Measuring and Correcting for Size Selection in Electrofishing Mark–Recapture Experiments

In electrofishing, the form of size selectivity is unknown, so parametric models of selection have not been developed. Capture probability can be estimated as a continuous function of fish size for two-sample mark–recapture experiments such as those often made to describe stream fish populations. One approach is based on nonparametric regression by smoothing splines, in which general linear models are fitted to data by penalized maximum-likelihood methods. Capture probabilities modeled this way allow the data to reveal the form of size selectivity and can be used to estimate population size. A confidence band around the estimated capture probability function and confidence intervals for the population estimate are obtained by bootstrapping. A second approach is based on parametric regression models and requires some knowledge of the form of the selection function. A confidence interval for the population estimate is based on the variance estimated by the delta method. These approaches are illustrated by analysis of a mark–recapture experiment on brown trout Salmo trutta in a Minnesota stream, and results are compared with those found in application of Chapman–Petersen estimates to size-groups. The biases of estimates of population size N and of SE (N) by these approaches were examined by using Monte Carlo simulations of known populations. For the size-group in which capture probability changed rapidly with size and for the total population, spline-based population estimates typically had less bias and better coverage than Chapman–Petersen estimates, and they typically had a smaller SE (N) and root mean squared error than parametric model estimates.