368 FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



Table 8. — Preliminary calculations for the determination of confidence limits for the 1959 Kvichak escapement 



ment was enumerated in a continuous count. In 

 1956, the variation in number of fish from sample 

 to sample was low, evidently because of the greater 

 magnitude of the run. The basic sampling design 

 of 10-minute counts taken hourly and supple- 

 mented by longer counts during a heavy run, 

 therefore, appears to be highly efficient. 



It is difficult to determine with any degree of 

 precision the most efficient sampling design, since 

 the size and nature of the migration vary from 

 year to year. Such factors as the proper distri- 

 bution of time, manpower, and equipment in ob- 

 taining accurate counts must also be considered. 

 On the Kvicliak Eiver, short frequent counts have 

 proved practical to obtain adequate estimates 

 under all operating conditions. 



SUMMARY 



1. A method of estimating red salmon escape- 

 ments by using systematic sample counts was de- 

 veloped and used on the Kvichak Eiver, Alaska, 

 from 1955 to 1959 by the Fisheries Research 

 Institute. 



2. The method was based on the fact that mi- 

 grating red salmon avoid swift midstream currents 

 and pass upriver in narrow bands close to the 

 shores, where observation towere, background 

 panels, turbulence reducers, and other counting 

 aids could be used to obtain accurate counts. 



3. Statistically, migrating red salmon wei'e 

 considered as a fluctuating finite population. The 

 design of the sampling procedure was aimed at 

 obtaining a reasonably accurate estimate of the 

 total run from properly distributed visual counts 

 throughout the migration season. 



4. The basic sample unit consisted of 10-minute 

 counts taken systematically each hour from each 

 tower. This design was varied to provide in- 

 creased or decreased coverage with the correspond- 

 ing variations in the intensity of migration. 



5. Estimates for a given period of time were ob- 

 tained by multiplying the sample count by the ap- 

 propriate factor. For longer periods when no 

 samples were obtained, the estimates were interpo- 

 lated by averaging the counts preceding and fol- 

 lowing the gap and multiplying by the appropriate 

 time factor. 



6. Daily estimates were calculated as the sum 

 of all estimates for all towers each day, and the 

 final escapement estimate was the sum of all daily 

 estimates. 



7. Kvichak River escapements, as estimated by 

 the sample count method, amounted to 250,546 fish 

 in 1955; 9,443,318 fish in 1956; 2,842,810 fish in 

 1957; 534,785 fish in 1958; and 680,000 fish in 1959. 



8. The accuracy of each sample count was af- 

 fected by different counters, migration intensities, 

 weather conditions, and disrupted migration pat- 

 terns. However, the factors were not found to 

 inject significant directional errors but showed 

 definite tendencies to cancel out. 



9. The accuracy of tlie calculated estimates was 

 affected by interruptions in the continuity of the 

 counts from highly turbid waters and darkness and 

 by fluctuations in numbers of fish between samples. 



10. A method of determining confidence limits 

 was illustrated. Applied to the 1959 Kvichak 

 River escapement, the confidence limits were estab- 

 lished at a plus or minus 3.99 percent at a 95 per- 

 cent level of significance. 



11. The calculated estimates were influenced by 

 varying the lengths and frequencies of the sam- 

 ples. The percentage of error tended to drop with 

 an increase in the length of the samples, and with 

 an increase in the frequencies of the samples. 

 Samples less than 40 minutes in length were found 

 to provide estimates usually within a plus or minus 

 6 percent of error when taken every 1 or 2 hours. 



