FISHERY BULLETIN: VOL. 75, NO. 3 



year are propagated through the simulation, it is 

 surprising that the model seems to recover after 

 occasional substantial deviations from the ob- 

 served yield. 



Sissenwine (1974) explained most of the vari- 

 ability in recruitment of the Southern New 

 England ground even though the size of the 

 spawning stock was ignored. This earlier work 

 noted that spawning stock size may have an im- 

 portant effect on recruitment, but the effect might 

 be obscured by environmental noise. The work 

 reported here demonstrates that models incor- 

 porating either linear or density independent 

 recruitment explain most past variability in catch 

 of the fishery. Nevertheless, the model incorporat- 

 ing recruitment linearly dependent on spawning 

 stock size is preferable for the following reasons: 



1. While the linear model only explained 2.2% 

 more variation than the density independent 

 model, it did explain 13% of the density in- 

 dependent model's residual variation with no 

 increase in number of parameters. 



2. While the density independent model is more 

 simplistic mathematically, a direct linear 

 relationship between stock size and recruit- 

 ment is a more basic biological relationship. 

 Obviously, recruitment cannot be independent 

 of spawning stock size over its entire range. 

 The density independent situation can only 

 exist as a special case of a more complex non- 

 linear stock-recruitment relationship. 



3. It seems unrealistic for recruitment to be un- 

 affected by size of spawning stock when stock 

 size varies by a factor of 3. 



4. The linear stock-recruitment model is a more 

 conservative management tool than the den- 

 sity independent model. Management prac- 

 tices designed to prevent a dangerous reduc- 

 tion in stock size of a population regulated by 

 a linear stock-recruitment relationship will 

 also prevent a reduction in stock size of a pop- 

 ulation regulated by a density dependent 

 stock-recruitment relationship. 



No attempt was made to use the Ricker (1954, 

 1958) stock-recruitment function or other non- 

 linear functions because the results obtained 

 using the linear and density independent func- 

 tions (Equations (17) and (18)) indicated that most 

 likely these more complicated functions would not 

 significantly increase the accuracy of the model. 

 When using the linear model where the Ricker 



function (for example) is more appropriate, the 

 linear model is expected to be accurate at low 

 population levels but overestimates recruitment 

 (and catch) at higher population levels. The re- 

 verse situation is expected when the density in- 

 dependent model is used where a Ricker function 

 is more appropriate. In neither case was the more 

 complex Ricker function indicated. 



Based on the above discussion, the linear stock- 

 recruitment function ( Equation (17)) seemed most 

 appropriate over the observed range of population 

 size. Therefore, only the linear model is used in 

 the remainder of this paper. 



The linear stock-recruitment model was run for 

 1943-65 without temperature dependent growth 

 (c 14 = 0.0), without temperature dependent re- 

 cruitment (c 12 = 0.0), and without temperature 

 dependent growth or recruitment (c 12 = c 14 = 0.0). 

 None of these situations explained a significant 

 portion of variation in catch. This fact does not 

 constitute rigorous evidence that incorporation of 

 T g and T r into the model is necessary to explain 

 most of the variability in catch because no attempt 

 was made to tune the model for the temperature 

 independent cases. Earlier work by Sissenwine 

 (1974, 1975) demonstrated the influence of tem- 

 perature on the fishery and supports the incor- 

 poration of T g and T r into the model. 



APPLICATIONS 



The effects of several alternative fishing strat- 

 egies were examined using the model. These ex- 

 amples deal with some aspects of the model which 

 are not common components of other fishery mod- 

 els (such as discard mortality, temperature de- 

 pendence, and seasonal growth and fishing rate). 



The impact of discarding at sea fish shorter than 

 300 mm was evaluated by running the model with 

 the assumption that the minimum size retained 

 by a net equaled this value. The results for L gmin 

 = 300 mm are compared with the model results as 

 described earlier (L gmin = 250 mm) in Figure 6. 

 Landings in excess of 30,000 metric tons are not 

 shown because these have not been observed dur- 

 ing the history of the fishery; thus simulations 

 indicating these high values are extrapolative in 

 nature. These higher simulated landings result 

 because the model assumes a linear stock- 

 recruitment relationship at all stock sizes, while 

 in reality the relationship probably becomes 

 density dependent as stock size becomes large. 

 By eliminating discard mortality of fish shorter 



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