How many trawl hauls, and how many fish from each haul are needed to obtain a given precision in the age structure estimate for Norwegian spring spawning herring? A bootstrap approach

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The Norwegian spring spawning herring is assessed each year from acoustic surveys. The age structure in the stock is estimated from trawl samples. Typically, about 10 trawl samples are taken per survey, and 100 fish from each sample are age measured. The uncertainty in the age structure estimate depends both on the number of trawl hauls and the number of fish for which the age is measured within each haul. The same is true for the length structure. Length is much easier to measure than age, and in the Vestfjorden survey in December 2002, more than 6000 fish distributed on 72 trawl samples were length measured, making possible the investigation undertaken in this paper, where the bootstrap is applied to estimate the number of hauls/fish needed to obtain a given precision in the length distribution. It is reasonable to believe that the precision in the age distribution will depend on the number of fish/hauls in the same way. The sampling intensity needed to obtain a given CV for the most abundant length groups was much lower than for the less abundant length groups. In terms of standard errors it was the other way round. A doubling of number of fish measured per haul from 1 to 2 allowed for about 50% decrease in the number of hauls needed to keep the same precision. A doubling from 128 to 256 allowed for about 10% decrease.