Ci = Q.i + j-^ \ i-exp {-(F, + ;;:, ) \\s,.. 



i^/+^. 



jl-exp [-(Pi+ X,) m] Ri.v, 



and 



S,= S,., exp[-(f, + J?,)] 



where 



C. 



Si 



Ri.y, 



Pi 



Pi 



Xi 



+ Ri.,^ exp[-(f, + X,)/2], 



= total catch in numbers at time t = i, 

 = number offish surviving in fishery att = i, 

 = number of recruits entering fishery in pulse 



at ^ = 1-V2, 

 = average exponential fishing rate between 



t = i-l and t = i if season is open, 

 = if season is closed between t = i-l and 



t = i, and 

 = average exponential other-loss rate be- 

 tween t = t'-l and t = i. 



The seasonal rate of exploitation is found by dividing 

 the total catch at the end of the season by the size of 

 the total run. The exploitation rate may now be 

 represented as a response surface that is a function of 

 two variables, a fishing intensity multiplier that is 

 used to scale all of the exponential fishing rates used 

 during the season and the fraction of the basic period 

 that the fishery is open (Paulik and Greenough 1966). 

 Exploitation isopleths were computed for 1938, 

 1939, 1941, and 1942. The various times associated 

 with entry patterns and fishing seasons were es- 

 timated from Figures 16, 17, 19, and 20 and Table 1. It 

 was necessary to approximate the entry patterns from 

 the weekly catch-per-trap data. Of the several 

 different entry patterns tried, the one that showed the 

 closest agreement with both the catch data and the 

 tagging data for all years peaked 5 wk after starting 

 and ended 2 wk after the close of the season. For the 

 isopleth calculations it was assumed that the ex- 

 ponential fishing mortality rate remained constant 

 from the beginning to the middle of the fishing season 

 and then increased linearly so that its value at the end 

 of the season was 1 V2 times what it had been at the 

 beginning. The yearly averages given in Table 16 of 

 the other-loss rates computed from tagging ex- 

 periments were used in the isopleth computations for 

 1938, 1939, and 1942. For 1941 the other-loss rate was 

 set equal to 0.444 (the average value for tagged fish 

 released in Icy Strait) from the beginning of the entry 

 triangle to its peak and was then increased linearly to 

 0.820 (the average for the middle Chatham Strait 

 releases, excluding the anomalous results obtained 

 from the release of 10 August). This intraseasonal 



modification of the other-loss rate followed from the 

 assumption that the average rate of escapement for 

 the total run at any time during the season in 1941 

 depended on the location of the center of density of 

 the run, which varied with time. 



Exploitation isopleths for the years 1938, 1939, 

 1941, and 1942 are shown in Figures 21-24. In these 

 figures the number of days in the weekly open period 

 is shown on the abscissa and the weekly exponential 

 fishing mortality rate (the constant rate applied dur- 

 ing the first half of the season) on the ordinate. The 

 maximum rate of exploitation in each of these figures 

 appears at the upper right-hand corner of the figure 

 when fishing is permitted for 7 days a week and the 

 exponential fishing mortality rate is highest. The 

 highest fishing exponential rate in this series of figures 

 is 1.19 for the first part of the season, which cor- 

 responds to an average rate of 1.34 for the entire 

 season. The highest fishing rate computed from a 

 single tagging experiment was 1.21, which is very close 

 to the value of 1.23 obtained using data from the 1950 

 tagging experiments by EUing and Macy (1955). For a 

 5 V2 -day weekly open period the total seasonal rate of 

 exploitation at the highest F value was 0.46 in 1938, 

 0.43 in 1939, 0.61 in 1941, and 0.56 in 1942. The 

 average over the 4 yr (0.51) indicates that the fishery 

 captured about one-half of the total run entering the 

 northern part of southeastern Alaska. It is of interest 

 to note that if the same computations were carried out 

 for a weekly fishing period of 7 days, the seasonal ex- 

 ploitation rate would be increased to 0.56. 



1.19 



1 2 3 4 5 6 



LENGTH OF WEEKLY OPEN PERIOD (DAYS) 



Figure 21.— Exploitation isopleth for the total pink salmon run 

 entering the northern part of southeastern Alaska, 1938. Tri- 

 angular entry pattern and periodic fishery assumed; fj = rate 

 of exploitation or fraction of run taken in catch. 



35 



