504 



Fishery Bulletin 105(4) 



-o 



5 



F3 



;;rfj^?=*^* 



'-a'-^/o-o-^' 



500 



O 8 = 0.05 



A 5 = 0.1 



+ 5 = 0.2 



X 6 = 0.5 



500 1500 2500 500 1500 2500 



Number of tag releases 



Figure 3 



Effect of changing the number of releases at various proportions of observer 

 coverage (b) on the percent median bias (i.e., ( median-true )/true x lOC^^f ) 

 of the parameter estimates. Results are shovk-n for scenario 1 (see Table 

 1) and are based on 1000 simulation runs per combination of tag releases 

 and observer coverage. A/,= natural mortality rate for age i fish; F,= fish- 

 ing mortality rate for age / fish; P,= population size of tagged cohort at 

 age 1; A = tag reporting rate for the unobserved component of the fishery 

 (assumed to be constant for scenario 1). 



Fj had a median bias of only -3% but a mean bias of 

 -1-16%). Thus, with small TV and 6, the real issue was not 

 with biases, but with the non-normality and very high 

 variability (as seen next) of the estimates. 



We now consider how changes in A^ and 6 affected the 

 precision of parameter estimates. For a given value of 

 6, increasing A^ reduced the CVs of all estimates in an 

 exponential fashion (Fig. 4). For the fishing mortality 

 estimates, the rate of decline became greater with 

 age, and was particularly notable for Fj. The CVs of 

 the fishing mortality, abundance, and reporting rate 

 estimates all decreased as d increased; however, the 

 natural mortality estimates did not change much. 

 Overall, larger gains were achieved in the precision of 

 the fishing mortality, abundance, and reporting rate 

 estimates by increasing b from 0.05 to 0.50 than by 

 increasing A'^ from 500 to 2500 (note that going from 

 250 to 500 releases led to significant decreases in the 

 CVs of most parameter estimates). On the contrary, 

 much larger gains were achieved in the precision of 



the natural mortality estimates by increasing A'^ than 

 by increasing d. 



As a specific example of using such simulation re- 

 sults to aid in the design of a tagging study, suppose a 

 researcher's goal was to achieve a CV of 0.20 or lower in 

 the estimate of abundance. This could be accomplished 

 under scenario 1 with the following: 7V=250 and d= 

 0.50; Af=500 and d=0.20; A^=1000 and 6=0.10; or, N= 

 2000 and 6=0.05. If, in addition, the researcher's goal 

 was to achieve a CV of 0.30 or lower in all of the fishing 

 mortality estimates, then only the latter two of these 

 options would still be acceptable. 



Although the magnitude of the CVs varied sig- 

 nificantly between scenarios (as seen in Table 3), the 

 relative changes that resulted from increasing N or 6 

 were very similar to those seen for scenario 1. The most 

 significant difference came from constraining natural 

 mortality to be constant (scenario 8), in which case the 

 precision of the natural mortality parameter became 

 influenced by changes in 6 (Fig. 5). 



