Correcting length-frequency distributions for imperfect detection

Sampling gear selects for specific sizes of fish, which may bias length-frequency distributions that are commonly used to assess population size structure, recruitment patterns, growth, and survival. To properly correct for sampling biases caused by gear and other sources, length-frequency distributions need to be corrected for imperfect detection. We describe a method for adjusting length-frequency distributions when capture and recapture probabilities are a function of fish length, temporal variation, and capture history. The method is applied to a study involving the removal of Smallmouth Bass Micropterus dolomieu by boat electrofishing from a 38.6-km reach on the Yampa River, Colorado. Smallmouth Bass longer than 100 mm were marked and released alive from 2005 to 2010 on one or more electrofishing passes and removed on all other passes from the population. Using the Huggins mark–recapture model, we detected a significant effect of fish total length, previous capture history (behavior), year, pass, year×behavior, and year×pass on capture and recapture probabilities. We demonstrate how to partition the Huggins estimate of abundance into length frequencies to correct for these effects. Uncorrected length frequencies of fish removed from Little Yampa Canyon were negatively biased in every year by as much as 88% relative to mark–recapture estimates for the smallest length-class in our analysis (100–110 mm). Bias declined but remained high even for adult length-classes (≥200 mm). The pattern of bias across length-classes was variable across years. The percentage of unadjusted counts that were below the lower 95% confidence interval from our adjusted length-frequency estimates were 95, 89, 84, 78, 81, and 92% from 2005 to 2010, respectively. Length-frequency distributions are widely used in fisheries science and management. Our simple method for correcting length-frequency estimates for imperfect detection could be widely applied when mark–recapture data are available.