94 



Fishery Bulletin 104(1) 



spawner-recruit relationship for any grouper species. 

 A Beverton and Holt model was assumed in this study 

 because it is difficult to envision a mechanism for the 

 strong density dependence in mortality rates required 

 by the Ricker model. A prior for the value of o (Fig. 2) 

 was constructed from a subset of the values collected 

 by Myers et al. (1999) that corresponds to larger, highly 

 fecund fishes with long life spans (the 'periodic' strate- 

 gists of Rose et al., 2001). 



• observed 

 — fitted 



Figure 2 



Lognormal prior for the maximum lifetime fecundity 

 parameter (o) derived from the values in Myers et al. 

 (1999) that correspond to species categorized as periodic 

 strategists by Rose et al. (2001). The lognormal density 

 was fitted to the values of «-l (with median 9.8 and 

 log-scale variance 1.31) and then was shifted 1 unit to 

 provide a prior for a. 



Fecundity and growth To date there are insufficient 

 data for estimating a fecundity-at-age relationship for 

 goliath grouper. We followed Legault and Eklund^ and 

 substituted the weight at age relationship: 



E,. 



(<' =1.31xl0"'^/3°'^** 



a<6 



a>6 



(22) 



Z = 200.6(l-e-''^26,a.0.49lj 



where w = weight in kg; and 



/ = length in cm expressed as a von Bertalanffy 

 function of age (see Bullock et al., 1992). 



Natural mortality The maximum observed age of 37 

 years (Sadovy and Eklund, 1999) suggests a value for 

 M of about 0.11/yr according to the method of Hoenig 

 (1983). Legault and Eklund"* suggested a plausible range 

 of 0.037 yr to 0.19/yr (midpoint 0.11) based on an analy- 

 sis of the fraction surviving to various maximum ages. 

 To reflect this uncertainty, a lognormal prior with a 

 median of 0.11 and CV of 0.4 was used (Fig. 3A). 



Fishing mortality rate and relative vulnerability A large 

 fraction of the recreational landings of goliath grouper 

 appear to come from the Ten Thousand Islands area in 

 Southwest Florida, where most of the animals caught 

 have been between the ages of one and five years. How- 

 ever, large animals were often targeted by commercial 

 and recreational fishermen in other areas. Accordingly, 

 we assumed the vulnerability of goliath grouper gener- 

 ally increased with age according to 

 the sigmoid-shaped logistic curve 



(23) 



1-i-e 



-(n-a„, l/rf 



Estimates for the parameters ar,o and 

 d were obtained by fitting the curve 

 (weighted by cumulative mortality at 

 age ) to the relative frequency of ages 

 in two different data sets. The first 

 data set included mostly juveniles 

 animals between the ages of and 

 5, obtained during creel censuses 

 of recreational catches in the Ten 

 Thousand Islands area of the Ever- 

 glades National Park (see Porch et 



3 Legault, C. M., and A.-M. Eklund. 

 1998. Generation times for Nassau 

 grouper and jewfish with comments 

 on M/K ratios. Sustainable Fisher- 

 ies Division Contribution SFD-97/98- 

 lOA, 5 p. Southeast Fisheries Science 

 Center, 75 Virginia Beach Drive, Mi- 

 ami, Florida 33149. 



