62 



BULLETIN OF THE BUREAU OF FISHERIES 



10,000,000, a deviation of 100,000 in the first case would be just as significant as a 

 deviation of 1,000,000 in the second case. 



In our analysis of these fluctuations we have not made use of the data collected 

 previous to 1904. The Bureau of Fisheries began the collection of statistics in that 

 year and it seemed best to confine this analysis to data obtained by a single agency. 

 Furthermore, as we pointed out above, the fishery apparently became fully developed 

 about this time, and it is quite probable that the fluctuations during the period of 

 rapid growth were largely obscured by great changes in the intensity of fishing. 



The use of deviations from a moving average by fives has one disadvantage, in 

 that two years are lost at each end of the series; thus, our series of data extends from 

 1904 to 1927, both inclusive, but our trend of moving averages extends only from 

 1906 to 1925. It would be possible, of course, to use some sort of a straight-line 

 trend or to extend more or less arbitrarily the trend of moving averages so as to 

 make use of the extreme values, but we have not thought it advisable to do either. 

 The straight-line trend certainly does not fit some of the localities, and any extra- 

 polation of the line of nioving averages will introduce a personal element, which 

 we have been anxious to avoid. 



Figure 8 shows the deviations from the moving average for each of the four 

 districts in Bristol Bay, and in Table 3 we present various coefficients of correla- 

 tion (Pearsonian), which we have calciilated and which measure the degree of asso- 

 ciation in the fluctuations at 4, 5, and 6 year intervals. We have made some esti- 

 mates of the correlation between fluctuations at 3 and 7 year intervals, also, but 

 these were invariably without significance, and we have therefore omitted them from 

 consideration. 



Table 3. — Coefficients o/ correlation between catches of red salmon at intervals of 4r 5> <md 6 years 

 for the four districts in Bristol Bay and Karluk River 



Examination of Figure 8 shows that in all of the districts of Bristol Bay there is 

 a strong tendency toward a repetition of conditions at intervals of four or five years. 

 The extent to which the catches are correlated with the catches of 4, 5, and 6 years 

 earlier or later is shown in Table 3. For purposes of comparison we have added to this 

 table a similar series of correlation coefficients for the nin of red salmon in the Karluk 

 River. While the exact significance of an association between catches at four or five 

 year intervals can not be stated definitely , it seems more than probable that it is indica- 

 tive of the prevailing age groups in the run in question. In the case of the Karluk 

 River we know definitely that a large percentage of the fish are in their fifth year when 

 they return to spawn. This is reflected in the relatively high coefficient of correlation 

 between catches at five-year intervals — over seven times its probable error — and 



