HUNTSMAN ET AL.: YIELD PER RECRUIT MODELS 



Yield per recruit models may be especially appro- 

 priate to the snapper- grouper fishery, because carry- 

 ing capacity and growth, rather than recruitment, are 

 apparently the principal limiting factors (Ehrlich 

 1975). Since reef habitat occupies a relatively small 

 proportion of the outer continental shelf (Parker and 

 Colby in press), recruitment is probably always suffi- 

 cient to replace losses from fishing mortality and 

 natural mortality. New reefs, such as wrecks and 

 artificial fishing reefs, are almost immediately 

 colonized (Anonymous 1971; Stone et al. 1979; 

 Stone 5 ). 



MATERIALS AND METHODS 

 Species Studied 



Species were selected on the basis of their impor- 

 tance to the recreational and commercial catch and, 

 to a lesser extent, on the amount and quality of infor- 

 mation available. Huntsman's (1976a, b) and Hunts- 

 man and Dixon's (1976) descriptions of the headboat 

 fishery, and Ulrich et al.'s (1977) description of the 

 handline and trawl fisheries suggested the in- 

 clusion of: 



1) red porgy, Pagrus pagrus; 



2) vermilion snapper, Rhomboplites auroru- 

 bens; 



3) white grunt, Haemulon plumieri; 



4) red snapper, Lutjanus campechanus; 



5) black sea bass, Centropristis striata; 



6) Epinephelus groupers (the important species 

 are the speckled hind, E. drummondhayi, and 

 snowy grouper E. niueatus); 



7) Mycteroperca groupers (gag, M. microlepis, 

 and scamp, M. phenax, are the most impor- 

 tant species). 



Estimates of Growth and 

 Mortality Parameters 



In general, reliable estimates of growth parameters 

 are available (Table 1) from both published and 

 unpublished sources. Reliable estimates of M 

 (instantaneous natural mortality rate) are not avail- 

 able. Determining M is a difficult but common prob- 

 lem solved by many authors by assuming single (Low 

 1981) or multiple (Houde 1977a, b; Chittenden 

 1977;Breiwicketal. 1980; LenarzetaL 1974) values. 

 M can be reasonably estimated by computed 



estimates of Z (instantaneous total mortality rate), 

 which provide maximum estimates of M, and by the 

 relationship of growth parameters to M, described 

 generally by Beverton and Holt (1959) and more 

 specifically by Pauly (1980-81). 



For most species we provided two or more 

 estimates (Table 1), one of which was, or was very 

 close to, the Pauly estimate. For three groupers 

 (scamp, snowy grouper, and speckled hind), we used 

 only the Pauly estimate because the other analyses 

 indicated that changing M had little effect on the pat- 

 tern of yield response. 



Yield Per Recruit Computations 



Computer program BM007, 6 which requires a 

 relatively small amount of memory, is written in 

 FORTRAN and can be used on most computer sys- 

 tems for calculating yields per recruit. The program 

 output is tabular and must be transposed by hand to 

 graph paper if isometric yield lines are to be drawn. 



Y/R = FW„ ( 



1 - e~ zx 3e _A> (l - e ^ z+K)X ) 



Z Z + K 



Se~ 2Kr (1 — e~ iZ+2K)X 



) e~ 3Kr (l — e ~ {Z+3K)X )\ 

 Z + 2K Z + 3K 



and t r = age at recruitment to the gear 



t„ = theoretical age at length "0" 

 t x = maximum age in fishery 

 F = instantaneous rate of fishing mor- 

 tality 

 M = instantaneous rate of natural mor- 

 tality 

 Z = instantaneous rate of total mortal- 

 ity, M + F 

 L„ = asymptotic length of a fish 

 W„o = asymptotic weight of a fish 

 K = growth coefficient from von Berta- 



lanffy growth equation for length 

 r = t r —t , theoretical age of cohort en- 



tering fishery 

 X = t x — t r , amount of time cohort is in 



fishery 

 Y = yield in weight 

 R = number of recruits at t, 

 Y/R = yield per recruit. 



-R. B. Stone, Office of Fisheries Management, National Marine 

 Fisheries Service, NOAA, Washington, DC 20235, pers. commun. 

 1975. 



''Written by John E. Hollingsworth, Southeast Fisheries Center 

 Beaufort Laboratory, NMFS, NOAA, Beaufort, NC 28516-9722 

 and Larry L. Massey, Southeast Fisheries Center, NMFS, NOAA, 

 Virginia Key, Miami, FL 33144-1099. 



681 



