A bootstrap approach to account for uncertainty in egg production methods applied to small fish stocks

The Daily Egg Production Method is a well-established methodology to assess the spawning biomass of fish species with indeterminate fecundity. However, final biomass estimates are often affected by high uncertainty, especially when funds are limited, such as in the case of small stocks. We discuss how an approach based upon a two-stage (stratified) non-parametric bootstrapping can be used to account properly for uncertainty in demographic parameters and provide a basis for an informed management of the fishery. We exemplify its use by applying the method to the assessment of a small stock of European anchovy (Engraulis encrasicolus). Spawning biomass showed marked inter-annual variation (2800–8600 tons) over a 5-year period (2004–2008), but actual differences from year to year were blurred by high uncertainty. Bootstrapped probability distributions of egg and adult parameters were significantly non-normal, justifying the use of a non-parametric technique. Due to the high skewness of spawning biomass distributions, median estimates can be used to set more conservative reference points (compared to mean estimates) for fishery management decisions, and can therefore be used to support the development of risk-averse management policies.

► We propose a stratified bootstrapping procedure for the Daily Egg Production Method.
► Bootstrapping allows accounting for uncertainty when assessing small fish stocks.
► Traditional DEPM techniques can underestimate the uncertainty of biomass estimates.
► Bootstrapped means are too optimistic if parameter distribution is very skewed.
► Bootstrapped medians can be useful to set conservative reference points.