REILLY ET AL.: POPULATION ASSESSMENT OF GRAY WHALE 



TABLE 3.— Parameters of the gamma models of migratory timing for each of the 

 13 annual gray whale censuses. S t is the standard error of the scaled mean day.' 

 a, /?, their variances, and covariances are maximum likelihood estimates, as in 

 Greenwood and Durand (1960). 



means and variances are not equal statistically. 

 Following adjustment on the time scale so that mean 

 days align, however, we cannot reject the hypothesis 

 of equality of parameters for the gamma distribution 



between years. For the as,F = 1.33 < F V2 



00 , 0.05" 



For 



the /J's, F = 1.54 < F l2 „ 005 , where the F statistics 

 were calculated as in Equation (7). Figure 6 illus- 

 trates data on daily proportions of the population 

 passing Monterey, pooled over the 1 3 yr, as fit by the 

 cumulative gamma. The use of the gamma represents 

 a marked improvement in fit over the normal dis- 

 tribution, which we employed previously (Reilly et al. 

 1980). The error sum of squares from gamma model 

 was 0.0179, while that from the normal fit to the same 

 data was 0.1998, one order of magnitude greater. 



30 40 50 



nlORflTION DAY- = 10 DEC. 



FIGURE 6. — Cumulative proportions of total count of gray whales by 

 day (averaged) fit by the cumulative gamma function. Error sum of 

 squares = 0.0179. 



Effect of Visibility Conditions 

 on Censusing 



There are significant differences between visibility 

 categories in the residuals (differences) of the ob- 



served from expected daily proportions of the pop- 

 ulation passing the census site (ANOVA: F = 



63.99 >F 



). Three separate multiple range tests 



5,749.0.05 



(Duncan's, Student-Newman-Kuel's, Scheffe's) gave 

 the following nonsignificantly different subgroups of 

 visibility codes, arranged in order of increasing 

 magnitude of residuals: 



1. visibility = 1,2,3 



2. visibility = 1, 3, 4 



3. visibility = 5 



4. visibility = 6. 



A simple interpretation of these results is that for 

 conditions ranging from 1 (excellent) to 4 (fair), there 

 is no significant interference from weather in shore 

 censusing of gray whales. A plot of the mean squared 

 residual for each category (Fig. 7) graphically illus- 

 trates this. Consequently, for days with average 



mean souare error of daily proportions of total hhales seen 

 by visibility categories. all years 



f .00025- 



5.00015 



3 4 



VISIBILITY CATEGORY 



FIGURE 7. — Mean squared errors from comparison of daily propor- 

 tions of total number of whales seen per season to proportions pre- 

 dicted by the gamma distribution, by visibility categories, all 13 

 yr included. 



275 



