46 



Fishery Bulletin 101(1) 



Table 1 



Estimated life history parameters for Georges Bank sea scallops. Von Bertalanffy growth parameters are from Serchuk et al. ( 1979). 

 Relations of shell height (SH) to meat weight (MW) (see Eq. 7) were obtained by combining the data of Serchuk and Rak' with that 

 of NEFSC (Footnote 2 in the general text). The natural mortality estimate is from Merrill and Posgay (1964). The selectivity pattern 

 is based on the current gear configuration of scallop dredges with 89-mm rings (NEFSC, Footnotes 1 and 2 in the general text). 



Value 



0.3374 



152.46 



0.1 



-11.6038 



3.1221 



65 



75 



0.2 



Serchuk, F. M, and R, S. Rak. 1983. Biological characteristics of offshore Gulf of Maine scallop populations: size distribution, relations of shell 

 height to meat weight, and relative fecunditv patterns. Reference document 83-07, 42 p. [Available from Northeast Fisheries Science Center, 166 

 Water St.. Woods Hole, MA 02543.1 



area is given by Fj, F.^ 



of individuals remaining alive after p years would be 



F , respectively, then the number 



N'p = No exp 



-pM-Y^F, 



(4) 



In order for the long-term survivorship of the two strate- 

 gies to be equal (i.e., A^ 



=N^' ), the uniform fishing mortal- 



ity F|^ must equal the average fishing mortality 



AVG 



= it.. 



P 



L 



1=1 



(5) 



of the rotation plan. Therefore, F^vc. ^^ used to scale all the 

 graphs and per-recruit comparisons. 



The model described above and in the Appendix was 

 implemented as a Fortran-90 program where the integrals 

 were numerically computed with a time step of 0.01 y. 

 Parameters used in the model are given in Table 1 and 

 represent estimates for growth and mortality of Atlantic 

 sea scallops (Placopecten magellanicus), for which rota- 

 tional management is currently under consideration. 



Results 



Yicld-per-recruit curves for no rotation (continuous uni- 

 form fishing), three-year pulse rotation (i.e. the area is 

 closed for two years and fished for one year), six-year pulse 

 rotation, and nine-year pulse rotation are given in Figure 

 1. Note that the x axis in Figure 1 is the mean fishing 

 mortality rate Fi^vi;- ^^^ they axis is mean (i.e. expected) 

 yield-per-recruit V^vc- averaged over cohorts. Because the 

 mean fishing mortality rate is the same for all points at 

 the same .v coordinate, the three-year rotation has a fish- 

 ing mortality rate during years when fishing occurs (F ) 

 that is throe times as high, and the six-year rotation six 

 times as high, as the constant F i no rotation ) strategy with 



the same F, 



AVG- 



Rotation affects the yield-per-recruit curve for sea scal- 

 lop in three different ways (see Fig. 1). First, rotation 



modestly increases the maximum mean yield-per-recruit 

 Yf^js^; the maximum mean yield-per-recruit for the nine- 

 year rotation is about 9% greater than without rotation. 

 Second, Fj^l« *i-^- the value of Fj^vc, where Yt^j^x '® °^" 

 tained) increases somewhat under rotation, especially for 

 longer rotation periods. Third, there is less yield penalty in 

 rotational management for exceeding Fiy^a^x. For example, 

 fishing at F = 1 results in a 38% loss of yield if there was 

 no rotation, but only an 8% loss under a six-year pulse 

 rotation. Although 6-yr pulse rotation results in only a 5% 

 increase in yield-per-recruit over no rotation at their re- 

 spective F^y^ values, the advantage of 6-yr pulse rotation 

 atF= 1 is43'7c. 



Maximum yield-per-recruit for pulse fishing as a func- 

 tion of the rotation period p is shown in Figure 2. The 

 best yield-per-recruit is obtained for long periods of 9 to 

 10 years. However, this type of strategy would imply that 

 a number of years would pass before any yield would be 

 obtained from most recruits and this strategy would only 

 slightly increase maximum yield-per-recruit over that of 

 steady fishing. Depending on management goals, it might 

 be reasonable to discount future yields, so that the pres- 

 ent value of yield taken t years into the future would be 

 discounted by exp(-&), where 5 is the annual discount rate 

 (assumed 10%/yr). The rotation period that maximizes 

 discounted yield-per-recruit is 6 years (Fig. 2). If prices 

 as a function of meat weight are known, it would also be 

 possible to do a similar analysis to maximize discounted 

 value-per- recruit. 



Yield isopleths, commonly used to visualize yield-per- 

 recruit analysis (Beverton and Holt, 1957), are given in 

 Figure 3A (yield-per-recruit) and 3B (discounted yield- 

 per-recruit). For rotational analyses, fishing mortality is 

 placed on the .v-axis and rotational period on the y-axis. 

 Note again that for longer rotation times, the decline in 

 yield for fishing mortalities greater than F^,^^ is much 

 less than without rotation. The value of F^^^j^^ and maxi- 

 mum yield-per-recruit increases slightly with longer rota- 

 tion periods. 



Biomass-per-recruit for no rotation, 3-, 6- and 9-yr pulse 

 rotation strategies is given in Figure 4. Compared to con- 

 stant fishing, rotational fishing gives increased biomass- 

 per-recruit; this increase is most evident for the longer 



