Focusing on the front end: A framework for incorporating uncertainty in biological parameters in model ensembles of integrated stock assessments

Abstract

Uncertainty in population status estimates from stock assessments is important for providing a comprehensive picture of current knowledge of a stock. The use of model ensembles to encapsulate model uncertainty has become increasingly prevalent. The uncertainty of biological parameters that are often fixed in stock assessment models can be quantified for presentation of management advice through model ensembles. An ensemble can be created by randomly drawing values from the likely parameter space using a Monte-Carlo/bootstrap (MCB ensemble) or fixed at either a high, medium, or low value that encapsulates the variability in the parameter and applied in a full factorial grid across the fixed parameters (factorial ensemble). We calculated the management advice from MCB ensembles of various sizes and a 243 model factorial ensemble for Southwest Pacific swordfish (Xiphias gladius) and compared reference points which included model uncertainty only, model and estimation uncertainty, or both uncertainties weighted by sampling importance resampling. Median reference points were significantly different between the two ensemble types with the factorial ensemble having a significantly larger estimate of model uncertainty than the MCB ensemble. Stock assessments with fixed biological parameters can characterize uncertainty in these parameters more efficiently using a MCB ensemble approach. A factorial ensemble approach is appropriate for comparing different model structure assumptions and functional forms of relationships and can be used in combination with a MCB ensemble approach. Incorporation of both model and estimation uncertainty in estimates of reference points is important when providing management advice because including only model uncertainty can lead to biased estimates of the precision of reference points. Further work is needed regarding appropriate weighting of ensembles which incorporate different data sources or have different likelihood weightings.