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Fishery Bulletin 108(1 ) 
Figure 4 
Paired-tow comparative fishing simulation results for log relative efficiency (ft) of the test 
vessel compared to the control vessel. Simulations were based on the yellowtail flounder 
(Limanda ferruginea) scenario and data were generated for different assumed values of 
1 3 (i.e., ft 0 ) and spatial heterogeneity (a 2 ) in fish densities encountered in each tow. Three 
models of spatial heterogeneity, described in Table 1, were used to estimate ft, and three 
line patterns are used to show the results from each model. Panel columns are for levels of 
a 2 (i.e., a 2 = 0 in A, E, I, and M, etc.) and the x-axis of each panel are for levels of ft. Bias 
(A-D) is the simulation median estimate of ft minus ft 0 . Cl indicates confidence interval, 
and Pift eCI) indicates the probability the Cl contains ft, etc. References lines (solid) are 
shown in each panel, at zero (A-D), 0.95 (E-H), and 0.025 (I-P). 
variability has a similar effect to that of spatial hetero- 
geneity in stock densities encountered by both vessels at 
a trawl station. Hence, these two sources of variability 
are confounded in paired-trawl experiments and the 
random effects represent the cumulative impacts of both 
types of variability. For reasons outlined in the previous 
paragraph, we recommend the GLMM approach when 
there is between-set variability in catchability. 
Our power analyses indicated that 50% changes in 
catchability could not be detected with high probability 
(i.e., 0.95) for some species. For example, with data like 
that obtained for Atlantic cod (see Table 2, and Cadigan 
et al. 3 ) the power was fairly low. For this stock, the es- 
timate of a 2 was 0.99 and our power analysis indicated 
that we could detect only large changes in catchability 
(>90%) in this situation. Estimates of a 2 were closer to 
0.5 for most other species, in which case the power to 
detect a 50% change in catchability would be between 
0.8 and 0.95. The exception was for yellowtail floun- 
der which would have even lower power when ct 2 =0.5 
because of the smaller number of positive sets (n= 24) 
for this species. Changes in catchability between 20% 
