Poussard et al.: Discriminating between high- and low-quality field depletion experiments 277 
experiments conducted on Atlantic surfclam and ocean 
quahog stocks by using a series of experimental quality 
measurements. The simulated depletion experiments have 
the advantage of being fully controlled, and the accuracy 
and precision of the measurement estimates they provide 
can be evaluated. In this analysis, a set of simulated exper- 
iments was matched to each field experiment. This set of 
simulated experiments was assumed to represent a suite of 
conditions that might also occur in the corresponding field 
experiment. The results of these comparisons allow exam- 
ination of the quality of field experiments and provide evi- 
dence for weighting the results of field experiments beyond 
traditional measures of uncertainty. 
Materials and methods 
The Patch model 
For estimation of the catchability coefficient (q), depletion 
experiments allow correction of survey catch by using the 
equations N=SA/q and q=F where WN is stock abundance 
or biomass and SA is the swept area average of all tows 
in the experiment area. The q is obtained from a, the area 
swept by the sampling gear; e, the dredge efficiency; and A, 
the spatial domain of the estimates (Paloheimo and Dickie, 
1964). The o@ is calculated as the distance the dredge is 
towed multiplied by the width of the dredge. See Figure 2 
for a visual representation of the dredge tows in an exper- 
iment area. 
The expected catch of organisms in any tow 1, E(C;), 
given initial density of the target organisms (D,) and the 
cumulative catch from previous tows, T,_,, can be calcu- 
lated as follows: 
E(C;) = q(Do = ae) (1) 
assuming each tow covers the same spatial domain. In 
reality, this relationship is more complex because each tow 
covers only a portion of the area of the experiment. Incor- 
porating the portion of the area that has already been hit 
by the dredge prior to tow i, also known as the hit matrix 
(Hennen et al., 2012), gives the expected catch per tow i 
as follows: 
E(C,) = (EAS,)Dp, (2) 
where EAS is the effective area swept, defined as the total 
area swept by the dredge in tow 1, taking into account the 
portion of the experimental area hit by the dredge in pre- 
vious tows. The EAS is calculated as follows: 
EAS = ea; ¥)_,f,;(1- ey)", (3) 
where e = the capture efficiency as estimated by the Patch 
model; 
a; = the area swept by tow 1; 
f,; = the fraction of the area a; hit by the dredge j 
times in previous tows; and 
y = the ratio of cell size to dredge width. 
Rago et al. (2006) divided the experimental area into 
cells twice the width of the dredge. Hennen et al. (2012) 
removed y by reducing the cells to points, eliminating the 
need to calculate cell size and, as a result, improving accu- 
racy and precision of efficiency estimates. In this study, 
the latter method was used. 
The negative binomial distribution was used to describe 
the dispersion of animals in the area of the experiment in 
order to account for extra variation in observed catches 
and for catch from previous tows when estimating catch 
in tow 1. In this method, the cumulative spatial pattern of 
removal of animals is used to define capture probability 
for each organism. The negative binomial distribution of 
catch can be expressed as a function of Do, k (the disper- 
sion parameter), and EAS (Rago et al., 2006): 
P(C, |] Dool2, EAS) = | |_2yss) | 
D)(EAS)+ K } | Do EAS) +k 
C k+j-1 
Sf fee (4) 
j=l 
J 
The log likelihood (LL) function allows estimation of the 
dispersion parameter, initial density, and capture effi- 
ciency, given the hit matrix, catch, and area swept: 
LL(Dp, k, e, Y|C;, EAS) = RY), log(h) 
—log(D) (EAS) + k) 
+ Yi" log (D)(EAS)) 
—log(D) (EAS) + k) 
+ DD jloe(é +j- 1) 
=a, 1 (5) 
where n = the total number of tows in the sequence; and 
! = a factorial. 
Simulated data sets 
Poussard et al. (2021) reported the results of 5400 depletion 
experiments simulated in a block design in which animal 
density, “true” dredge efficiency, the number of tows per 
experiment, and the dispersion of animals on the bottom 
were varied. For the purposes of the study we describe here, 
3600 additional simulations with 15 and 25 dredge tows 
were conducted in order to provide a simulated data set 
that is comparable to the data from experiments conducted 
in the field, for a total of 9000 simulations (Table 1). The 
simulated data set included 5 options for the number of 
dredge tows for each experiment, 4 dispersions of individual 
clams in the area, 3 clam densities, and 3 values for the true 
efficiency of the dredge. Fifty simulations were conducted 
for each combination of factors (e.g., 50 simulations were 
conducted with 25 tows that had a dredge efficiency of 0.9 
and clams distributed evenly through the area with a den- 
sity of 3.00 individuals/m?, and 50 more simulations were 
