Vauglian and Prager Decline in abunidance of Pagrus pagrus off tfie soutfieastern United States 



355 



We estimated natural mortality rate empirically (Pau- 

 ly. 1979) from parameters L_ and K of the von Berta- 

 lanffy growth function and mean environmental tempera- 

 ture. Estimates ranged frotn M = 0.27/yr to M = 0.57/yr, 

 based on mean sea temperature of 22°C (Manooch et al., 

 1998) and the range of growth parameters estimated in 

 our study (Table 2). A similar method, that of Ralston 

 ( 1987) and based solely on growth parameter K. provided 

 estimates from M = 0.22/yr to M = 0.64/vr. Given the un- 

 certainty in M, we chose a base M = 0.28/yr (Vaughan et 

 al., 1992). We also performed bracketing estimates of most 

 quantities using M = 0.20/yr and M = 0.3.5/yr. 



Fishing mortality rate F was estimated by subtracting 

 the assumed natural mortality rate from the total mortal- 

 ity rate. These estimates of F were used only as terminal- 

 year values in the separable VPA. 



Virtual population analyses 



Primary and alternate catch matrices were analyzed by 

 using virtual population analysis (VPA) to obtain annual 



age-specific estimates of F and population size. First, 

 a separable VPA (Doubleday, 1976; Pope and Shepherd, 

 1982), as implemented by Clay (1990), was used to esti- 

 mate partial recruitment by age for later use in calibrated 

 VPA. Data from 1992-97 were used for this purpose 

 because a 12-inch minimum size limit was introduced in 

 1992 (amendment 4|SAFMC''| ), and using data from both 

 before and after imposition of the size regulation would 

 likely violate the separability assumption. The starting 

 value of F for the separable VPA was the mean of three 

 final year-class estimates of Z (~0.78/yr), less M.; i.e. F ~ 

 0.50/yr. 



A calibrated \TA (Pope and Shepherd, 1985; Gavaris, 

 1988) was then applied, as implemented in the FADAPT 



' SAFMC (South Atlantic Fishery Management Council). 1991. 

 Final, amendment 4, regulatory impact review, initial regula- 

 tory flexibility analysis and environmental assessment for the 

 fishery management plan for the snapper grouper fishery of the 

 South Atlantic region. South Atlantic Fishery Management 

 Council, Charleston, SC, 99 p. + appendices. 



