REILLY ET AL.: POPULATION ASSESSMENT OF GRAY WHALE 



Table 9 lists the mean of five subsample population 

 estimates for each year, and the alternate variances 

 (Sr) estimated from these, as well as statistics com- 

 paring variances from both methods. In 5 of the 1 3 yr, 

 the variances from different methods are not equal, 

 with the subsample estimates being generally larger. 

 In all cases, however, the estimates are of the same 

 general order of magnitude. 



TABLE 9.— Mean estimates from five 2-h/d subsamples of 

 each year's data, with variance (from the mean). These vari- 

 ances are compared with those derived for each year in- 

 dependently (col. 4) byx 2 test. 



'Significant at a = 0.05. 



Changes in Population Size, 

 1967-68 to 1979-80 



There was a significant, positive rate of change in 

 gray whale population size of 2.5%/yr during the 13 

 yr observed. The annual estimates are plotted, along 

 with 95% C.I., in Figure 8. The unweighted simple 

 linear model results are 



N t = 11,502.29+ 390.3  t. 



(16) 



1966 1968 1970 1972 1974 1976 1978 1980 



YEAR 



FIGURE 8. — Population estimates for the California stock of gray 

 whales for 13 yr (1967-68 to 1979-80) with 95% confidence inter- 

 vals. Fitted line is from exponential regression weighted by vari- 

 ances. 



The coefficient of determination is 0.516, the slope is 

 significant {t = 3.427 > t lli0M ), and the 1980 popula- 

 tion level estimate from this model is 16,186, with 

 95% C.I. (14,608, 17,763). The weighted log,, model 

 results are 



lniV ( = 9.3313 + 0.02513 -t. 



(17) 



The retransformed intercept is 11,285 for the 1967 

 population level. The slope is also significant (t = 

 2.61 > t n 005 ), and is an estimate of the net annual 

 rate of increase. Expressed as a percentage, r = 

 2.513 with a standard error of 0.964. The estimated 

 1980 population level from this model is 15,647 with 

 95% C.I. (13,450, 18,201). 



DISCUSSION 



Five areas of investigation were mentioned at the 

 beginning of this paper as necessary to extrapolate 

 confidently from counts of whales passing during 

 daylight hours to estimates of total population size. 

 We have addressed four of these quantitatively: 1) 

 Animals missed as a function of their distance from 

 shore, 2) animals missed due to poor visibility con- 

 ditions, 3) miscounting of the number per pod, and 4) 

 whales passing before and after the census period. 

 The fifth area, night travel rates (and extrapolation of 

 daylight counts to cover these), has not been ade- 

 quately addressed to date by direct observation. Our 

 last 2-yr data show a lower count for 0700-0800 h. 

 The low value for this hour can be interpreted in two 

 ways: The counts may be reduced due to limited 

 visibility during the first half of this hour before the 

 sun is up over the coastal mountains, or the animals 

 are in fact increasing their rate of travel as the sun 

 rises, having slowed down at night. As discussed pre- 

 viously (Reilly et al. 1 980), the small amount of direct 

 evidence that does exist on night travel rates, from 

 Cummings et al. (1968) and Rugh and Braham 

 (1979), supports the concept of a constant 2 4-h rate. 

 Lacking conclusive data on this, and for consistency, 

 we have treated the abundance estimation for these 

 last years in the same manner as the earlier years. 

 That is, an hourly mean rate calculated for the 10 

 sampled hours is used to extrapolate over the 14 h of 

 darkness each day. If in fact the rate is slower at night, 

 then our estimates are biased upward by an unknown 

 proportion. For example, if the whales slow down at 

 night to about one- half of the daytime rate of travel, 

 our estimate from 1979-80 would be reduced from 

 17,577 to 12,450. Estimates from the other 12 cen- 

 suses would be similarly reduced. If the rate is indeed 

 constant, and the depressed 0700-0800 h rates for 



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