REILLY ET AL.: POPULATION ASSESSMENT OF GRAY WHALE 



3) To estimate the proportion of the population 

 passing the census station on days for which the 

 visibility conditions were worse than a critical 

 value, as determined by the results of the 

 visibility analysis (2). 



The data on pod-size estimation from all years were 

 examined both for differences between years and for 

 a pattern in distance from shore. 



The offshore distance frequency distribution of ob- 

 servations was investigated for significant differ- 

 ences between the two locations, as a preliminary to 

 post facto application of correction factors for whales 

 missed offshore. 



Field Methods: 

 Verification Experiments 



The aerial transects to determine the offshore dis- 

 tribution of the migratory corridor were repeated in 

 1979-80 following our previous methods (Reilly et al. 

 1980). We flew a Cessna 172 3 aircraft at 305 m (1,000 

 ft) altitude, at a speed of 145 km/h (90 mi/h), along a 

 series of predefined tracklines (Fig. 2). These lines 

 were situated along a 25 km stretch of the coast which 

 included both the Yankee Point and Granite Canyon 

 census stations. Distances of whales from shore were 

 calculated from the timed difference between their 

 position and the shore edge, and the plane's speed. 

 During 1979-80 we flew a total of 13 flights for 34 h, in 

 periods of good to excellent visibility. Flights were 

 continued until a number greater than the minimum 

 sample size of whales was obtained (330) for 90% 

 precision in correctly classifying the population into 

 the seven distance intervals used in the shore census 

 (Reilly et al. 1980). Sample-size determination was 

 based upon Cochran's (1977:74-76) formulae for 

 sampling for proportions. Data from the 1974-75 

 shore counts were used as a presample of the propor- 

 tions expected within the distance intervals from 

 shore. The seven-interval experimental design also 

 presented the opportunity to analyze the data in a 

 pooled, less demanding interval scheme, with result- 

 ing higher precision in estimating the within-inter- 

 val proportions. 



Additive bias corrections were previously deter- 

 mined from the results of the observer bias ex- 

 periments regarding estimation of the number of 

 whales present in passing groups. Specifically for es- 

 timates of group size n (see Appendix 1 for explana- 

 tion of notation) 



E[n] = n + b n 



{ 



n + 0.350 n = 1 



n + 0.00 n = 2,3 (1) 



n + 0.333 n > 4 



with variances as in Appendix 2. 



Analysis Methods: 

 Verification Experiments 



Aerial sightings were analyzed for effects on off- 

 shore distance estimates from: differences between 

 the two individual observers; the side of the plane 

 from which the whales were seen; and the period of 

 day (morning or afternoon flight) by ANOVA. The 

 distance distributions from the 2-yr surveys were test- 

 ed by x 2 (chi-square) for the possibility of pool- 

 ing. 



To address the misclassification bias suggested by 

 the results of the 1978-79 experiments, the data from 

 those experiments were reanalyzed by using a less 

 demanding classification scheme of three broad in- 

 tervals: 0-0.75 mi (1.2 km); 0.76-1.5 mi (2.4 km); 1.6 

 mi + (2.6 km). From this characterization, a series of 

 reclassification parameters (probabilities) were cal- 

 culated, p ab , being the proportion of whales estimated 

 to be within interval a, that were determined to be ac- 

 tually passing within interval 6. The actual census 

 data, structured in the same three intervals, were re- 

 structured by application of these parameters as 



m b = Z,(m a p ab ), 



(2) 



where m a includes the whales originally classified in- 

 to interval a, and m b comprises the whales redis- 

 tributed into interval b, which were originally 

 (erroneously) estimated to be in a. For example, for a 

 = 1 and 6=1, sightings correctly classified into inter- 

 val 1 are summed into the newm b=l . For a =2,6= 1, 

 sightings incorrectly classified during the censuses 

 into interval 2 are reclassified, or summed, into rh 6=1 . 

 Inthecaseofa= 2,6= l,p 2 i = 0.2367 of the whales 

 originally put in interval 2 would be placed into inter- 

 val 1. The redistributed census data were then com- 

 pared with the "true" distribution from the aerial 

 surveys. As a simple correction factor, the ratio of the 

 cumulative proportions seen within 2.4 km (1.5 mi) 

 was calculated for each year {k): 



h{k) = CJC 



p- 



(3) 



'Reference to trade names does not imply endorsement by the 

 National Marine Fisheries Service, NOAA. 



A necessary assumption of this method is that at least 

 during periods of good or better visibility, all groups 

 of whales passing within 2.4 km (1.5 mi) were 

 recorded. 



271 



