Parrack: Estimating stock abundance from size data 



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Example 3 was the limited-data case. The growth 

 measurement error was large (cv 0.20) and the sam- 

 ple size for growth parameter estimation was moderate 

 (95% CI of width ± 5%, 77 fish). The precision of catch 

 estimates was low (cv[C] = 0.4) and relative abundance 

 sampling was meager (95% CI of width ±30%, two 

 samples each period). 



Error variances of the smallest seven size class abun- 

 dance estimates were very large (Table 6), but error 

 variances were low for size-classes 25 and larger. 

 Usefully narrow confidence intervals on the bias of 

 these estimates were obtained with few trials. Signif- 

 icance levels suggested that abundance estimates of 

 size-classes 17-21 might not have been biased and un- 

 biased estimation seemed likely for size-classes 22 and 

 larger. Estimates of sampling gear efficiencies (q(s)) 

 also seemed accurate although error variances were 

 high. 



Example four simulated sufficient sampling. A 

 growth parameter measurement error (cv 0.05) and 

 sample size (99% CI of width ±1%, 829 fish) more 

 characteristic of databases for heavily sampled fisheries 

 were used. Catches were precisely estimated (cv[C] 

 = 0.2) and relative abundance sampling was at a very 

 sufficient level (99% CI of width ±3%, 295 samples 

 each period). 



Biases (Table 6) were very similar to those of exam- 

 ple 3. Abundance estimates for the smaller size-classes 



that appeared in relative abundance samples just once 

 were probably biased by more than 10%, but the rest 

 were not. Estimates of q for the smallest 10 size-classes 

 were biased by more than 10% and the rest were prob- 

 ably not. Most error variances for stocksize estimates 

 were several times smaller than those of example 3, 

 and some were an order of magnitude smaller. Like- 

 wise, the error variance of q estimates was also smaller. 

 As may be expected, sufficient sampling levels in- 

 creased precision but did not affect bias. Abundance 

 estimates of sizes that appeared in abundance samples 

 more than once were estimated accurately when over- 

 fishing occurred, whether or not sampling levels were 

 sufficient or not. 



Estimates of historical stock sizes are usually used 

 to find out if stock abtmdance is increasing or decreas- 

 ing. Errors of virtual population analysis back-calcu- 

 lations of cohort- specific abundances converge as dates 

 decrease (Agger et al. 1971, Pope 1972, Jones 1981). 

 Conventional wisdom is thus that abundance estimates 

 for the last period are extremely uncertain, but due to 

 the convergence, estimated abundance trends are 

 reliable. For this size-based estimator, (2) provides 

 abundance calculations before date y(T) from the 

 estimates available at the solution of (4). 



Error characteristics of historical abundance esti- 

 mates (Table 7) were unexpected. Bias and error 

 variance increased as dates decreased. Last-period 



