FISHERY BULLETIN: VOL. 80, NO. 3 



predictors using the same data (Ulanowicz, Ali, 

 and Richkus 1980). The major predictors cited in 

 the previous work were either identical to, or 

 qualitatively similar to, the initial variables 

 selected by the more usual analysis. In that 

 earlier work up to seven terms appeared in one 

 regression equation (F-to-enter criterion of 4.0), 

 and R 2 values ranged as high as 0.86 with four 

 variables. Despite having dropped the F-to-enter 

 criterion below the90% confidence level, the joint 

 criterion that the variables chosen also be reason- 

 ably good "internal predictors" appears to have 

 resulted in a more stringent combined test for 

 selecting variables. Fewer spurious predictors 

 are likely to appear using the new criteria. 

 Although the regression with the full set of data 

 will not be as tight as might otherwise be pos- 

 sible, there is less likelihood that predictions on 

 independent data will be wildly in error. In the 

 words of Ivakhnenko et al. (1979), the "fan of pre- 

 dictions" has been narrowed. 



When the number of possible predictor vectors 

 is large compared with the number of observa- 

 tions (as it is in this study), there is concern 

 that multiple regression R 2 values can be in- 

 flated (Rencher and Pun 1980). Fortunately, the 

 method described herein does not rely on R 2 

 values alone. Before a variable is chosen for fur- 

 ther consideration, it must explain a significant 

 fraction of the variance in several randomly 

 assembled groups of test data. To see how well 

 this might screen against including spurious 

 variables, the search procedure for the men- 

 haden predictor was rerun with the yearly obser- 

 vations randomly scrambled. Out of 28 possible 

 trials with the original data, at least one variable 

 was added in exactly half the trials (with an aver- 

 age F-to-enter of 9). In all but 2 of those 14 suc- 

 cesses the first variable entered was identical 

 (Ep). By contrast, only 5 successful trials were 

 recorded with the scrambled data (average F-to- 

 enter was 5), although one variable did appear in 

 3 of those successful trials. Nonetheless, there is 

 an evident decrease in the frequency and num- 

 ber of variables with successful F-to-enter ratios 

 in the trials with scrambled data. The only spe- 

 cies studied giving results nearly as poor as the 

 scrambled data was blue crab, and those find- 

 ings were disregarded. 



Unfortunately, the results of the present anal- 

 ysis must still be viewed with caution. Although 

 the possibility of identifying a spurious correla- 

 tion as a predictor has been decreased, it cannot 

 be totally eliminated. The fact that substantial 



portions of the variability in landings of all the 

 species considered can be explained by a few en- 

 vironmental variables suggests the important 

 role which environmental conditions play in de- 

 termining stock size. However, our inability to 

 interpret many of these relatinships in a causal 

 manner reflects both a lack of knowledge of 

 mechanisms influencing fish population dynam- 

 ics as well as an unfamiliarity with the auto and 

 cross correlative relationships between the vari- 

 ables introduced into the regression process. 

 (Because the procedure employed was stepwise, 

 true causal variables may have been displaced in 

 the regressions by spurious variables which by 

 chance were closely correlated. No detailed anal- 

 ysis of the independent variable data sets was 

 performed to address this issue. More analyses 

 would be required to fully account for this possi- 

 bility.) 



Despite these limitations, the analyses appear 

 to have been fruitful, particularly in the case of 

 the soft clam. As for the other species, the value 

 of the models will be determined when sufficient 

 data are available to assess their predictive value 

 for future landings. Only then can it be ascer- 

 tained whether any chosen predictor was spuri- 

 ous or reflected some unknown causal relation- 

 ship between environmental variation and stock 

 dynamics. Meanwhile, the terms appearing in 

 the regressions may engender new research 

 projects into the mechanisms determining the 

 sizes of these important fisheries stocks. 



ACKNOWLEDGMENTS 



This work is a result of research sponsored in 

 part by the NOAA Office of Sea Grant, Depart- 

 ment of Commerce, under grant no. 04-7-158- 

 44016. Mohammed Liaquat Ali's internship at 

 the Chesapeake Biological Laboratory was 

 jointly sponsored by the Directorate of Fisheries, 

 Government of Bangladesh, and the World 

 Bank. Alice Vivian was supported by the Envi- 

 ronmental Protection Agency's Chesapeake Bay 

 Program, Eutrophication Project, grant no. Sub 

 R806189010. William A. Richkus and J. Kevin 

 Summers were supported under a contract to the 

 Martin Marietta Environmental Center from 

 the Coastal Resources Division, Maryland Tide- 

 water Administration. Edward Houde and Mar- 

 tin Wiley provided comments helpful in revising 

 the manuscript. The Computer Science Center of 

 the University of Maryland donated some of the 

 computer time used in this project. The authors 



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