% fewer sampled quadrats per transect than the current sampling method to achieve the same variance as that method, but it had a median bias of 10%. Finally, the restricted adaptive cluster sampling design gave estimates that had lower variance than the current method and used 18% fewer sampled quadrats, but the median urchin density estimate was biased downward by 8%. Choosing among sampling designs thus involves making trade‐offs among bias, precision, and sampling cost as well as considering practical constraints on scuba divers who attempt to implement complex designs in field situations.