Clupea pallasi. used for reduction in Alaska, 1929- 

 66. U.S. Dep. Commer, NOAA Tech. Rep. NMFS 

 SSRF-634, 25 p. 

 SCHAEFERS. E. A., AND K. A. SMITH. 



1954. Shellfish explorations in the Yakutat Bay area, 

 Alaska, by the John N. Cobb, spring 1953. Commer. 

 Fish. Rev. 16(3):1-12. 



David M. Clausen 



Northwest and Alaska Fisheries Center Auke Bay Laboratory 



National Marine Fisheries Service, NOAA 



P.O. Box 155 



Auke Bay, AK 99821 



USE OF GRIFFIN'S YIELD MODEL FOR 

 THE GULF OF MEXICO SHRIMP FISHERY* 



For analyzing the harvest of the Gulf of Mexico 

 shrimp fishery, Griffin et al. (1976) have developed 

 an equation that relates shrimp yield to freshwa- 

 ter discharge of the Mississippi River and fishing 

 effort of Gulf shrimp vessels. The yield equation 

 (referred to as Griffin's equation) is a modified 

 Spillman production function (Heady and Dillon 

 1972). The Spillman function had its origin in ag- 

 riculture where it was derived to predict the re- 

 sults of fertilizer experiments on tobacco yield in 

 North Carolina. An important feature of the func- 

 tion is that it allows for environmental consider- 

 ations in predicting yield. The modified form of the 

 equation proposed by Griffin et al. (1976) is: 



y = /3o^'Mi-^f) 



(1) 



where Y = yield of shrimp (million pounds), 

 D = average daily discharge of the 

 Mississippi River during the 

 months that shrimp are in their 

 nursery grounds (cubic feet per 

 second), 

 E = vessel effort (thousand units), 

 )8q, /3j, /Sg = parameters to be estimated from 

 data of the fishery. 



The coefficients of Equation (1) were estimated 

 from individual vessel records collected by the 

 National Marine Fisheries Service and from mea- 



surements of water flow rates on the Mississippi 

 River for the years 1962-74. According to Griffin 

 and Beattie (1978), the fit was quite good, namely: 

 "All estimated coefficients were significant at the 

 1% level; R^ was 78.5; and the Durbin-Watson 

 statistic was 2.25. The simple correlation 

 coefficient between catch and effort was 0.64 and 

 between catch and discharge was -0.63." 



Griffin's equation has found numerous uses in 

 the Gulf shrimp management literature. Griffin 

 and Beattie (1978) used the equation to estimate 

 the impact of effort reallocation as a result of Mex- 

 ican extended jurisdiction; the Gulf Coast Re- 

 search Laboratory at Ocean Springs, Miss., 

 (Christmas and Etzold 1977) used the equation for 

 similar purposes; and the Center for Wetland Re- 

 sources, Louisiana State University^ used the 

 equation to estimate maximum sustainable yield 

 for management considerations. 



Despite the extensive usage, users have not 

 critically reviewed Griffin's equation. Such a re- 

 view is necessary because of the large-scale poten- 

 tial impact of proposed shrimp management 

 plans. In view of this need, therefore, I subjected 

 Griffin's equation to such a review. 



The review consisted of two tests relevant to the 

 usage of Griffin's equation in management deci- 

 sions. In the first test, I estimated the error in 

 expected yield introduced by the typical user who 

 ignored the fact that the independent vari- 

 ables — effort and river discharge — have var- 

 iances. For convenience, this was termed the "ex- 

 pected value test." In the second test, I depicted the 

 error in yield estimate that would result from mis- 

 specification of model parameter estimates. For 

 convenience, this test was termed the "sensitivity 

 test." 



The results were mixed. The expected value test 

 produced a large absolute error in expected yield 

 of shrimp. However, when compared with expected 

 yield, the error was proportionally small. The sen- 

 sitivity test produced some startling results. Yield 

 turned out to be very significantly sensitive to a 

 fixed model parameter whose constancy was con- 

 ceptually questionable in the first place. This ex- 

 treme sensitivity of yield raises questions regard- 

 ing the reliability of Griffin's equation as a shrimp 

 management tool. 



Each test is discussed below in detail. 



'Contribution No. 80-54M, Southeast Fisheries Center, 

 National Marine Fisheries Service, NOAA, Miami, Fla. 



^The original equation was estimated by Griffin et al. (1976) in 

 nonmetric units and its nonlinear nature excludes conversion to 

 metric units. 



^Louisiana State University. 1979. Draft fishery- manage- 

 ment plan for shrimp fisherv-. Prepared by Center for Wetland 

 Resources, L.S.U., Baton Rouge, 226 p. 



FISHERY BULLETIN: VOL. 78. NO. 4, 1981. 



973 



