A Bayesian state-space model to estimate population biomass with catch and limited survey data: application to the thornback ray (Raja clavata) in the Bay of Biscay

Abstract

The thornback ray (Raja clavata ) in the Bay of Biscay is presumed to have declined during the 20th Century. To evaluate this decline and estimate biomass trajectories, a hypothetical catch time series was created for the period 1903–2013. A Bayesian state-space biomass production model with a Schaefer production function was fitted to the hypothetical catch time series and to a shorter research vessel Catch Per Unit Eeffort (CPUE) time series (1973–2013, with missing years). A censored likelihood made it possible to obtain biomass estimates without a CPUE time series or only with an estimate of biomass depletion. A simulation-estimation approach showed a high sensitivity of results to the prior for the intrinsic growth rate. The model provided biomass trajectories which corroborated and quantified the decline of the Bay of Biscay population. The estimated biomass corresponding to the maximum sustainable yield, B MSY , was 32 000 tonnes, which is 17 times higher than the estimated biomass in 2014. The biomass estimates obtained without a CPUE time series were highly uncertain. Adding a current biomass depletion observation improved precision, though the biomass time trend was sensitive to this value. Results should be interpreted carefully as several assumptions were necessary to create the long catch time series and to define informative priors, notably for the intrinsic growth rate. Despite this, the results confirm the depleted state of the thornback ray in the Bay of Biscay with the estimated biomass in 2014 being around 3% of carrying capacity.