340 



Fishery Bulletin 94(2). 1996 



tionally, we were able to examine whether differences 

 in mean discard were due to different proportions of 

 zero observations or to different distributions of posi- 

 tive observations. In contrast, computing sampling- 

 based estimates of population mean and variance 

 would not give any indication of the patterns in the 

 individual observations. While average or total dis- 

 card is of significant interest, it is also important to 

 quantify the amount of discard possible for an indi- 

 vidual set. Assuming that the parametric model is 

 accepted as appropriate, one can estimate, for ex- 

 ample, the probability that, owing to random chance 

 alone, discard from a particular boat will exceed a 

 certain limit in a fixed number of sets. One can also 

 estimate the percentage of zero observations which 

 actually represent small amounts of discard. Finally, 

 a parametric model provides a natural framework 

 for predicting future discard. 



Acknowledgments 



We thank Al Jackson for his generous help and ad- 

 vice about data collection methods and data form 

 interpretation, Pierre Kleiber for his comments on 

 an earlier version of this manuscript, and the Inter- 

 American Tropical Tuna Commission for making avail- 

 able their data on U.S. tuna vessel tuna discards. We 

 especially thank Cleridy Lennert of the IATTC for her 

 helpful suggestions. We also thank Ronald Hardy and 

 two anonymous reviewers whose helpful suggestions 

 added to the clarity of our manuscript. 



Literature cited 



Aitchison, J. 



1955. On the distribution of a positive random variable 

 having a discrete probability mass at the origin. J. Am. 

 Stat Assoc. 50:901-908. 

 Berger, J. D., R. F. Kappenman, L. L. Low, and 

 R. J. Marasco. 



1989. Procedures for bycatch estimation of prohibited species 



in the 1989 Bering Sea domestic trawl fisheries. U.S. Dep. 



Commer., NOAATech. Memo. NMFS-F/NWC-173, 23 p. 

 Caillouet, C. W., Jr., M. J. Duronslet, A. M. Landry Jr., 

 D. B. Revera, D. J. Shaver, K. M. Stanley, R. W. Heinly, 

 and E. K. Stabenau. 



1991. Sea turtle strandings and shrimp fishing effort in the 

 northwestern Gulf of Mexico, 1986-89. Fish. Bull. 89:712- 

 718. 



Coe, R., and R. D. Stern. 



1982. Fitting models to daily rainfall. J. Appl. Meterol. 

 21:1024-1031. 



Collins, M. R., and C. A. Wenner. 



1988. Occurrence of young-of-the-year king, Scom- 

 beromorus caualla, and Spanish. S. maculatus, mackerels 

 in commercial-type shrimp trawls along the Atlantic coast 

 of the southeast United States. Fish. Bull. 86:394-397. 



Efron, B. 



1992. Six questions raised by the bootstrap. In R. LePage 

 and L. Billard leds. I, Exploring the limits of the bootstrap, 

 p. 99-126. John Wiley and Sons, New York, NY. 



Federal Register. 



1989. Interim final rule with request for comments;Tuesday, 

 7 March 1989. Federal Register, Vol. 54(43), Rules and 

 Regulations:9438-945 1. 



IATTC (Inter-American Tropical Tuna Commission). 



1989. Annual Report: 1988. Inter-American Tropical Tuna 

 Commission, La Jolla, CA. 



Johnson, N. L., and S. Kotz. 



1969. Distributions in statistics: discrete distribu- 

 tions. Houghton Mifflin, Boston, MA, 187 p. 

 Joseph, J. 



1994. The tuna-dolphin controversy in the eastern Pacific 

 < v. .in: biological, economic, and political impacts. Ocean 

 Developments and International Law 25:1-30. 

 Lambert, D. 



1992. Zero inflated Poisson regression, with an application 

 to defects in manufacturing. Technometrics 34( 1):1— 14. 

 Lawless, J. F. 



1987. Negative binomial and mixed Poisson regres- 

 sion. Can. J. Stats. 15(3):209-225. 



Mangel, M., and P. E. Smith. 



1990. Presence-absence sampling for fisheries manage- 

 ment. Can. J. Fish. Aquat. Sci. 47(101:1875-1887. 



McLachlan, G. J., and K. E. Basford. 



1988. Mixture models: inference and applications to 

 clustering. Marcel Dekker, New York. NY', 253 p. 



NRC (National Resource Council). 



1992. Dolphins and the tuna industry. National Academy 

 Press, Washington, D.C., 176 p. 

 Pennington, M. 



1983. Efficient estimators of abundance for fish and plank- 

 ton surveys. Biometrics 39( 1 ):28 1-286. 



