COMPARISON OF THE PRECISION OF DIRECT VERSUS AGE LENGTH KEY METHODS OF ESTIMATING CATCH-AT-AGE PROPORTIONS

Catch-at-age proportions can be estimated directly using a simple random sample (SRS) of fish in the catch, determining the ages in the sample, and calculating proportions in each age class. This “direct” method can be replaced by the age length key (ALK) method if there are in addition to the SRS of ages, which have also been measured for length (the age-length sample), a large SRS where fish are measured only for length and tallied by length bins (the LF sample). The ALK method uses the extra information in the LF sample to calculate proportions by age by multiplying the probability by length bin estimated from the LF sample by the conditional probability of age given length bin estimated from the age-length sample and summing over the bins. Since this conditional probability is employed, the ALK method can be used to obtain unbiased estimates from age-length samples that have been collected using unequal probability schemes with respect to length such as length bin random sampling (LBrs). LBrs can be easily implemented by directing observers to sample length-bins for fish to have their otoliths removed until a fixed number of fish in each length bin have been obtained and further sampling from any “full” bins is discontinued for the remainder of the cruise. LBrs ensures that the tails of the length frequency distribution, and thus that of the age distribution, are over-represented in the age-length sample compared to a SRS scheme. Formulae for the precision of the estimates of proportion by each age class are given for each of the direct, ALK_SRS, and ALK_LBrs sampling/estimation methods. Since the formulae depend on the values of proportion by length bin and conditional probability of age given length as well as sample sizes, typical values were generated to allow the comparison of precision. The ALK_SRS method always has a greater precision across all age classes than the direct method, with the difference diminishing as the sampling fraction of the LF sample that is sub-sampled for age determination increases. The ALK_LBrs method is slightly inferior to the other two sampling/estimation methods for most of the age classes that dominate the catch but is significantly superior for the less well represented age classes. For older, mature-age fish this improvement in precision, being important in estimation of spawning stock biomass, may more than compensate for the slight loss of precision for the younger age classes in terms of the accuracy of integrated assessments that employ catch-at-age proportions.