192 
Fishery Bulletin 116(2) 
Figure 1 
Fishery selectivity for the time-invariant case during (A) the his¬ 
torical and rebuilt periods and (B) the overfished period and for 
the time-varying case during the (C) historical and rebuilt periods 
and the (D) overfished period. These 2 alternative cases were used 
in the operating model to account for the potential effects of time- 
varying natural mortality and fishery selectivity on simulated rock- 
fish stocks. A standard error of 0.05 was applied annually for size 
at maximum selectivity, which defined the variability of the ascend¬ 
ing limb of the selectivity curve (in panels C and D, and a standard 
error of 0.20 was applied for the width at maximum selectivity that 
defined the length at which the dome in selectivity began while the 
stock was estimated to be overfished (in panel D) (for additional 
details on double normal selectivity, see Methot and Wetzel, 2013). 
of new biological data is severely limited 
because of harvest restrictions. 
An understanding of the long-term effect 
of reduced data on the ability to monitor a 
stock during rebuilding would provide in¬ 
sight and guidance for management. Nu¬ 
merous simulation studies have evaluated 
the impact of data quality and quantity on 
the performance of stock assessment meth¬ 
ods (e.g., Hilborn, 1979; Chen et al., 2003; 
Yin and Sampson, 2004; Magnusson and 
Hilborn, 2007; Wetzel and Punt, 2011; Lee 
et al., 2012); however, studies often focus 
on the ability to estimate either manage¬ 
ment quantities or biological parameters. 
The simulation performed in our study 
evaluated the ability to accurately monitor 
rebuilding of an overfished, long-lived rock- 
fish stock for which harvest and the collec¬ 
tion of fishery data are restricted during re¬ 
building. This simulation study addressed 3 
main questions: 1) Do limited data result in 
increased uncertainty that affects the abil¬ 
ity to detect when an overfished stock has 
rebuilt, 2) Can limited data from the fish¬ 
ery be used to detect a shift in fishery se¬ 
lectivity that results from changing fishing 
behavior during rebuilding, and 3) How are 
model estimates of stock size and biological 
parameters affected during periods of lim¬ 
ited data? 
Materials and methods 
General approach 
A rockfish life-history type common to the 
U.S. west coast was simulated (Table 1). 
West coast rockfish species are assumed to 
have a range of natural mortality and pro¬ 
ductivity levels, from long-lived and slow 
growing (e.g., yelloweye rockfish) to medium-lived and 
intermediate-growing life histories (e.g., black rockfish 
[Sebastes melanops ]). The operating model was param¬ 
eterized by using intermediate natural mortality and 
steepness values to represent the general life-history 
dynamics of a U.S. west coast rockfish species. 
Two alternative cases were simulated by using the 
operating model to account for the potential impacts of 
time-varying natural mortality and fishery selectivity. 
The first case, referred to as time-invariant, involved 
a single fixed rate of natural mortality over the en¬ 
tire time period. The fishery selectivity was assumed 
(and fixed) to be asymptotic during the historical pe¬ 
riod, dome-shaped during the overfished period, and 
then again asymptotic after the simulated stock was 
rebuilt (Fig. 1, A and B). The simulated stocks were 
reduced to an overfished state (below MSST) at the 
time of the first assessment in year 50. The shift in 
selectivity during the period in which the simulated 
stock was estimated to be overfished was designed to 
represent potential changes in fishing behavior that 
result from harvest restrictions that could affect the 
estimation performance, if not detected because of lack 
of data to inform the model about the shape of fishery 
selectivity. 
The second case, referred to as time-varying, in-_ 
volved annual deviations in natural mortality and in 
the parameters on which the fishery selectivity pat¬ 
tern was based during the historical, overfished, and 
rebuilt periods (Fig. 1, C and D). All time-varying pa¬ 
rameters were designed to produce data that would 
be less informative about either the biology or the 
fishery behavior and to better emulate the complex¬ 
ity of real fishery data. Annual deviations in fishery 
selectivity were applied to 2 selectivity parameters: 
1) the length bin (in centimeters) at which the as- 
