relationship (the LDRaS model gave a larger 

 R'-, but y,_i was not statistically significant). 

 However, the LDRa model was marginally 

 significant over the LCRa model (R- of 0.88 

 versus 0.85). There is evidence of positive auto- 

 correlation for the LDRa function. The Gulland- 

 LCRb does give somewhat different estimates of 

 y* and x* than unadjusted LCRb. Figure 8 shows 

 the LCRa and LDRa functions. 



So far, we think that the logistic-decreasing- 

 returns function has considerable merit. It 

 should, of course, be tested further. Other func- 

 tions should also be tried, including those 

 assuming a Gompertz growth function and the 

 more generalized function used by Tomlinson 

 and Pel la. It is also hoped that this effort by 

 economists will be reviewed by people in the 

 field of biology. 



Cape Flattery Sablefish 



Table 5 shows the results for the Cape Flattery 

 sablefish fishery. Again, the LDRa model is 

 superior in explaining the catch-effort relation 

 with an R- of 0.54. The stock adjustment co- 

 efficient was not statistically significant at the 

 5% level. Positive autocorrelation was found for 

 the LDRa function. There does not seem to be an 

 appreciable difference between the Gulland- 

 LCRb and the unadjusted LCRb. 



On the basis of the sample fisheries it would 

 seem that the LDRa fiinction is a more realistic 

 description of the catch-effort relation than the 

 LCRa model employed by Schaefer. In addition, 

 it is apparent that for the above species the Gul- 

 land method of adjusting this data yields very 

 similar results to the unadjusted. Catch-effort 

 data have been gathered on 49 stocks of fish by 

 the Economic Research Laboratory. We plan to 

 carry out similar investigations for the other 

 stocks since the basic computer programs have 

 been written. Figure 9 shows the LCRa and 

 LDRa functions. 



CONCLUSIONS 



We do not claim to have discovered the "true" 

 relation between effort and yield for the stocks 

 of fish discussed in this paper. We have no 

 guarantee either that biological growth is exactly 

 a logistic function, or that y, = m,(l — z,^ ) 

 is exactly the relation of effort to yield from a 

 fixed biomass. But we believe that (1) the 

 decreasing-returns functions y, = m, (1 — Z; t) 

 is theoretically better than the constant-returns 

 function y, = km, employed by Schaefer; and 

 (2) the decreasing returns function also gives 

 better statistical results as shown graphically 

 in Figures 6 to 9 and is confirmed by the 

 correlation coefficients. 



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