Poussard et al.: Discriminating between high- and low-quality field depletion experiments 281 
estimate of efficiency with the known efficiency used in 
the simulation (Equation 8). The error term Err3 was 
modified as a simple difference between the averages 
(observed and true efficiencies) obtained from the simu- 
lation subset as Err4: 
Err4 = abs(ObsEff — TrueEff). (11) 
Caveat lector. No characteristic can be used to defin- 
itively estimate the accuracy of a field depletion exper- 
iment because the true efficiency perforce is unknown. 
Estimates of the 4 error terms relate attributes of a large 
set of simulated experiments, in which combinations of 
4 different depletion experiment characteristics are used 
to describe how precisely the Patch model estimate of effi- 
ciency returned the known efficiency specified in the simu- 
lation. In this study, comparing field experiments directly 
to the simulations permitted inference of the quality of field 
experiments. Comparisons were made by using estimates 
of the 4 error terms to identify field experiments that have 
characteristics that resemble the 4 performance character- 
istics in the simulations of Poussard et al. (2021). 
Statistics 
Unless otherwise indicated, statistical evaluation of the 
quality of field depletion experiments was done with SAS 
9° (SAS Institute Inc., Cary, NC). Field experiments that 
had estimates for 1 or more of the 4 error terms at or above 
the 80th percentile were compared with the remaining 
experiments that had 1 or more error estimate below the 
80th percentile by using a Wilcoxon rank sum test (Sokal 
and Rohlf, 1998) to determine if the flagged subset of field 
experiments was a random subset of all field experiments, 
as determined by the error estimates and other character- 
istics as earlier described. 
The relationship between descriptors of Patch model 
performance, including efficiency and density estimates, 
and descriptors of the experiment, such as location, depth, 
and target species in the field experiments, were resolved 
by using correspondence analysis (Clausen, 1998). For 
this purpose, continuous variables were classified into 
quartiles (1-4), and error terms were entered as 1 (below 
the 80th percentile) or 2 (at or above the 80th percen- 
tile). The variables used to specify the coordinate system 
for the correspondence analysis and a series of supple- 
mentary variables assigned coordinate positions include 
dredge efficiency and its CV, clam density and its CV, the 
k parameter, EAS, OS, latitude, depth, species, region, 
dredge width, and the 4 error terms. Of note, the error 
terms were all designated as supplementary variables, 
meaning that they did not determine the axes in the cor- 
respondence analysis and were added retrospectively to 
provide context. 
Pearson’s correlation coefficients were calculated by 
using statistical software R (vers. 3.6.0; R Core Team, 
3 Mention of trade names or commercial companies is for identi- 
fication purposes only and does not imply endorsement by the 
National Marine Fisheries Service, NOAA. 
2019) for variables describing the field experiments to 
determine how factors, such as dredge width, experiment 
area width, number of tows, year, and latitude correlated 
with Patch model estimates of efficiency, density, and the 
k parameter. 
Results 
Characteristics of field depletion experiments 
The mean and median estimates of efficiency, density, 
and the k parameter for the 50 field depletion exper- 
iments are provided in Table 4. The mean estimate of 
efficiency for the 31 depletion experiments that targeted 
Atlantic surfclams is 0.635, and the mean efficiency 
estimate for the 19 depletion experiments that targeted 
ocean quahogs is 0.586 (Fig. 3). The mean density esti- 
mate for depletion experiments with Atlantic surfclams 
is 1.50 individuals/m”, and the mean density estimate 
for depletion experiments with ocean quahogs is 1.18 
individuals/m?. These densities are well above the aver- 
age stock density for both species because the depletion 
experiments were purposely sited in high-density areas. 
The mean estimate of k for the experiments with Atlantic 
surfclams is 12.10, and the mean for the experiments 
with ocean quahogs is 7.72. 
Most depletion experiments that targeted ocean qua- 
hogs were conducted at higher latitudes and at deeper 
depths than depletion experiments that targeted Atlantic 
surfclams (Table 5). For depletion experiments with 
ocean quahogs, higher efficiency estimates were pro- 
duced at the most northern locations (Fig. 1). Depletion 
experiments with Atlantic surfclams produced efficiency 
estimates that were higher off the coast of New Jersey 
than off the coasts of Long Island and the Delmarva 
Peninsula (Fig. 1). 
Over the 14 years that depletion experiments were 
conducted, method and gear changed. Dredge width, for 
example, gradually increased from 2.55 to 3.81 m. The 
number of dredge tows used in each experiment varied 
through the years as well. The majority of experiments, 
especially in later years, used between 15 and 20 tows, but 
some experiments between 1997 and 2000 used as few as 
4 tows and as many as 389 tows. 
Correlation analysis 
Efficiency estimates for depletion experiments that tar- 
geted ocean quahogs are significantly positively correlated 
with latitude (Fig. 1) and the width of the dredge (Fig. 4). 
Efficiency is incorporated into the equation to calculate 
EAS; therefore, the correlation between efficiency and EAS 
was expected, and correlations between efficiency and other 
variables were reflected by correlations between EAS and 
those same variables. Year was incorporated into the cor- 
relation analysis to examine how characteristics changed 
over time. As noted, dredge width increased with year, and 
tow number and depth decreased over time. The CV, is 
