278 
Table 1 
Characteristics from the analysis done with simulation 
of depletion experiments in a block design. All combina- 
tions of the 4 parameters were simulated: 50 simulations 
for each tetradic combination were conducted. The type 
of clam distribution is denoted as follows: uniform across 
the area (NP), patches oriented across the narrow dimen- 
sion (P), patches oriented longitudinally (HP), and patches 
of a triangular nature emanating from one side of the rect- 
angle (T). True efficiency is efficiency of the dredge for cap- 
ture of shellfish. The data set used in the simulations came 
from depletion experiments conducted for populations of 
ocean quahogs (Arctica islandica) and Atlantic surfclams 
(Spisula solidissima) off the mid-Atlantic coast of the 
United States between 1997 and 2011. 
Characteristic Values 
True efficiency i 0.6 0.2 
Clam density 1.50 3.00 
(individuals/m”) 
Clam distribution HP 
No. of tows 
conducted with all the same factors except with a density of 
1.50 individuals/m”, and so on). Fifty tow patterns were ran- 
domly generated for each tow number. 
Here we discuss 4 useful measures for comparing deple- 
tion experiments, along with the estimates of efficiency and 
density. The 4 characteristics are the EAS (Equation 3), the 
coefficient of variation (CV) for the efficiency estimate (CV,), 
the CV of the & parameter (CV) (the negative binomial dis- 
persion parameter), and the overlap score (OS) describing 
tow overlap (Equation 7). The CVs were calculated by using 
the delta method standard deviation of estimates from the 
Patch model divided by the means of the estimates obtained 
from the log likelihood equation (Equation 5). 
The OS is a measure that describes tow overlap that 
does not depend on estimated efficiency or the spatial 
dimensions of the site. The OS is derived directly from the 
hit matrix (Hennen et al., 2012), where the n rows equal 
the number of tows in the experiment and the m columns 
are the number of points touched m times previously. The 
highest possible amount of overlap for any depletion site 
would be the exact duplication of the longest tow in each 
sequence (the row with the most total points touched), 
repeated n times (OS,,,,). For tow i, the OS is calculated 
with this equation: 
OS, =, (Pin); (6) 
where p; , = the number of points in hit matrix row 7 and 
column h. 
The OS for each tow sequence is then calculated with 
this equation: 
>; Os 
aR 5100. (7) 
OS 
max 
OS = 
Fishery Bulletin 119(4) 
The value of OS varied nonlinearly with tow number. 
As a consequence, the values were detrended by using the 
mean OS value for that tow number to standardize all 
OS values of the same tow number. A higher value of OS 
equates to more dredge overlap in the tow structure of an 
experiment for a given number of tows. 
For the simulations, where the true efficiency (TrueEff) 
was already known (efficiency values were 0.2, 0.6, and 
0.9), Poussard et al. (2021) calculated the percent error 
in efficiency from the Patch model estimate of efficiency, 
EstEff, and the inherent efficiency specified in the simula- 
tion, TrueEff, as follows: 
EstEff — TrueEff 
TrueEff 
On the basis of the results of their analysis of simulated 
depletion experiments, Poussard et al. (2021) concluded 
that a depletion experiment is more likely to produce accu- 
rate gear efficiency estimates if it employs a high num- 
ber of dredge tows (e.g., 40 tows per experiment compared 
with 10 or 15 tows), maximizes the amount of intersec- 
tion in tow paths, occurs over a homogenous as opposed 
to patchy distribution of clams, and uses a highly efficient 
dredge. The results of these simulations were compared 
with those of the field depletion experiments by using the 
set of 4 characteristics to match the field experiments to 
simulated experiments with similar characteristics. The 
known errors in the set of comparable simulated experi- 
ments were then used as a proxy for the reliability of each 
of the 50 field experiments. 
Error = x 100. (8) 
Application of simulations: error estimates 
Field experiments varied in the length of the depletion site 
and the width of the dredge used. For statistical analysis, 
EAS was standardized to a dredge width of 3.81 m and a 
site length of 960 m, consistent with the simulation data 
set of Poussard et al. (2021), by using a proportional stan- 
dardization. All EAS values used were the average values 
per tow, rather than the total values, to take into account 
the large range in tow numbers among experiments. 
A principal components analysis was conducted on the 
simulation data set to determine if the 4 measures that 
describe depletion performance (EAS, CV,, CVx, and OS) 
were correlated and, if so, to derive new orthogonal met- 
rics. The data were standardized to a mean of 0 and a 
standard deviation of 1, and factors were designated by 
using Varimax rotation. Factor loadings indicate each of 
the 4 characteristics loaded on separate axes with loads 
exceeding 0.95; therefore, the 4 measures in their orig- 
inal form are approximately orthogonal and provide 
independent information for evaluating experimental 
performance. 
Field experiments were matched to a subset of the 
simulated depletion experiments through an iterative 
process. For each field experiment, the values of the 
4 characteristics were compared with values from the 9000 
simulations. Data from field experiments were compared 
with the simulation data set by determining whether the 
