On the pile-up effect and priors for Linf and M/K: response to a comment by Hordyk et al. on “A new approach for estimating stock status from length frequency data”

Abstract

There is a recognized need for new methods with modest data requirements to provide preliminary estimates of stock status for data-limited stocks (e.g. Rudd and Thorson, 2018). Froese et al. (2018) provide such a method, which derives estimates of relative stock size from length frequency (LF) data of exploited stocks. They show that their length-based Bayesian biomass estimation method (LBB) can reproduce the “true” parameters used in simulated data and can approximate the relative stock size as estimated independently by more data-demanding methods in 34 real stocks. However, in a comment on LBB, Hordyk et al. (2019) claim (i) that the master equation of LBB is incomplete because it does not correct for the pile-up effect caused by aggregating length measurements into length classes or “bins”, (ii) that LBB is highly sensitive to equilibrium assumptions and wrongly uses maximum observed length (Lmax) for guidance in setting a prior for the estimation of asymptotic length (Linf), and (iii) that the default prior used by LBB for the ratio between natural mortality and somatic growth rate (M/K) of 1.5 (SD = 0.15) is inadequate for many exploited species. These comments are addressed below