PENNINGTON: TECHNIQUES FOR ESTIMATING ABUNDANCE 



yellowtail flounder fisheries are off southern New 

 England (strata 5, 6, 8, 9) and on Georges Bank 

 (strata 13-21). The two stocks are fairly distinct but 

 with some intermixing (Clark et al. 1984). 



The nonzero catch per tow survey data for yellow- 

 tail flounder are approximately lognormally distrib- 

 uted within a stratum. Therefore, the estimators 

 based on the A-distribution [Equations (1) and (2)] 

 were used to estimate the mean catch per tow and 

 its variance in each stratum. The regional estimates 

 for southern New England and Georges Bank were 

 then calculated in the usual manner for each survey 

 (see, e.g., Pennington and Brown 1981). 



Model (9) was fit to each series (spring 1968-84 

 and fall 1963-84 in both regions) and the model's 

 adequacy checked (Box and Jenkins 1976, Chap. 8). 

 Table 1 contains summary statistics and parameter 



Table 1.— Summary statistics and parameter estimates for the 

 yellowtail flounder survey series. The first three sample autocorre- 

 lations (r v r 2 , and r 3 ) are for the first differenced logged series. 



'Assuming the estimates of 8 are independent. 



estimates for the four series. Since the series are 

 relatively short, the averages of the areal and 

 seasonal estimates are used as the final estimates 

 of and o 2 c (last line in Table 1). 



Abundance indices for the two regions and 

 seasons were calculated by applying to each series 

 Equation (4) with 6 = 0.4, the rc-weights given by 

 Equation (11), and the c t 's (for each series) gener- 

 ated by model (9). An estimate of 6] equal to 0.20 

 and of o\ equal to 0.18 were obtained from Equa- 

 tion (10). The estimated variance of the index equals, 

 from Equation (6), 0.12 for the current value and 

 declines to 0.09 for values not near the series' end 

 points. This compares with a variance of 0.20 ( = 

 of) for the original index. Figures 3 (log scale) and 

 4 (linear scale) show plots of the estimated index and 

 the observed catch per tow series for the fall sur- 

 veys off southern New England. 



DISCUSSION 



The major advantage of estimating an index of 

 abundance from the entire survey series is that it 

 can produce an index with a variance considerably 

 smaller than the variance of the observed series. But 

 the application also demonstrates that estimates of 

 the accuracy of an index based only on the within 

 survey sampling variance can be misleading. For ex- 

 ample, the 1972 survey value for yellowtail flounder 

 off southern New England is considered an anom- 



o 1 — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i 



1963 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 



YEAR 



Figure 3.— Logged average catch per tow and the estimated index of abundance for southern New England 



yellowtail flounder. 



523 



