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Fishery Bulletin 119(1) 
Testing the expansion of the stepwise approach 
To test our expansion of the approach of Nadon and Ault 
(2016), we compared the probability distributions of 
the values of life history parameters obtained through 
use of the stepwise approach with the probability dis- 
tributions from published growth and maturity studies 
on a species in each of the new taxonomic groups. We 
selected these species on the basis of the availability 
of published values of life history parameters from in- 
depth studies and the availability of an independent 
estimate of L,,,, that we obtained from visual census 
data collected during NOAA diver surveys. We selected 
the blacktip reef shark (Carcharhinus melanopterus) 
(Chin et al., 2013), the camouflage grouper (Epinephelus 
polyphekadion) (Rhodes et al., 2011), the javelin grunter 
(Pomadasys kaakan) (Al-Husaini et al., 2002), and 
the redbreasted wrasse (Cheilinus fasciatus) (Hubble, 
2003). The NOAA diver surveys are conducted every 
3 years around approximately 50 islands and atolls in 
the central Pacific Ocean (the main and Northwestern 
Hawaiian Islands, American Samoa, and the Mariana 
Archipelago). For these surveys, a stratified random 
sampling design is used to select locations around the 
islands at which to count fish by using a stationary- 
point-count approach (Ayotte et al.'). During surveys, 
divers also record approximate total lengths of sighted 
fish to the nearest centimeter; divers are consistently 
trained in this exercise. 
Next, we compared the precision and accuracy of the 
estimates of life history parameters from use of the 
stepwise procedure for the 4 new taxa included in this 
study. We used the same criteria as Nadon and Ault 
(2016) to evaluate the precision and accuracy of esti- 
mates made with the stepwise approach. We compared 
the widths of distributions of standard deviations (pre- 
cision) and the distances between medians (accuracy) 
from the stepwise analysis with those from aging and 
maturity studies. We ran the stepwise simulation for 
these species, starting with local L,,,, values obtained 
from a data set of lengths of blacktip reef sharks, red- 
breasted wrasse, and camouflage grouper from NOAA 
diver surveys. We did not have an independent data 
set of lengths of javelin grunter; therefore, we used the 
99th percentile of the lengths in the original growth 
study (Al-Husaini et al., 2002) as the L,,,,, value for this 
species. 
Finally, we evaluated the performance of the stepwise 
approach when determining a simple stock status metric, 
the spawning potential ratio (SPR) (Goodyear, 1990), by 
measuring its precision and accuracy as we did for the 
life history parameters. Spawning potential ratio is the 
ratio of spawning stock biomass (SSB) per recruit under 
' Ayotte, P., K. McCoy, A. Heenan, I. Williams, and J. Zamzow. 
2015. Coral reef ecosystem program standard operating pro- 
cedures: data collection for rapid ecological assessment fish 
surveys. NOAA, Natl. Mar. Fish. Serv., Pac. Isl. Fish. Sci. Cent. 
Admin. Rep. H-15-07, 33 p. [Available from website.] 
a certain fishing mortality rate (F) divided by the same 
metric when fishing is absent: 
SSB =) N,W,, (9) 
at 
where A,,,, = the age at maturity (derived directly from 
Jb) LOM AN 8 
N, = the number of individuals; and 
W, = the expected individual weight (derived from a 
length—weight relationship; see Equation 10) 
in each age class a, beginning from A,,,,+. 
The number of individuals in an age class is obtained by 
using the following exponential mortality equation: 
IN enn = IN (10) 
where S, = the knife-edge selectivity at age a (set to age 2 
for all species, to simplify comparisons). 
Given that the SPR is a per-recruit metric, the number of 
fish at age 0 is simply set to 1 (i.e., N,_p=1). Values for param- 
eters of the dependent relationship of weight (W) to length 
(L) (a and B, where W=oaxL'), necessary for SPR calculations, 
were obtained from FishBase. Using the above equations, 
we calculated SPR values for all 4 test species at different 
fishing rates ranging from 0 to F>4M from values of both 
the life history studies and stepwise approach. We then com- 
pared the SPR probability distributions of the test species in 
a fashion similar to that used for life history parameters. We 
calculated the SPR at different F values given the curvilin- 
ear relationship between the SPR and F. 
Finally, we compared the stepwise parameter esti- 
mates to those from use of the alternative meta-analytical 
approach FishLife (Thorson et al., 2017). The FishLife 
approach fits a multivariate model with a taxonomic struc- 
ture to generate probability distributions of life history 
parameters at different taxonomic levels (species, genus, 
family, order, and class). Using the R package FishLife 
(Thorson, 2017), we generated probability distributions 
for our 4 test species at the genus and family levels. We 
plotted these distributions with the results from use of the 
stepwise approach as well as with the published parame- 
ter estimates to evaluate their accuracy. All analyses were 
conducted in R. 
Results 
Life history parameter models for new taxa 
The parameter L,,,,, had a close relationship with L,, for all 
4 taxonomic groups (Fig. 2). All 4 relationships were best 
explained by a linear function with a relatively narrow nor- 
mal error distribution. The standard deviation for sharks 
was much larger than for the other 3 groups (Table 2), an 
outcome that was expected given their larger size ranges. 
Larger (>1000 mm total length) grouper species had higher 
variability associated with L,, estimates in comparison to 
smaller species; therefore, for analysis of the L..~L,,,, 
