384 
Fishery Bulletin 1 10(4) 
Table t 
Biomass and variance estimators for 2 sampling designs, simple random sampling (SRS) and Trawl and Acoustic Presence/ 
Absence Survey (TAPAS), the latter of which was evaluated as a way to reduce the variability in estimated biomass for Pacific 
ocean perch {Sebastes alutus ). B=estimated biomass (kg), = e stimated catch per unit of effort (CPUE, kg/km 2 ) in trawl i, 
d=the mean CPUE, A=total sampling area (km 2 ), a=the amount of A sampled (km 2 ), n=total sample size, p=the estimated 
proportion of the trackline in patches, /.=the estimated length (km) of trackline in patch i, /'=the estimate of length (km) of 
total trackline in patches, f=the mean patch length, and L=the length of the entire trackline, /=the number of patches, /*=the 
number of patches excluding those originally in the background, and n L = an estimate of the effective number of independent 
samples on the trackline; the denominator of 12 was derived from the range parameter of the acoustic variogram. 
Estimator 
Biomass 
Variance 
SRS 
TAPAS 
ITa 
n-I* 
B=A 
ir 7< *. L-i 
n-I L 
y " i A t 
■ ^n-I + 1 1 1 1 
i l 
1>[B> 
( 
V 
(i-p) 2 v[4]+p 2 v[4] 
+(4-4) 2 v[p] 
+ 2 p(A - 4 )Coe[A.p] 
v[6„> 
i 4 ~ df 
n n-I - 1 
Hp-A-df „ p, - p : 
s=J±L + d 2 Y P. 
( n-I-l)p 2 p 2 n L 
V[p]= 
p(l-p) 
n.=LI 12 
Coi;[4,p]= 
II 
i=lj=l 
y cdv[d,p)^-+ 
s v ’ p 
' . 1 . ^ 
d-iP- 'LpA 
c °v{p,’Pj) tttI 
(p) 
by Everson et al. (1996): pairs of patch lengths and 
associated values of patch CPUE were resampled to pre- 
serve any correlation between patch length and CPUE. 
The number of patches selected was parametrically 
bootstrapped by drawing from a Poisson distribution 
with the realized number of patches as the mean of 
the distribution. An additional Poisson random vari- 
able was drawn to determine whether a patch station 
was included in the SRS estimator. The mean of this 
second Poisson distribution was the number of planned 
stations that occurred in a patch during the survey. 
This source of variability reflects the probability that 
any of the observed patch stations could have been lo- 
cated at one of our planned stations. Bootstrapping was 
conducted 10,000 times with the R statistical package 
(R Development Core Team, 2009). For the TAPAS es- 
timators, both the CPUE values and the patch lengths 
were resampled with replacement, but, for the SRS 
estimator, only the CPUE values were resampled. Per- 
centile confidence intervals were constructed with the 
bias-corrected method of Efron and Tibshirani (1993) 
that was used in Everson et al. (1996). This method 
centers intervals on the analytically estimated mean. 
To improve the precision of the biomass estimates 
obtained with our planned design, we re-analyzed the 
data with alternative patch definitions. First, we ex- 
amined the relationships of trawl CPUE to other vari- 
ables, such as the maximum S v , variance or standard 
deviation of S v , median S u , depth, products and ratios 
of these quantities, and multiple regressions. These 
examinations were done to see if focusing on different 
quantitative characteristics of the acoustic backscatter 
could result in an improved threshold. We then chose 
a number of alternative patch definitions and, with the 
