FISHERY BULLETIN: VOL. 84, NO. 3 



5 

 o 



80-1 



70 



60- 



o 50 

 a. 



.e 

 o 

 T3 40 



0) 



ro 30 



> 

 < 



20 



10 



Survey catch perjow _ 

 Survey index o( abundance 



N / 



"1963 64 6 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 



YEAR 



Figure 4.— Average catch per tow and the estimated index of abundance for southern New England 



yellowtail flounder. 



aly (Collie and Sissenwine 1983). It does appear 

 anomalous if comparisons are made using 0.11, the 

 estimated variance based on the within survey 

 variance, but not if the estimate of 0.20 (= of) is 

 considered (Fig. 3). 



Assessing the accuracy of an index of abundance 

 for marine stocks is difficult since the true levels 

 are never known with certainty. But they can be 

 compared with other indicators of abundance. The 

 methods were applied to the haddock stock on 

 Georges Bank (Pennington 1985) for which a VPA 

 exists. It was found that model (7) adequately 

 describes the dynamics of the VPA series, and the 

 survey series follows model (9). The resulting index 

 of abundance is quite similar to the VPA estimates. 



Collie and Sissenwine (1983) give a method for 

 estimating the relative abundance of a fish stock 

 using survey data and commercial catch statistics. 

 They observe that their method produces estimates 

 which compare favorably with VPA estimates. 

 Figure 5 shows plots of Collie and Sissenwine's 

 estimate of the relative abundance of southern New 

 England yellowtail flounder and the index based 

 only on the survey data. 



Finally, it should be noted that the purpose of the 

 modeling stage in the estimation procedure is not 

 necessarily to develop a realistic model for the 

 population, but to describe the important stochastic 

 properties of the series. As the observed series 

 becomes longer, more precise estimates can be 

 made. For shorter series, given the large variabil- 



ity inherent in marine trawl surveys, a preliminary 

 estimate of between 0.3 and 0.4 for the smoothing 

 parameter 6 appears to be an appropriate initial 

 value to use for estimating an abundance index un- 

 til more information becomes available. 



LITERATURE CITED 



AlTCHISON, J., AND J. A. C. BROWN. 



1957. The lognormal distribution. Cambridge Univ. Press, 

 Lond., 176 p. 

 Box, G. E. P., and G. M. Jenkins. 



1976. Time series analysis: forecasting and control. Rev. ed. 

 Holden-Day, San Franc, 575 p. 

 Byrne, C. J., T. R. Azarovitz, and M. P. Sissenwine. 



1981 . Factors affecting variability of research trawl surveys. 

 Can. Spec. Publ. Aquat. Sci. 58:238-273. 

 Clark, S. H. 



1979. Application of bottom trawl survey data to fish stock 

 assessment. Fisheries 4:9-15. 

 Clark, S. H., M. M. McBride, and B. Wells. 



1984. Yellowtail flounder assessment update. U.S. Dep. 

 Commer., NOAA, Natl. Mar. Fish. Serv., Woods Hole Lab. 

 Ref. Doc. No. 84-39, 29 p. 



Collie, J. S., and M. P. Sissenwine. 



1983. Estimating population size from relative abundance 

 data measured with error. Can. J. Fish. Aquat. Sci. 40: 

 1871-1879. 

 Grosslein, M. D. 



1969. Groundfish survey program of BCF Woods Hole. 

 Comm. Fish. Rev. 31(8-9):22-30. 

 Pennington, M. 



1983. Efficient estimators of abundance, for fish and plank- 

 ton surveys. Biometrics 39:281-286. 



1985. Estimating the relative abundance of fish from a series 



524 



