Use of the bootstrap for error propagation in estimating zooplankton production

Error propagation is the calculation of statistical error in a quantity that comprises multiple components each with associated error. Such quantities constitute the end point of many ecological studies, but composite errors are rarely incorporated so that uncertainty in the final estimate is either unknown or underestimated. In this study we present the use of both parametric (observations are resampled from standard probability distributions) and nonparametric (raw observations are resampled) bootstrap techniques to propagate errors through the many steps involved in the egg-ratio estimation of seasonal production for the freshwater zooplankter Bythotrephes longimanus. We first compute parametric and nonparametric bootstrap estimates of the standard deviation in seasonal production of B. longimanus, showing that it ranges from 21% to 27% of observed seasonal production. We demonstrate that our bootstrapping procedures are robust by developing a theoretical model and showing that the true variance of a parameter is included in 96% of the simulated 95% confidence intervals. We also show that the choice of probability distribution in the parametric bootstrap can change the standard deviation of seasonal production by up to 90%. We argue that ecologists should use such error propagation techniques more routinely than is currently the case.