Assessing the impact of Sampling Error on Model-Based Management Advice: Comparison of Equilibrium Yield per Recruit Variance Estimators

Abstract

The assessment offish stocks often relies on data estimated from complex sampling schemes. For instance, catch and weight-at-age estimates result from sampling commercial landings. This paper studies the propagation of sampling error in catches in an equilibrium yield per recruit model. The covariance matrix of catch estimators is calculated for a given design using sampling theory. The impact of this uncertainty on estimated yield per recruit is assessed by three techniques: the delta method, trials from a multinormal distribution of catches (Gaussian approximation), and bootstrap. The comparison of results leads to the following conclusions, (i) For the model studied, the delta method probably overestimates the variance of the response, (ii) Gaussian approximation and bootstrap give similar values. As the latter is free of approximation and of restrictive assumptions, this suggests that the yield model chosen is to some extent insensitive to the distributional form of catch estimators, (iii) Bootstrap is the method of choice, provided that resampling accurately mimics the whole complexity of the original sampling design. If resampling is not properly achieved, variances could be severely underestimated.