MSY analyses for herring and sprat in the Baltic Sea, methods and suggested reference points

• The concept of maximum sustainable yield (MSY) rests on the notion that an intermediately sized stock exists at which the biomass production is at its maximum. the maximum is a result of density-dependent negative feedback on percapita production with increasing stock size. the harvesting is sustainable if it equals the stock productivity. the stock productivity depends on environmental variables, typically food-availability but also temperature and salinity may be important. Predation does not affect the productivity directly, but it is important to consider how the annual surplus production is shared with predators and hence affects the fishing yield. In the stock model we use for MSY analyses we differentiate between internal factors affecting density-dependence and external factors that either drive productivity or represent predation.To estimate MSY reference points we modelled some stocks with Monte-Carlo simulations (see WD6 for details). The stochastic properties of the stock are estimated and implemented in the stochastic behaviour of the model in order to find the natural range of stock ariables under MSY management. This can be a basis for B trigger in ICES framework, the SSB at which the F MSY is re-evaluated or an adjusted F is adopted according to the harvest control rule. Under some conditions, stochastic simulations will have F MSY that are different from deterministic runs, i e yields are asymmetrical around their means.The stock model has two variables, NAA (numbers at age) and WAA (weight at age). The functions and their parameters to update the variables annually were obtained from statistical analyses of the data and results from XSA runs provided by the WGBFAS stock coordinators. Four functions were estimated statistically:1) Number of recruits per SSB as a linear function of SSB2) Age-specific natural mortality as a linear function of predator abundance ( e. g. Cod SSB)3) Weight of recruits as a linear function of average parent weight4) Average weight increase as a linear function of WAA and year-specific growthThe MS errors of the regressions were used as variances of the normal distributions from which a random parameter was generated. If body growth is negatively correlated with weight it indicates a Von Bertalanffy type of growth. Also, if number of recruits per SSB is negatively correlated with SSB, there is a density-dependence required for a maximum production to exist.There are also two external variables that affect the analyses: predator abundance and year-specific growth (named year-growth). The year-growth is a statistical variable tha t encapsulates all year-specific growth common for all age-classes. The year-growth is externally linked driver for variation in productivity of the stock. A Fourier function including the four longest wave-lengths was fitted to the predator abundance and the year-growth respectively. The Fourier functions were representing long term changes in the external conditions, and the residuals as uncorrelated inter-annual variation. The MS of the residuals was also used or generating randomscatter in the external variables between years.The stock model was run for 10 500 (for sprat 40 500) years, under which the  first 500 years were not generating data and were only used to release the dependence on the initially set conditions. The time series of yields and SSB were collected. The runs were repeated for intervals of F to frame the maximum average yields with a step of 0.01. A weighted catchability (as estimated for each species) was applied so that the  F denoted the average for a given range of age-classes. We also present F MSY max and F MSY min which frames the range in which the average yields within 95% of the MSY (WKFRAME-2 2011). The B trigger is set as the lower 2.5 % percentile of the SSBs from the simulation.

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