Wetzel et al.: The effect of reduced data on monitoring overfished fish stocks 
195 
method used to assess the simulated stocks. Stock syn¬ 
thesis was applied for the first time in year 50 and 
then every 6 th year thereafter. Assessment frequency 
for U.S. west coast groundfish species varies as a con¬ 
sequence of commercial importance (an indicator of 
exploitation), the time since last assessment, and life 
history dynamics of the stock (Methot, 2015). Long- 
lived rockfish species generally have slow dynamics, 
resulting in minimal fluctuations in biomass from year 
to year (assuming non-extreme harvesting). To mimic 
the likely cycle of assessments for this type of stock in 
real life, we conducted the assessment every 6 th year. 
Parameters determining unfished recruitment (Ro), 
steepness, growth, annual recruitment deviations, ini¬ 
tial age-structure deviations, and the size and width at 
maximum selectivity for the fishery selectivity that as¬ 
sumed a double normal parameterization (same as as¬ 
sumed in the operating model). Steepness was estimat¬ 
ed by using a diffuse beta prior within the estimation 
method. All other parameters were estimated without 
priors. Natural mortality, the variation of length-at- 
age, weight-at-length, the fecundity relationship, and 
the variation of recruitment (c>r) were assumed known. 
The ratio of spawning biomass to unfished spawning 
biomass (termed relative spawning biomass) in the as¬ 
sessment year was estimated and the forecasted catch¬ 
es were determined by using the harvest control rule 
adopted by the Pacific Fishery Management Council 
(PFMC) for rockfish species. The catches were removed 
from the operating population without error, and then 
the fishery CPUE index and length- and age-composi¬ 
tion data were generated for the subsequent 6 years. 
The harvest control rule adopted by the PMFC for 
rockfish species involves a linear reduction in catch 
when a stock falls below 0.40Sfi 0 , and no fishing when 
the stock falls below 0.10SS 0 . The maximum catch, 
termed the overfishing level catch was defined as the 
catch corresponding to the proxy for the fishing mor¬ 
tality rate at which maximum sustainable yield is 
achieved and if surpassed would constitute overfishing, 
was set equal to the target harvest rate measured as 
spawning biomass per recruit (F 0 50 ) multiplied by SB t . 
Spawning biomass per recruit is a measure of fishing 
mortality on the projected average contribution of each 
recruit to the spawning biomass. Applying an F 0 50 har¬ 
vest rate reduces the spawning biomass per recruit to 
50% of the unfished condition. The catch predicted by 
the overfishing level was reduced by a management 
buffer to determine the acceptable biological catch 
level (i.e., the default reduction for the PMFC for an 
age-structured assessment sets the acceptable biologi¬ 
cal catch equal to 95.6% of the overfishing level catch, 
Ralston et al., 2011). The annual catch limit was set 
equal to the acceptable biological catch when the simu¬ 
lated stock was above the target biomass, 0.40 SB 0 , or 
reduced from the acceptable biological catch according 
to the harvest control rule when the simulated stock 
fell below 0.40SB 0 . 
One major simplification in this simulation design 
was the omission of the rebuilding plans that are im¬ 
plemented when a stock is assessed to have fallen be¬ 
low the MSST (defined as 0.25SS 0 for U.S. west coast 
rockfish species). In reality, harvest for stocks that fall 
below the MSST is not based on the standard harvest 
control rule but rather on a rebuilding plan in which 
catches are determined until the stock is rebuilt to 
the target biomass (for additional details on PFMC re¬ 
building plans, see Wetzel and Punt, 2016). 
Data scenarios 
Three data scenarios were created to explore the impact 
of data availability on the ability to monitor rebuilding 
of an overfished stock (Fig. 2). The data scenarios were 
designed to emulate a stock, similar to many rockfish 
species off the U.S. west coast, that is infrequently 
encountered by a fishery-independent survey (e.g., be¬ 
cause of depth or habitat) and for which only fishery 
data were available. The sample sizes of the histori¬ 
cal length and age data generally were based on the 
effective sample sizes observed for yelloweye rockfish. 
Historical length and age data from the fishery begins 
in year 35, 15 years before the first assessment, and 
the fishery CPUE data starts in year 45. Following the 
first assessment in year 50, the 3 scenarios have differ¬ 
ent data availability based on estimated stock status 
(e.g., overfished versus rebuilt) in the assessment year. 
The full data scenario maintained the fishery 
CPUE index and length- and age-composition data at 
the historical levels (before the stock being declared 
overfished in year 50) during rebuilding (Fig. 2). The 
reduced data scenario decreased the amount of data 
available from the fishery during rebuilding (Fig. 2). 
The length- and age-composition data were reduced to 
20% of the historical sample sizes during rebuilding 
and the fishery CPUE index was eliminated during 
the rebuilding period. When the simulated stock was 
estimated to have rebuilt to the target biomass, the 
CPUE index resumed and the sample sizes of composi¬ 
tion data reverted to historical levels. The eliminated 
data scenario had no fishery data during rebuilding 
(Fig. 2). The fishery CPUE index and composition data 
resumed at historical sample sizes when the simulated 
stock was projected to be rebuilt. 
The estimation method in the full and reduced data 
scenarios was allowed to estimate a change in selec¬ 
tivity from asymptotic to dome-shaped during the re¬ 
building period through the application of a time block 
on selectivity. However, the eliminated data scenario 
assumed constant asymptotic selectivity in the assess¬ 
ment for all years because no fishery composition data 
were available to detect a potential shift in selectivity. 
In reality, input from fishermen may be used to justify 
an updating of the selectivity form. Methods that have 
been used for stocks off the U.S. west coast have ap¬ 
plied a default assumption for asymptotic selectivity in 
assessments that do not incorporate composition data. 
Incorrectly assuming dome-shaped selectivity when the 
true form is asymptotic could result in overly optimis¬ 
tic estimates of the population status because dome- 
