Erickson and Nadon: Stepwise stochastic simulation for distributions of missing life history parameter values 81 
Table 3 
Summary of estimates of life history parameters and other information in the data set for 6 taxonomic groups created through a 
literature review and used in this study. Data types include the asymptotic length (L..), growth coefficient (K), oldest recorded age 
(Ajax), ratio of maximum length (L,,,,) to L.., ratio of natural mortality (M) to K, ratio of the length at which 50% of individuals are 
mature (L,,,,) to the expected length at the oldest recorded age (La,,,,), and ratio of L,,,, to L... For the family Labridae, species from 
small-bodied genera were not included; for the family Serranidae, the Anthias genus was not included; and, for the shark group, 
only families from the orders Carcharhiniformes and Lamniformes were included. Standard deviations are provided in parentheses 
for ratios. All length values are total lengths. 
Haemulidae 
Data type (grunts) 
No. of species considered 134 86 
No. of species with growth study 14 2 
No. of species with maturity study 5 2 
L., (mm) 203-917 
K (year"}) 0.19-1.00 
Amax (years) 5-36 
Dy ree tO 1b 1.02 (0.11) 
MtoK 0.55 (0.29) 
Pa StO ee 0.80 (0.14) 
Ib WO Ih, 0.79 (0.15) 
mat 
we selected only estimates for males and females com- 
bined. As a result, we were able to combine estimates from 
these studies more easily with data from others in which 
sex was undifferentiated. Further, sexes are not differen- 
tiated in most size-composition data sets in data-limited 
situations, and growth curves that are not sex specific are 
typically needed to run simple length-based assessment 
models with such data sets. For maturity, we obtained L,, 
for females only, given that the reproductive potential of 
a stock is almost always tied to mature female biomass 
in population models. We converted all length values to 
total lengths in millimeters; total length was the length 
measurement used in this study and by Nadon and Ault 
(2016). Conversion factors obtained from FishBase were 
used to do so. In a limited number of cases in which multi- 
ple studies were available for a single species, we selected 
the most reliable source, on the basis of sample size and 
publication source. 
For the parameter A,,,,, the age of the oldest reported 
fish in a study was selected. If multiple longevity val- 
ues were available for a certain species, we selected the 
oldest recorded age as the A,,,, value. Values of M were 
obtained by using the approach presented in Hewitt and 
Hoenig (2005), under the assumption that 5% of a cohort 
is left at the oldest recorded age (S=0.05; see Equa- 
tion 2). Note that this assumption was used to obtain 
M estimates to fit model C (i.e., M~K+L,,,,)- In practice, 
when using the stepwise approach, we can convert the 
M estimates output from the model back to A,,,, values 
and calculate a new M estimate under a different set 
of assumptions (e.g., S=0.01; Pauly, 1980; Then et al., 
2015). These options are available in the R package that 
implements the stepwise approach (see the “Discussion” 
section). 
Holocentridae 
(soldierfishes) 
Siganidae 
(rabbitfishes) 
Serranidae 
(groupers) 
Labridae 
(wrasses) Sharks 
334 29 
12 6 
9 
133-981 148-2006 733-4218 
0.07—0.89 0.06—1.39 0.04-1.01 
7-18 4-76 7-44 
1.12 (0.13) 1.10 (0.14) 0.95 (0.11) 
0.68 (0.39) 0.81 (0.48) 1.53 (0.82) 
0.48 (0.16) 0.60 (0.10) 0.78 (0.10) 
0.48 (0.17) 0.58 (0.12) 0.70 (0.12) 
Quality control was performed on the studies found 
during the literature review by using the same guidelines 
outlined in Nadon and Ault (2016). Requirements included 
discarding any growth studies that involved length— 
frequency analysis or back-calculations. We kept only stud- 
ies based on the aging of fish through the use of hard parts, 
primarily otoliths, vertebrae, and dorsal spines for sharks 
(Natanson et al., 2018; Natanson and Deacy, 2019). Finally, 
any studies that occurred in waters with mean sea-surface 
temperatures (SST) below 20°C were removed from consid- 
eration because of the well-established negative correlation 
between longevity and water temperature (Pauly, 1980; 
Jobling, 1994; Choat and Robertson, 2002). Exclusion of 
studies from regions with low temperatures was a sensi- 
ble choice given that many of the families examined in our 
study are typically found in tropical waters where tempera- 
tures are usually well above the threshold of 20°C. Given 
that the ranges of our taxonomic groups center on tropical 
areas, only 3 species were excluded because of temperature 
criteria (1 wrasse and 2 groupers). The models also excluded 
genera that were clear outliers in certain families. 
After obtaining the new data set of life history traits and 
putting it through quality control, we visually explored the 
shape of the functional relationships between paired 
parameters (L,,,,~L.., K~L.., M~K, and Ly, at~Lamax) by plot- 
ting data points in scatter plots for each new taxon (by new, 
we mean taxa added to those already included in the work 
of Nadon and Ault, 2016). We then tested the fit of lin- 
ear, power, and exponential functions to these data points 
and obtained the maximum likelihood estimates for all 
parameters of models A-D by using the mle2 function of 
the package bbmle (vers. 1.0.19; Bolker, 2008; Fox, 2008) 
in the R statistical computing and programming environ- 
ment (vers. 3.4.0; R Core Team, 2017). 
