Table 4 
Overall coefficients of determination for the linear models 
of the relationships of the length at which 50% of individ- 
uals are mature (L,,,,) as a dependent variable to either 
expected length at infinite age (L..) or to expected length 
at the oldest recorded age (L,,,,,) for 3 families of trop- 
ical coastal fish species and for sharks from the orders 
Carcharhiniformes and Lamniformes. 
Taxon Dnat ~ Ls pny © Mop e 
Haemulidae (grunts) 0.86 
Labridae (wrasses) 0.36 0.46 
Serranidae (groupers) 0.86 0.90 
Sharks 0.91 0.95 
All families 0.79 
600 700 800 900 
~ 
100 200 300 400 
Probability density 
600 700 
S 
° 
00 — 0 = 
1000 1500 2000 2500 0.0 0.2 0.4 
L..(mm TL) K (year’) 
Fishery Bulletin 119(1) 
were reasonably accurate (i.e., useful for management pur- 
poses), generating median values within 25% of the esti- 
mates from life history studies for 14 of the 16 combinations 
of parameters and species (Table 5). Across all 4 test spe- 
cies, the stepwise predictions for M appear to be the most 
accurate. The blacktip reef shark was the test species with 
the most accurate results from the stepwise approach for 
all 4 parameters. The stepwise approach performed moder- 
ately well for the grunts on the basis of our test species 
javelin grunter. Despite high levels of variability, the step- 
wise approach appeared to be accurate for camouflage 
grouper, especially for L.., K, and M. The L,,,,, value was 
estimated at 352 mm in the test life history study and at 
284 mm by using the stepwise approach, a result that can 
be explained by this species being an outlier with its L,,.4 
close to 80% of its L,, (as opposed to 60% of the L,. for grou- 
pers, on average). 
0.025, 
0.020} 
0.0154 
0.0104 
0.005; J 
0 00g 
300 400 500 600 
0.020; 
0.0154 
0.010} 
0.005 
0.000 | Auf th. 
200 300 400 
rai 
1000 2000 
Lemar (mm TL) 
Figure 3 
Probability distributions of estimates of life history parameters from life history studies (light gray areas and solid lines) 
and from use of the stepwise stochastic simulation approach (dark gray areas and dashed lines) 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 parameters include the asymptotic length 
(L..), growth coefficient (K), length at which 50% of individuals are mature (L,,,,), and natural mortality (M). TL=total 
length. 
