Hanselman et al.: Application of an acoustic-trawl survey design to improve estimates of rockfish biomass 
383 
every 100-m interval. These calculations were compared 
with results from summing the number of cells to verify 
that all cells were very close to 100 m in length and 
that the GPS systems functioned correctly. For example, 
using the GPS coordinates, we checked that a 10-cell 
window in Echoview was ~1 km in length. 
We computed biomass estimates with 2 types of meth- 
ods to compare magnitude and precision. With the first 
method, we omitted the patch stations, except when 
a patch station was originally a planned station, and 
calculated the abundance with an SRS estimator with 
the sample size used as if the full number of trawls had 
been sampled by simple random sampling (Thompson, 
2002). For the second method, we used the estimator 
derived for the TAPAS design. The TAPAS estimator 
is functionally similar to an SSRS estimator, with an 
important exception: in the TAPAS estimator, CPUE 
values from patch stations are treated as multiple 
strata weighted by their associated patch size, but, in 
an SSRS estimator, only the total area estimated to 
be in the patch stratum is used. An SSRS estimator 
was not used in our study for 2 reasons: 1) each patch 
is a separate stratum with a sample size of one, and 
therefore within-strata variances cannot be computed 
and 2) the sampling design introduces patch length as 
an additional random variable that may or may not 
correlate with CPUE. If there is no correlation with 
patch length and CPUE, and the relationship between 
S v and CPUE is weak, then using the TAPAS design 
is similar to suboptimally allocating samples in an 
SSRS design. This suboptimal allocation would cause 
the TAPAS estimator to perform slightly worse than an 
SSRS estimator because of the extra random variable 
introduced, and the SSRS estimator would in turn be 
no better than an SRS estimator. 
The focus of the TAPAS design is to reduce the sam- 
pling variance in estimating biomass based upon the 
degree to which acoustic backscatter corresponds with 
trawl CPUE. Each of these measures shows a relation- 
ship with true fish density, and systematic biases rela- 
tive to true density may exist in either measure because 
of processes such as fishes herding to trawl nets or 
responding to vessel noise. For Alaskan groundfishes, it 
is commonly assumed that trawl CPUE is less variable 
than acoustic backscatter as a measure of fish density 
(over the path of the trawl), although scenarios could oc- 
cur where this assumption was not realistic (Freon and 
Misund, 1999). Information that addresses systematic 
biases, such as catchability and availability of fish to a 
sampling method, could be incorporated into the TAPAS 
design, although this approach would not address the 
central issue of the imprecision of survey estimates that 
result from variable spatial distributions of rockfish. 
For stocks with quantitative stock assessment models, 
the degree of systematic biases potentially can be ad- 
dressed by estimating catchability and gear selectivity 
parameters. 
The stratum-wide TAPAS and SRS estimates of bio- 
mass were calculated with the following formulae based 
on Everson et al. (1996): 
& 
1 
BA 
,2) 
4=AD,fl-U, (3) 
m> 
JLj 
B=B 0 + B U (5) 
where D 0 = 
n = 
I = 
d t = 
A = 
V = 
4 = 
A = 
L = 
4 = 
B = 
B SRS = 
I * = 
>B=A 
D n 
+ A 
( 6 ) 
n-i 
14 
^SRS —A 
n-I ’ 
(7) 
the mean CPUE (kg/km 2 ) of the back- 
ground trawls; 
the total sample size; 
the total number of patches encountered; 
the CPUE (kg/km 2 ) of trawl i; 
the mean CPUE of the patch trawls; 
the total track length within patches; 
the estimated biomass for swept areas at 
background stations (kg); 
the total sampling area (km 2 ); 
the total length (km) of the trackline trav- 
eled by the vessel throughout this study; 
the estimated biomass for swept areas at 
patch stations (kg); 
the TAPAS estimate of total biomass in the 
sampling area; 
the SRS estimate of total biomass in the 
sampling area; and 
the number of patches that were not 
planned stations. 
The variance derived in Equation 7 of Everson et al. 
(1996) left out covariance and area terms. We derived 
an improved estimator of the variance (Table 1) using 
the delta method (Quinn and Deriso 1999); this deriva- 
tion is presented in the Appendix. We computed confi- 
dence intervals with the “log-Bayes” method suggested 
by Everson et al. (1996). Finally, we computed SRS and 
TAPAS confidence intervals with the bootstrap method 
(Efron and Tibshirani, 1993). In complex sampling de- 
signs, there are alternative ways to bootstrap confidence 
intervals (Rao and Wu, 1988; Smith, 1997; Christman 
and Pontius, 2000). For our study, we examined several 
bootstrap methods and found that the results among 
them were similar. Thus, for comparison with analyti- 
cal results, bootstrapping was conducted as suggested 
