Chesapeake Bay Menhaden 



Table 1 shows the empirical results for this 

 fishery. Based upon the R- criterion, LDRa 

 represented the "best" function where total 

 catch was used as an independent variable. 

 There is no doubt from the statistical analysis 

 that the Schaefer function (LCRa) is definitely 

 inferior when compared to the LDRa model in 

 its ability to describe the catch-effort relation 

 in the menhaden fishery. No evidence of auto- 

 correlation was detected in the LDRa function. 

 As shown by LDRaS, there seems to be no 

 stock adjustment effect as the coefficient on the 

 lag variable is not statistically significant. 

 Among all the functions, LDRb shows the best 

 fit when catch per unit of effort is used as the 

 dependent variable. From a theoretical point of 

 view, there should be no difference between the 

 "a" and "b" functions. However, the statistical 

 estimation procedure does yield two estimators 

 for each parameter. LDRa and LDRb do yield 

 similar estimates of y* and x*. Also, the 

 Gulland -LCRb equation yielded very similar 

 estimates of y* and x* as the LCRb (unadjusted 

 data). Further the choice between the "a" and 

 "b" functions should be made on the basis of 

 just what one wants to predict — catch or catch 

 per unit of effort. The LCR and LDRa functions 

 are shown in Figure 5. It should be noted that 

 in equation (16) M = A. Thus, the LDRa 

 equation estimated by least-squares will also 

 yield the maximum biomass irithout fishing. 

 That is, MSY = M/4 = 158.7 thousand tons. M 

 is therefore equal to 634.8 thousand tons. The 

 logistic function can be directly computed since 

 a = AIB and a = 1.1512, and if f = at the 

 point of maximum growth, then 



_M_ 634.8 

 '"''2"l+5eO 



, so b = 1, or 



m, 



634.8 thousand tons 

 1 + e-1.1512/ 



This is one additional advantage of the LDRa 

 over the LCRa function. 



Atlantic and Gulf Blue Crab 



Table 2 shows the empirical re.sults for this 

 fishei-y. Based upon the R- criterion, it would 



seem that we have little basis on which to 

 choose between the LCRaS and the LDRaS 

 models, each having an R~ of 0.94. Both show a 

 strong stock adjustment effect. The half-life 

 for the adjustment process was 0.57 years. In 

 this case, the data cannot adequately distinguish 

 between the two functions. The MSY ranges 

 from 129.6 million pounds in the LCRaS model 

 to 189.0 million pounds in the LDRaS model. 

 The autocorrelation test for the two functions is 

 inconclusive. Hence, the choice between the 

 functions must be made on a priori grounds. 

 Since the LDRaS model seems more plausible 

 on a priori grounds, it would seem that this 

 function should be selected for fishery manage- 

 ment purposes. As the fishery expands, addition- 

 al data will be generated to verify the existence 

 of one or the other function. This general 

 prescription will probably apply to many 

 fisheries where data are only available in the 

 upward expansion phase (i.e., catch is below 

 MSY). Finally, as with Chesapeake Bay men- 

 haden, there seems to be little difference between 

 Gulland LCRb and LCRb unadjusted. Figure 6 

 shows the two functions discussed above. 



Atlantic Longline Tuna 



Table 3 shows the results for the Atlantic 

 longline tuna fishery. On the basis of R-, the 

 LDRa model is superior in predicting changes 

 in catch in response to effort. The stock adjust- 

 ment coefficient was not statistically significant. 

 The autocorrelation test is inconclusive for 

 LDRa. The MSY for the LDRa fianction is 106.7 

 thousand metric tons with 140.1 million hooks 

 of effort. Notice that the MSY's associated with 

 the LCRa and LDRa functions are not appre- 

 ciably different; however, the number of hooks 

 necessary to harvest MSY is vastly different. 

 This is due to the flatness of the function 

 generated by the LDRa model. The GuUand- 

 LCRb gives a much higher estimate of y* and 

 a lower estimate of x* than the unadjusted 

 LCRb. Figure 7 shows the LCRa and LDRa 

 functions. 



Bering Sea King Crab 



Table 4 shows the results for the Bering Sea 

 king crab fishery. On the basis of R-, the LDRa 

 model is the best in "explaining" the catch-effort 



78 



