Erickson and Nadon: Stepwise stochastic simulation for distributions of missing life history parameter values 
Table 5 
Comparison of descriptive statistics of the probability distributions of life history parameters obtained 
from published life history studies to those from the use of the stepwise stochastic simulation approach for 
the 4 selected test species: javelin grunter (Pomadasys kaakan), redbreasted wrasse (Cheilinus fasciatus), 
camouflage grouper (Epinephelus polyphekadion), and blacktip reef shark (Carcharhinidae melanopterus). 
The life history and other model parameters include the maximum length (L,,,,), asymptotic length (L..), 
growth coefficient (K), length at which 50% of individuals are mature (L,,,,,), natural mortality (M), spawn- 
ing potential ratio (SPR) at which fishing mortality (Ff) was equal to M, and SPR at which F was equal to 
2 times M. The median, standard deviation (SD), ratio of the SD from stepwise simulation to the SD from 
life history studies (SD ratio), and the standardized distance between the stepwise medians and medians 
from life history studies (relative error [RE]) are presented for each parameter, except L,,,,, which was a 
measured value in the study. The median L,,,,, values used to obtain probability distributions for the 4 test 
species are provided. TL=total length. 
P. kaakan C. fasciatus C. melanopterus 
E. polyphekadion 
Parameter Study Stepwise Study Stepwise Study Stepwise Study Stepwise 
Lynax (1am TL) 
L., (mm TL) 
Median 
SD 
SD ratio 
RE (%) 
K (year) 
Lat (tam TL) 
Median 
SD 
SD ratio 
RE (%) 
M (year“!) 
Median 
SD 
SD ratio 
SD ratio 
RE (%) 
To test the influence of the estimates of life history 
parameters from use of the stepwise approach on stock 
status, we used stepwise parameter predictions to calcu- 
late SPR distributions at F values ranging from 0 to more 
than 4 times M. The use of the stepwise approach and 
life history studies generated relatively similar median 
SPR values across the range of F, but the stepwise- 
derived SPR values were more variable, as expected, 
because of higher variability in life history parameters 
(Fig. 4). Higher variability was especially true for the 
redbreasted wrasse, given the low number of studies that 
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were available for the wrasse family and the resulting 
higher uncertainty in parameter estimates from stepwise 
simulation. Averaged across all 4 test species, the abso- 
lute distance between the stepwise-derived SPR values 
and those from life history studies was 0.05 when Ff was 
equal to M and was 0.03 when F was equal to 2 times M. 
It is worth noting that, for 3 of the 4 test species, the SPR 
curve for estimates from use of the stepwise approach 
was higher than that for study values, but it is unclear 
if this bias is an implicit one, given the small number of 
species included in tests. 
