Erickson and Nadon: Stepwise stochastic simulation for distributions of missing life history parameter values 
L mat ~ L Amax 
Haemulidae 
L,.(mm TL) 
Labridae 
L..(mm TL) 
750 1000 
L..(mm TL) 
Co) 
© 
1g) 
Cc 
© 
— 
— 
® 
icp) 
1000 2000 3000 4000 
L amax (MM TL) 
1000 2000 3000 4000 0.00 0.25 0.50 0.75 1.00 
L..(mm TL) 
1000 2000 3000 4000 
te max (mm TL) K (year ') 
Figure 2 
Modeled statistical relationships between life history parameters, the asymptotic length (L,,), maximum length (L,,,,), growth 
coefficient (K), natural maturity (M), and expected length at the oldest recorded age (La,,,x), in 4 pairs for grunts (Haemulidae), 
wrasses (Labridae), groupers (Serranidae), and sharks from the orders Carcharhiniformes and Lamniformes. Black circles indi- 
cate the estimates of life history parameters obtained from studies. The solid dark gray lines are the lines of best fit, produced 
by using a linear or power model. Gray areas indicate the 95% confidence intervals of the lines of best fit. Note that model C 
(see Figure 1) also includes the L,,,,, parameter for most families, but only the 1-variable M~K relationships are presented here. 
TL=total length. 
relationship, we divided the grouper species into 2 size 
ranges by using an L,,,, break point of 1000 mm total 
length. The growth parameter K had a negative curvilinear 
relationship with the L,, parameter (Fig. 2). A power func- 
tion best matched this relationship, and a lognormal error 
distribution was used to account for the decrease in vari- 
ability that occurred as L,, values increased. A power func- 
tion with a lognormal error distribution was also used to 
model M as a function of K and L,,,, (Fig. 2). Most of the 
available M and K data points were toward the lower end of 
the ranges of these parameters with only a few available 
data points at high values. It is likely that these limited 
data points had an outsized influence on the model fit. A 
positive, curvilinear relationship between M and K indi- 
cates slower growing fish have lower M, as was expected. 
A linear model was used for all 4 relationships between 
Lat ANd Lamax (Fig. 2). Parameters for sharks, wrasses, 
and groupers were modeled with a lognormal error dis- 
tribution because variability increased with larger La max 
values, and parameters for grunts followed a normal error 
distribution. Maturity data were available for only 5 spe- 
cies of grunts, and the relationship would likely benefit 
from a larger sample size. As previously reported by Nadon 
and Ault (2016), Lama, was a better predictor of L,,,, than 
L,,, as indicated by the higher coefficients of determina- 
tion (r*) for results from the Lynat~Lamax Models (Table 4). 
Comparing distributions: stepwise approach, life history 
studies, and FishLife 
For the 4 test species, we compared the probability distri- 
butions for key life history parameters generated by using 
the stepwise approach with those found in species-specific 
life history studies (Fig. 3). Like the results of the tests 
used by Nadon and Ault (2016), the estimates of life his- 
tory parameters resulting from use of the stepwise 
approach had greater standard deviations than those from 
actual studies. The estimates from the stepwise simulation 
