An evaluation of statistical methods for estimating abundances of migrating adult sea lamprey

We evaluated statistical methods for estimating abundances of adult sea lamprey (Petromyzon marinus) migrating in Great Lakes tributaries. The sea lamprey is the target of a basin-wide, bi-national control program. Abundance estimates from mark-recapture data are used to evaluate program success and the efficiency of sea lamprey trapping. Recent tracking studies suggested the mark-recapture estimates of abundance could be biased. We compared four estimators of abundance using stratified (weekly) mark-recapture data for 19 years of trapping in the St. Marys River. Abundances from the pooled Petersen estimator were similar to abundances from the stratified Schaefer and stratified Petersen estimators, but substantially lower than abundances from a stratified Bayesian P-spline estimator. In simulations of virtual populations, pooled Petersen and Bayesian P-spline estimates were similar across a range of conditions where catchability differed between marked and unmarked lamprey and changed over the trapping season, with one exception. Abundances from the Bayesian P-spline estimator were strongly positively biased when catchability of marked lamprey increased over the season, while catchability of unmarked lamprey did not. Estimates from both estimators were negatively biased when lamprey displayed consistent individual differences in catchability and positively biased when a proportion of marked lamprey fell back. Discrepancies between mark-recapture and tracking studies cannot be reconciled by the choice of abundance estimator, but could be an outcome of bias due to individual differences in catchability. Sea lamprey managers could also switch from the stratified Schaefer to the pooled Petersen estimator to simplify field operations without losing accuracy and precision.