owing to stochastic displacement of datum points 

 at biomass levels remote from locations p and B-^. 

 As revealed by Equation (14), exponent n is quite 

 unstable to small perturbations in the ratio p/B-^. 

 The variational response in n exceeds the pertur- 

 bation in p/B^ by an order of magnitude near n = 

 1, and the instability increases as p/fi^-^1. But the 

 location of p with respect to fix is far more critical 

 to management analysis than graph curvature 

 and its associated "good fit," since, to the left of p, 

 the stock produces biomass at a positively acceler- 

 ated rate, while to the right of p productivity de- 

 celerates. 



The trait of degeneracy in the system has been 

 noted by Pella and Tomlinson (1969) and by Fox 

 (1971, 1975), but the exact relationships between 

 exponent n and the quantities m, p, and S^ have 

 been obscured heretofore by the conventional 

 castings of the system. With the restructured gov- 

 erning equations and the explicit formulations of 

 critical parameters, much of the statistical degen- 

 eracy associated with previous routines can be 

 constrained. And since the management parame- 

 ters appear directly in the equations of the system, 

 their variances can be calculated directly in the 

 estimation procedure and appeals to indirect 

 methods are avoided. 



FISHERY BULLETIN: VOL. 76, NO. 2. 



LITERATURE CITED 



Fletcher, R. I. 



1975. A general solution for the complete Richards func- 

 tion. Math. Biosci. 27:349-360. 

 FOX, W. W., JR. 



1970. An exponential surplus-yield model for optimizing 

 exploited fish populations. Trans. Am. Fish. Soc. 99:80- 

 88. 



1971. Random variability and parameter estimation for 

 the generalized production model. Fish. Bull., U.S. 

 69:569-580. 



1975. Fitting the generalized stock production model by 

 least-squares and equilibrium approximation. Fish. 

 Bull., U.S. 73:23-37. 



Graham, M. 



1935. Modern theory of exploiting a fishery, and applica- 

 tion to North Sea trawling. J. Cons. 10:264-274. 



PELLA, J. J., AND P. K. TOMLINSON. 



1969. A generalized stock production model. Inter-Am. 

 Trop. Tuna Comm., Bull. 13:419-496. 

 RICHARDS, F. J. 



1959. A flexible growth function for empirical use. J. 

 Exp. Bot. 10:290-300. 

 RICKER, W. E. 



. 1975. Computation and interpretation of biological statis- 

 tics offish populations. Fish. Res. Board Can., Bull. 191, 

 382 p. 

 SCHAEFER, M. B. 



1954. Some aspects of the dynamics of populations impor- 

 tant to the management of the commercial marine 

 fisheries. Inter-Am. Trop. Tuna Comm., Bull. 1:25-56. 



388 



