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cq 2 =l-(l-a 1 )*a 2 . (9) 
Step 5 For each captain, draw a value for the propor- 
tion of fish that will successfully be herded from the path 
of sweeps and bridles to the path of the net (one captain) 
or herded from the path of the doors to the path of the 
net (the other captains) (a 6n ). 
Step 6 For each captain, compute the fraction of fish 
between the doors that end up in front of the net, given 
the proportion of doorspread that is between the wing- 
tips (a 3 1 n ) (step 3 of previous section) for the following 
sections of the gear — the dead zone (a 3 2 n ), between the 
dead zone and the wingtips (of the area not in the dead 
zone) (a 4n ), and between the wingtips (of the area not 
in the dead zone) (a 5 n ) — and the fraction of fish herded 
into the path of the net (a 6 n ). 
For the captains that conditioned herding of fish into 
the front of the net on those fish that swim in the zone 
between the doors and the wingtips, the following for- 
mula applies: 
a 3.6,n,l = ^ 1 _ a 3,l ,n X a 6 ,n + a 3,l ,n ■ ) 
For the captain that conditioned herding of fish into the 
front of the net on those fish that swim in the area that 
does not include the dead zone, the following formula 
applies: 
a 3.6,n,2 = ^ -a 3,2,n^ X ^ a 4,;i X a 6 ,n +a 5,n^ 
Step 7 For each net type (n) and captain (c), draw a 
value for the proportion of fish that are captured of those 
that end up in front of the net (a 7 n c ). To do this, use the 
parameters of the triangular distribution provided for 
each captain for each net type. 
Step 8 Compute q net for each net type (n) and captain (c): 
Qnet,n,c = °1.2,c X °3.6 ,n,c X °7 ,n,c* d^) 
Step 9 Compute the q aross for each survey (s) for each 
captain (c): 
Q gross, s,c = Qnet t n,c X U n,c X S s /(g g X a 8 n ), (13) 
where U n c - the uncertainty random variable for each 
net type and captain; 
S s = the random variable for the fraction of 
exploitable stock biomass in the region s; 
g s = the random variable accounting for traw- 
lable area in region s; and 
a 8n - the fixed correction factor applied where 
the wingtip distance had been applied to 
compute the swept-area biomass. 
U n c , is applied to each q net n c to ensure that the density 
functions are not overly precise (i.e., it applies a multi- 
plicative uncertainty factor). 
Such factors have been applied in other situations 
where it is presumed that the distributions offered by 
experts are far too certain (e.g., Boyer et al., 2001). In 
our application, an uncertainty factor was drawn from 
a lognormal density function with a coefficient of varia- 
tion (CV) of 0.5 and a median of 1 for each captain and 
net type. See the discussion for further justifications 
for including this factor and for the choice of the value 
for the CV. 
Step 10 Give each captain’s q gross equal prior weight 
in the final q aross distribution such that the chance of 
including a given captain’s input has equal prior prob- 
ability. 
We applied a C-dimensional Dirichlet density function 
where C is the number of captains. This was applied 
as the multivariate prior pdf for the relative weight 
given to each captain’s q gross distribution for a given 
survey. All C input parameters for this density function 
were set to 0.5, which gives a relatively uninformative 
prior for the weight placed on each captain. In each 
Monte Carlo iteration, one of the C captain’s q gross val- 
ues was randomly chosen for the q aross random variable 
for each of the seven research surveys. Thus, without 
any Bayesian updating with new data, each captain’s 
inputs are given equal weight in the output probability 
distribution q gross for each regional survey. 
Step 1 1 Use observations of the ratio of average catch 
rates from the different survey gears, e.g., shrimp trawl 
and groundfish trawl, from comparative gear experi- 
ments in specific locations (intended or unintended) to 
update the q net c density functions for these survey nets 
(see Eqs. 14-15 below). 
The ratios of observed average catch rates for the 
different survey nets will give more weight to captain 
inputs that are more consistent with the observed ratios 
for these two net types. 
Step 12 Apply WinBUGS (or other Bayesian integra- 
tion software) to produce two or more sets of Markov 
chain results for the q net parameters for each net type 
and q gross parameters for each survey; apply diagnostics 
to remove the burn-in and summarize the posterior 
results. 
Step 1 3 Evaluate the posterior correlations between the 
Qgross parameters for the different surveys and identify 
a suitable multivariate density function to summarize 
the results. 
Because the q gross distributions for the different sur- 
vey regions in our application were computed with 
identical input values for q nei across survey regions, the 
q gross variables tended to be highly correlated across 
survey regions. There is the potential for multimodal- 
ity in the marginal density functions for q gross for the 
different survey areas and thus a mixture distribution 
may be appropriate. Should the results for each survey 
be unimodal, then a multivariate lognormal density 
function should be a good candidate. 
