  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 modern 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, total number of non-zero bins and the sampling of large-sized
individuals. A new pseudo-Rsquared index for the goodness-of-fit of VBGF models
to LFD data is proposed. For a large, perfect synthetic data set,
pseudo-RsquaredPhi was very high (88 to 100%), indicating an excellent fit of
the VBGF model. The small Abra alba data set showed a low pseudo-RsquaredPhi,
from to 54% to 68%, indicating the need for more samples 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 new suite of methods that are included in the new fishboot package.
