Optimal sampling designs for estimating salmonid run abundances from video recordings at a fishway on the Bois Brule River, Wisconsin, a tributary to Lake Superior

Abstract

Using a simulation program and video census data (2004–2018) from the Bois Brule River fishway, Wisconsin, USA, we compared alternative sampling designs to estimate spawning run abundances of steelhead, coho salmon, Chinook salmon, and brown trout. We evaluated two types of two-stage sampling designs, comprising varying numbers of days sampled within a year (1st stage samples) and varying numbers of hours sampled within a day (2nd stage samples). While days were sampled using stratified random sampling under both types of sampling designs, hours were sampled using uniform (1/24) or non-uniform (proportional to hourly runs) selection probabilities under the first and second types of sampling designs, respectively. Number of days sampled within a year, comprising three strata, varied from 30 to 200 days in 10-day increments, and number of hours sampled within a day varied from 2 to 24 h in 2-hour increments. Spawning run sizes of the salmonids could be estimated with a relative root mean square error (RMSE) of less than 10% on average by employing a two-stage sampling design with samples of 100 days·yr−1 and 8 hrs·day−1, i.e., 800 hrs·yr−1; by contrast, full census involved reviewing 250 days·yr−1 and 24 hrs·day−1, i.e., 6000 hrs·yr−1, of video. Sampling more days (>100) resulted in greater reductions in estimation error than sampling more hours (>8). Non-uniform (vs. uniform) selection probabilities for hours sampled slightly reduced error of estimates. Our results underscore that optimal sampling designs could ensure a considerable reduction in survey resources while maintaining relatively low error in estimation of salmonid abundances.