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Fishery Bulletin 119(1) 
Spawning potential ratio 
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Fishing mortality (year ') 
Figure 4 
The spawning potential ratios at various fishing mortal- 
ity rates derived by using parameter estimates from life 
history studies (dark gray areas and solid lines) and from 
use of the stepwise stochastic simulation approach (light 
gray areas and dashed lines) for the 4 selected test species: 
(A) javelin grunter (Pomadasys kaakan), (B) redbreasted 
wrasse (Cheilinus fasciatus), (C) camouflage grouper 
(Epinephelus polyphekadion), and (D) blacktip reef shark 
(Carcharhinidae melanopterus). Lines represent median 
values, and shaded areas represent 95% confidence inter- 
vals. Fishing mortality rates ranged from 0 to more than 
4 times natural mortality. 
Lastly, we compared the stepwise approach with the 
FishLife meta-analytical approach (Thorson et al., 
2017). On average, the stepwise approach was more 
accurate than the FishLife approach implemented at 
both the genus and family levels for all parameters 
except K (Table 6, Figs. 5 and 6). The accuracy of the 
ratios of L to L., was only slightly better for the 
mat 
stepwise approach. However, the accuracy of L.., M, Lynats 
and the ratio of M to K was significantly higher for the 
stepwise approach. For example, the L,,,, medians from 
stepwise simulation were on average 11% removed from 
the study values, and the L,,,, average median values 
from the FishLife approach where more than 30% 
removed from those in published studies. In terms of 
precision, the stepwise approach was more precise for 
L., M, and Lat. The FishLife distributions were slightly 
more precise for the ratios of L,,,; to L., and of M to K 
and more precise for the K parameter (standard devia- 
tions of 0.12 versus 0.17). 
Discussion 
Through this study, we have successfully extended the 
stepwise stochastic simulation approach to grouper, 
wrasse, grunt, and shark taxa. Our findings indicate that 
the stepwise approach could be further extended to fit 
specific management and scientific needs for additional 
families by replicating the effort in this study. The new 
models for these 4 taxa can now be used to calculate val- 
ues for key life history parameters in data-poor situa- 
tions and to implement stock assessment models (Nadon, 
2017, 2019). The model in which the stepwise approach 
is applied now includes 10 taxonomic groups and is 
available as the R package StepwiseLH on the GitHub 
website. 
Caveats 
The stepwise approach, as well as other similar meta- 
analytical approaches, carries a lot of uncertainty into 
estimates of life history parameters and is not meant to 
replace proper life history studies. These approaches are 
meant to be temporary solutions to alleviate the press- 
ing needs for assessment and management of data-poor 
fish populations. Although we tried to limit the sources of 
variability in our data set as much as possible, we had to 
make several compromises to retain a sufficient number 
of data points. For example, although most of the species- 
specific values of L,,,,, L.., K, and A,,,, used to create our 
data set are from single studies (and therefore single 
locations), maturity studies were often conducted sepa- 
rately and L,,,, values can therefore be from a location 
different from the area where values of other parameters 
are from for many species. Specifically, 2 of the 5 matu- 
rity studies for grunts and 12 of the 32 maturity studies 
for groupers were not conducted at the same location as 
their corresponding growth studies (although only 2 of 
20 shark maturity studies and none of the wrasse studies 
were conducted in different locations from those of their 
growth studies). This compromise may have added more 
variability to our L,,,, estimates but likely did not intro- 
duce any specific biases. 
Additionally, the lack of data points and different model 
fitting procedures for juveniles can have an effect on the 
L,, and K parameter estimates. We tried controlling for 
