500 



Fishery Bulletin 105(4) 



o - 

 o - 



o -J 



TR 



— I — I — I — I 



0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0,6 O.S 1.0 0,0 0,: 4 6 0.8 1.0 

 Mi M, Mi 



TL„ 



T 1— 



0.1 0.2 0.3 0.4 0.5 0.6 



True 



Median 



Mean 



0.5 1.0 1.5 2.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 



Figure 1 



Histograms of the 1000 estimates obtained for each parameter under sce- 

 nario 7 (see Table 1). The true parameter value, median, and mean of the 

 estimates are indicated by vertical lines. M, = natural mortality rate for 

 age i fish; F,= fishing mortality rate for age i fish; Pj = population size of 

 tagged cohort at age 1 (in 100,000s); A = tag reporting rate for the unob- 

 served component of the fishery (assumed to be constant for scenario 7). 



upper bound of 1.0, and the frequency 

 was greatest in scenario 5 where the 

 true value was 0.90. Nevertheless, the 

 median biases were still small. The 

 fishing mortality estimates generally 

 had distributions that were right 

 skewed, and the degree of skewness 

 became more pronounced at older 

 ages. The skewness was usually small 

 enough that the mean and median were 

 still similar (e.g., scenario 1; Fig. 2). 

 However, this was not always true. 

 For example, in scenario 7 (Fig. 1), the 

 median bias for Fj was 2.7%, whereas 

 the mean bias was 13.3'7f . 



In Polacheck et al. (2006), we used 

 mean bias to summarize simulation 

 results obtained with the BP model. 

 This meant that positive biases in 

 the fishing mortality estimates that 

 increased with age were reported, as 

 well as positive biases in the natural 

 mortality estimates. Had median bias 

 been used instead, the bias results 

 would have been similar to those 

 presented here (i.e., negative biases in 

 the natural mortality estimates, and 

 only small biases in any of the fishing 

 mortality estimates). In retrospect, 

 we believe that the median provides 

 a more reliable measure of bias. This 

 is especially true in cases where the 

 estimates have a skewed distribution, 

 but should also be true in cases where 

 a large proportion of the estimates 

 fall on a bound. 



