An improved mixed-error non-equilibrium stock-production model and its application to some Brazilian fish stocks

Abstract

A new and more comprehensive estimation method for stock-production models is proposed, to provide more reliable stock assessment when data availability is limited. Using difference equations to implement a non-equilibrium production model, the new approach (named POEEM, for Process and Observation Errors Estimation Method) incorporates uncertainties due to both process and observation errors, employing a non-linear model fitting approach. The method has been evaluated using both simulated and real data sets, and has been applied to data from some Brazilian fish stocks. The weighting ratio between process and observation errors has proved to be a crucial factor in determining the model results, and a fully satisfactory method for selecting this ratio is still required. Sensitivity analyses conducted with the simulated data have been used to study the behaviour of the method for a range of exploitation and noise levels. Data series with low and medium levels of noise yielded consistent results irrespective of the level of exploitation, whereas very noisy data series did not provide reliable results.
For comparison, data from a previously analysed stock was also tested with POEEM and resulted in peculiar results for the stock status and management advice. Data from four demersal species caught off southeastern Brazilian coast were also analysed employing POEEM, and more conventional methods. For all of them further analyses on mapping some parameters sensitivity must be conducted in order to increased the reliability of the results. Two species have the POEEM estimated assessment trend corroborated by independent biological studies. King weakfish is apparently on the verge of a collapse, with very low levels of production and biomass. Jamaican weakfish is around its maximum sustainable yield and the exploitation level on this stock should not be intensified. For the other two species, high levels of uncertainty were responsible for contradictory outcomes. For whitemouth croaker, the balance between process and observation error could not be consistently achieved, because of high amount of observation noises. For grey triggerfish, the assessment revealed a collapsed stock, but previous biological studies do not corroborate this scenario. Discarding onboard and fleet behaviour appear to be confusing the analysis of this data series.
In general, the new method seems to be capable of giving useful results, consistent with biological studies, when a limited amount of data is available. However, further work is needed to find a satisfactory method for fixing the weighting ratio. In order to improve the Brazilian stock assessments, both fishery and biological data must be continuously collected to maintain and update the results, and effort data needs to be collected for other fleets, and incorporated in the analysis.

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