Table l. — Data, including mean and variance of Mississippi 

 River discharge i thousand cubic feet per second) at Tarbert 

 Landing, Mi.ss.. and Gulf of Mexico commercial shrimp effort 

 ithousands of davsi from U.S. waters bv vessel, 1970-74.' 



s(y|« ^ ^°^'^> 



'Sources: U.S Army Corps of Engineers, Stages and discharges of the 

 Mississippi River and its tributaries and other watersheds in New Orleans 

 District. U.S. Army Engineer District. New Orleans Corps of Engineers, 

 Louisiana, and Christmas and Etzold 1977:28). 



Appropriate insertion of these numerical values 

 in Equation (7) produced the following estimates 

 of yield: 



EiY) = 89.09 million lb, a^ = 247.72. 



Ignoring the variances and covariances, as most 

 users of Griffin's equation do, we computed the 

 corresponding estimated yield to be: ,E(y) = 85.48 

 million lb. 



The expected value test indicated that an abso- 

 lute error of 3.6 million lb of shrimp is introduced 

 by ignoring the variances and covariances of the 

 independent variables. While an error of 3.6 mil- 

 lion lb is large in absolute terms, its significance is 

 diminished to 4% in relative terms. Furthermore, 

 although 4% error is sizable, it is probably in- 

 sufficient to alter economic management conclu- 

 sions. We may conclude, therefore, that the ex- 

 pected value test, if applied to other applications of 

 Griffin's equation, would not drastically alter 

 management conclusions. 



Parameter Sensitivity Test 



Griffin's equation contains three parameters, 

 each with its own significance and sensitivity. (Ab- 

 solute and relative definitions of sensitivity can be 

 found in Tomovic and Vukobratovic (1972) and 

 Truxal (1972).) In assessing the sensitivity of yield 

 to these parameters, I will relate proportional 

 changes in parameter values to proportional 

 changes in yield. (For this application of the sen- 

 sitivity test, the relative measure of sensitivity is 

 preferred because the results obtained are inde- 

 pendent of the units of measure used for effort and 

 discharge.) Mathematically, the sensitivity S of 

 yield to parameter ^ may be expressed as: 



^ dYlY 



9 (log J) a/3//3 



dYP 

 d(i Y 



= tf-T7. (14) 



In considering parameter ^o, note that it is the 

 dimensioned constant relating effort, discharge, 

 and yield. The sensitivity of yield to fio is ex- 

 pressed: 



S(r|/3o) = 1.0 



(15) 



In Equation (15), the sensitivity is small and 

 constant. Thus, small errors in misspecification of 

 /^o will not significantly affect yield estimates. 



Parameter (32 governs the relationship between 

 discharge of the Mississippi River and yield. Its 

 sensitivity can be expressed as: 



SiY\(i2) = 132 log,/) 



(16) 



The relationship is clearly linear and the sen- 

 sitivity relatively small (Figure 1). Again, the im- 

 plication being that misspecification of /Jj or fu- 

 ture changes in its value would have small impact 

 on yield. 



Figure l.— Sensitivity (S) of yield to parameter /Sa; i.e,, the 

 percentage change in yield corresponding to a l'7c change in Az. 



975 



