SPECIFYING A FUNCTIONAL FORM FOR THE INFLUENCE 

 OF HATCHERY SMOLT RELEASE ON ADULT SALMON PRODUCTION 



BiiNG-HwAN Lin' and Nancy A. Williams^ 



ABSTRACT 



The hypothesis of density independent marine survival of salmon has been tested extensively with con- 

 flicting results. Unduly restrictive functional form and data deficiency have been suggested as the major 

 contributing factors to the mixed results. Focusing on the issue of functional form selection, this paper 

 utilizes the extended Box-Cox flexible functional form which allows the data to determine the statistical 

 relationship between smolts and adult production without a priori restrictions. The model is applied to 

 Hokkaido chum salmon, Oncorhynchus keta, and Oregon coho salmon, 0. kisutch. Empirical results sug- 

 gest the existence of density dependence for both Hokkaido chum and Oregon coho salmon. Further, 

 an increasing variability of adult production with respect to an increase in smolts is found for Hokkaido 

 chum salmon but not for Oregon coho salmon. 



Two issues pertaining to the relationship between 

 the number of hatchery smolts released and the 

 number of adult salmon returned have been inves- 

 tigated recently in the literature. First, the hypoth- 

 esis of density independence in the relationship be- 

 tween salmon adults and smolts has been tested. The 

 null hypothesis is a linear relationship between 

 adults returned and smolts released, such that the 

 additional adult salmon produced from an increase 

 in smolts released is constant. The second issue is 

 the relationship between the variability of adult pro- 

 duction and the number of smolts released. If, in 

 fact, increases in smolts increase the variability of 

 adults produced, fishery management strategies can 

 be improved by considering the trade-off between 

 the mean and variance of adult salmon returned 

 (Walters 1975; McCarl and Rettig 1983). 



The empirical results of the test of density in- 

 dependence have been mixed. Nickelson (1986) pro- 

 vided an excellent discussion of previous results 

 pertaining to the test of density independence for 

 Oregon coho salmon. In short, this hypothesis for 

 marine survival of Oregon coho salmon is rejected 

 by McCarl and Rettig (1983) and Peterman and 

 Routledge (1983), but accepted by Peterman (1981), 

 Clark and McCarl (1983), and Nickelson (1986). In 

 addition, biologists in the Oregon Department of 

 Fish and Wildlife have examined several model 

 specifications and manipulations in data sets and 



'Department of Agricultural Economics and Rural Sociology, 

 University of Idaho, Moscow, ID 83843. 



^Department of Economics, Loyola College, 4501 North Charles 

 St., Baltimore, MD 21210-2699.' 



have drawn conflicting conclusions about density in- 

 dependence. This led McCarl and Rettig to suggest 

 that conflicting conclusions are caused by the use 

 of different functional form specifications and to 

 suggest further that resolution of the issue of den- 

 sity independence in Oregon coho salmon requires 

 more refined data. In the case of Hokkaido chum 

 salmon, the null hypothesis of density independence 

 fails to be rejected by McCarl and Rettig. 



Regarding the estimation of the variability of adult 

 salmon production, Peterman (1981) pointed out the 

 importance of functional form specification and 

 argued for the use of the multiplicative-error model 

 rather than an additive-error model. McCarl and 

 Rettig (1983) demonstrated that the specification of 

 a multiplicative-error model imposes unwarranted 

 restrictions on the estimation of the variability in 

 adult production. McCarl and Rettig utilized the 

 specification developed by Just and Pope (1978, 

 1979). As a result, the variability in adult salmon 

 production is estimated and conflicting conclusions 

 of the test of density independence emerged. 



It is apparent that functional form specification 

 is critical in the test of density independence and 

 the estimation of variability in adult production. The 

 purpose of this paper is to reexamine these two 

 issues by using the extended Box-Cox flexible func- 

 tional form. Both Hokkaido chum salmon, Oncor- 

 hynchus keta, and Oregon coho salmon, 0. kisutch, 

 data are used in this study. 



The next section of the paper discusses the im- 

 portance of the functional form specification and 

 demonstrates the superior flexibility of the Box-Cox 



Manuscript accepted July 1988. 



FISHERY BULLETIN: VOL. 86, NO. 4, 1988. 



655 



