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Fishery Bulletin 119(1) 
Fundamental relationships between life history traits 
in fish species were first observed by Beverton and Holt 
(1959). They pointed out that M and K are typically 
related by a ratio close to 1.5, that the ratio of L,,,, to L.. 
is typically around 0.66, and that L., and K have a nega- 
tive power relationship that has a general form of L,~K*, 
with a shape parameter (h), which is typically around 
0.5. These relationships are referred to as Beverton—Holt 
invariants in the literature (Charnov, 1993) and are likely 
conserved through natural selection because of their 
link with the maximization of offspring (Beverton and 
Holt, 1959; Jensen, 1996, 1997; Charnov, 2008). Results 
of recent meta-analytical studies indicate that ratios dif- 
fer significantly between taxa and are therefore better 
studied within taxa (Hordyk et al., 2015; Nadon and Ault, 
2016; Thorson et al., 2017). 
Relationships of life history traits are useful for the 
estimation of missing life history parameter values by 
relating ones, such as M, for which information is elu- 
sive to ones, such as L., and K, for which values are more 
easily obtained (Pauly, 1980), or by relating L,,,,, to other 
length parameters (e.g., L,,,,) (Froese and Binohlan, 2000, 
2008; Jari¢ and Gaéi¢, 2012). The aim of these studies was 
mainly to generate missing estimates for single param- 
eters, and these studies were not taxon-specific, limiting 
their utility by ignoring the complex multivariate distri- 
bution between key life history parameters. As a solu- 
tion, Nadon and Ault (2016) presented an approach that 
involves the use of Monte Carlo simulation draws and sev- 
eral regression model steps between life history parame- 
ters for 6 fish families. Their approach allows for complex 
relationships between parameters, while maintaining a 
multivariate error structure. This approach is analogous 
to the method in which a sequence of regressions is used 
for multiple imputation of missing data (Raghunathan 
et al., 2001; van Buuren, 2007; Ellington et al., 2015). 
Nadon and Ault (2016) determined family-specific rela- 
tionships between key life history traits after an exten- 
sive literature review for 6 families of coastal fish species: 
surgeonfishes, jacks, snappers, emperors, goatfishes, and 
parrotfishes. Peer-reviewed data-limited assessments of 
stocks in Hawaii (Nadon, 2017) and Guam (Nadon, 2019) 
have already been implemented by using this approach. 
The goal of our study was to extend the approach from 
Nadon and Ault (2016) to 3 additional families of trop- 
ical coastal fish species, groupers (Serranidae), wrasses 
(Labridae), and grunts (Haemulidae), as well as to sharks 
from the orders Carcharhiniformes and Lamniformes. We 
acknowledge that taxonomy is an evolving field and with 
new information can come new evidence for reclassifica- 
tion. Recently, this evolution has touched groupers with 
proposals to move the subfamily Epinephelinae, including 
the genus Epinephelus, under the family Epinephelidae 
instead of under the family Serranidae (Craig and 
Hastings, 2007; Smith and Craig, 2007; Ma and Craig, 
2018). Although some classifications put grouper taxa 
under Epinephelidae instead of Serranidae, for the pur- 
poses of this study, we used Serranidae as the family name 
for species of Epinephelinae and other grouper species. 
Additionally, we tested this approach against those of 
life history studies and against the approach of Thorson 
et al. (2017) as applied in their R package FishLife. We 
also developed, and present here, a new R package, Step- 
wiseLH, that simplifies the implementation of the step- 
wise approach for all 10 included taxonomic groups. Our 
results will improve the capability to conduct stock 
assessments for these taxonomic groups in data-limited 
situations. 
Materials and methods 
Details of the stepwise approach 
The approach presented in Nadon and Ault (2016) involves 
a series of regression models in which relationships 
between life history parameters are used to sequentially 
estimate missing values for life history parameters from 
the previously estimated parameters (Fig. 1, Table 1). Note 
that the regression models that relate these parameters 
Figure 1 
Depiction of one iteration of the stepwise stochastic simula- 
tion approach in which statistical relationships between key 
life history traits are used to estimate parameters related to 
growth, maturity, and longevity. The simulation starts with 
a local estimate of maximum length (L,,,,), and regression 
models A—D (solid arrows) are used successively to estimate 
a parameter from the one estimated in the previous model. 
The dashed arrows represent direct parameter calculations 
made by using deterministic equations (e.g., the oldest 
recorded age [A,,,,] is calculated by using natural mortality 
[M]). The rest of the parameters in this depiction include 
the asymptotic length (L..), expected length at the oldest 
recorded age (Lamax), growth coefficient (K), and length at 
which 50% of individuals are mature (L,,,,). 
