REILLY ET AL.: POPULATION ASSESSMENT OF GRAY WHALE 



estimates for the year were then calculated using 

 Equation (11). A simple variance of these estimates 

 about the mean estimate (S 2 R ) was then calculated. 

 Variances were compared for equality (H :S| = SI) 

 by the test statistic 



(" ~ PS 



si 



(12) 



where \ 2 i s distributed approximately as chi- 

 squared (Freund 1962:371) with rejection regions 



X 2 > XW2,n-l or X 2 < Xl - a /2fl-V 



Analysis Methods: 

 Trends in Population Size 



In order to test for a trend in population size during 

 the 13-yr study period, two models were chosen for 

 regression analysis. This first model was simple 

 linear regression, the second was a weighted log,, 

 model: 



N t = N e rt , 



(13) 



where N t is population size in year t,N is year zero, or 

 1967 for the shore census time series. Equation (13) 

 was fit linearly as 



InN, = lnN + rt, 



(14) 



CO 



c 



CO 

 CO 



D 

 O 



LU 



Z> 



o 



LU 

 DC 



10 



8 



CS 6 



> 



o 



4- 



i*i i ill i iiiii ^! nin^J^^^^^ 





1 2 3 4 5 6 7+ 

 GROUP SIZE ESTIMATE 



FIGURE 3. — Frequencies of group size estimates from Monterey 

 gray whales census, 1967-68 through 1979-80, n = 23,678 obser- 

 vations. 



with weights calculated as an inverse function of the 

 estimated variance of iV, in the log model: 



Var(lnfy) \f'(N t )\ 2 Var(N t ) 

 = Var(N t )/Nf 



(15) 



= ,M-1 



= W, 



RESULTS 

 Shore Census Data Base 



A histogram of group sizes as recorded from the 13 

 annual censuses is presented in Figure 3. The overall 

 mean was 2.086 (S 2 = 1.974, n = 23,749). The mean 

 group sizes by year are listed in Table 2. An ANOVA 

 indicates that there are significant differences be- 

 tween the mean pod sizes recorded by year (F = 8.282 

 > F\2.~,Q.ob)- Multiple range tests (Duncan's, Student- 

 Newman-Kuel's, Scheffe's) show that 1967-68 and 

 1977-78 are different from each other and the rest, 

 while all the others are homogeneous. In the 1967-68 

 census the unusually high mean is attributable to one 

 of the two observers that year. His individual mean 

 pod was 3.123 (S 2 = 2.651), and was significantly dif- 



TABLE 2.— Mean pod size estimates by year for the Monterey 

 gray whale censuses, 1967-68 through 1979-80. Group mem- 

 bership identifies placement by multiple range tests into one of 

 three nonsignificantly different subgroups. 



'Significant at a = 0.05. 



ferent from the other observer that year, whose mean 

 was 1.886 (S 2 - 1.959:^= 24.528>f . . 05 ). In 1977-78 

 however, the two observers did not differ significantly 



273 



