Assessing sources of uncertainty in length-based estimates of body growth in populations of fishes and macroinvertebrates with bootstrapped ELEFAN

The determination of rates of body growth is the first step in many aquatic population studies and fisheries stock assessments. ELEFAN (Electronic LEngth Frequency ANalysis) is a widely used method to fit a growth curve to length-frequency distribution (LFD) data. However, up to now, it was not possible to assess its accuracy or the uncertainty inherent of this method, or to obtain confidence intervals for growth parameters within an unconstrained search space. In this study, experiments were conducted to assess the precision and accuracy of bootstrapped and single-fit ELEFAN-based curve fitting methods, using synthetic LFDs with known input parameters and a real data set of Abra alba shell lengths. The comparison of several types of bootstrap experiments and their outputs (95% confidence intervals and confidence contour plots) provided a first glimpse into the accuracy of modem ELEFAN-based fit methods. The main components of uncertainty (precision and reproducibility of fit algorithms, seed effects, sample size and matrix information content) could be assessed from partial bootstraps. Uncertainty was mainly determined by LFD matrix size (months x size bins), total number of non-zero bins and the sampling of large-sized individuals. A new pseudo-R-2 index for the goodness-of-fit of von Bertalanffy growth models to LFD data is proposed. For a large, perfect synthetic data set, pseudo-R-Phi(2), was very high (88 to 100%), indicating an excellent fit of the growth model. The small Abra alba data set showed a low pseudo-R-Phi(2), from to 54% to 68%, indicating the need for more samples (length measurements) and a larger LFD data matrix. New, robust, bootstrap-based methods for curve fitting are presented and discussed. This study demonstrates a promising new path for length-based analyses of growth and mortality in natural populations, which are the basis for a suite of methods that are included in the new fishboot package.