McAllister et al.: Using experiments and expert judgment to model catchability of Pacific rockfishes 
295 
rapid burn-in and rapid mixing. 
The Gelman-Rubin (Brooks and 
Gelman, 1998) statistic was ap- 
plied to assess the burn-in period, 
which was judged to be about 500 
iterations. A total of 40,000 itera- 
tions with two chains were judged 
to be sufficient to provide precise 
approximations of the target den- 
sity function. Using the results 
after the burn-in, we found that 
the ratio of Monte Carlo error 
(analogous to standard error in 
the sampled posterior mean) to 
the posterior standard deviations 
(SDs) for all outputted variables 
was far less than the minimum 
standard of 5% (Best and Thom- 
as, 2000). 
Results 
127"30'W 12?°W 126‘30'W 126"W 125"3Q'W 
Figure 5 
Mapped zones and trawl tow positions (symbols) of the west coast Vancouver 
Island groundfish and shrimp trawl surveys where the two surveys overlapped. 
These two surveys provided the catch-rate ratio data for these two survey gears 
that were then used to update the groundfish-to-shrimp trawl-net catchability 
ratios for each of the experts. Polygons surrounding the overlapped survey areas 
were connected by hand and delimit the outer boundaries. Open and closed 
circles indicate the absence and presence, respectively, of bocaccio ( Sebastes 
paucispinis) in the groundfish surveys. Open and closed triangles indicate the 
absence and presence, respectively, of bocaccio in the shrimp surveys. 
We first considered the individual 
distributions computed from each 
captain’s inputs for the catchabil- 
ity of each of the three net types 
(q net ). For each of the three net 
types, a wide range of plausible 
values for q net were obtained from 
the 12 interviewed captains and 
there was considerable variability 
between the captains and some of 
the distributions were nonoverlap- 
ping (Fig. 6). The CVs in the q net distributions by captain 
for each net varied from about 0.1 to 0.6, reflecting con- 
siderable variability in individual levels of uncertainty 
in the q net inputs. 
The q gross values obtained for each captain and for 
each net type with no updating and no uncertainty fac- 
tor showed considerably wider distributions and more 
overlap in all cases between the captains than the q net 
distributions for each captain (Figs. 6 and 7). The q gross 
distributions for the different surveys showed varying 
amounts of overlap between the captains with the WCVI 
shrimp survey showing the least amount of overlap and 
the U.S. triennial survey showing the most overlap be- 
cause of very low precision in q gross among captains. The 
low precision was primarily due to the high uncertainty 
in the fraction of stock biomass in the U.S. triennial 
survey area (Table 2). The CVs in the q gross distribu- 
tions by captain ranged from about 0.3 to 0.7 for the 
DFO groundfish surveys and the WCVI shrimp survey 
(Fig. 7). However, the QCS shrimp survey showed high 
CVs of about 1.5-1. 8 because of the added uncertainty 
in accounting for the fraction of the stock in each sur- 
vey area and the ratio of bocaccio density in untraw- 
lable and trawlable areas. The q aross distributions for 
the shrimp trawl surveys (e.g., for WCVI) were centered 
considerably lower than those provided for the ground- 
fish surveys partly because of low values for q net and 
because a small fraction of the stock falling in these 
areas. Also for the shrimp trawl survey areas, the frac- 
tion trawlable was 100%, whereas the groundfish trawl 
survey areas this was closer to 70-80% (Table 2). 
We next consider different approaches to combining 
the q net distributions from the different experts into a 
single q uet distribution for each net type. When equal 
weighting was applied to the inputs from the different 
captains without Bayesian updating and without the 
uncertainty factor, the q net distributions for each net 
were multimodal (Fig. 8). Under these same conditions, 
the combined distributions for q aross for each net showed 
varying amounts of departure from unimodality; the 
q gross distribution for the WCVI shrimp survey showed 
the most pronounced bimodality (Fig. 9). When the un- 
certainty factor was applied without Bayesian updating, 
the q net distributions showed less pronounced multimo- 
dality (Fig. 8); multimodality was no longer seen in any 
of the q aross distributions and the distributions became 
slightly wider (Fig. 9, Table 6). 
We compared the ratios in values of q net for the 
groundfish survey to q net for the shrimp survey (pro- 
vided by the captains) with the observed ratios in 
values of q net for the groundfish survey to q net for 
the shrimp survey in the WCVI and QCS surveys 
