TABLE 1. — Catch per trap day that would be recorded with a 

 declining stock (decreasing a) with constant (column 6) and 

 variable (column 8) soak times. 







S 



^d=-t 



UTD 



ij 



2.94 

 2.44 

 1.94 

 1.44 



0.90 

 0.90 

 0.90 

 0.90 



0.383 

 0.383 

 0.383 

 0.383 



0.63 

 0.63 

 0.63 

 0.63 



6.52 

 6.52 

 6.52 

 6.52 



0.54 

 0.45 

 0.36 

 0.27 



652 

 5.24 

 4.07 

 2.94 



0.55 

 0.55 

 0.55 

 0.55 



Adjustment of Trap Days to Include Soak Time 

 as a Measurement of Fishing Effort 



"Trap days" is customarily the recorded 

 measurement of fishing effort. This index may not 

 accurately reflect relative fishing effort because it 

 only records two components of fishing effort, 

 number of traps and number of days fished. The 

 frequency with which traps are hauled (soak time) 

 is not reflected. Therefore, trap days is an accurate 

 measurement of effort only as long as soak time 

 remains constant. According to the determinants 

 of the profit-maximizing soak time, a constant 

 soak time seems unlikely. 



One method to adjust trap days to more accu- 

 rately reflect fishing effort would be according to 

 the relationship between the number of traps and 

 the soak time that will achieve the same total 

 catch. Taking the total differential of Equation (5) 

 and setting it equal to zero: 



dh 



&(dS) + $k(dT) = 



as 



dT 



(22) 



-/3aDTS" (/3+1) (dS) + aDS 1 * (dT) = (23) 



dT = BT 

 dS S 



(24) 



where T = number of traps 



4 = numeraire soak time 

 x = prevailing soak time 

 T* = adjusted number of traps 

 D = fishing days 

 T*D = adjusted number of trap days. 



When the prevailing soak time (x) differs sig- 

 nificantly from the base soak time (4), the in- 

 tegration of the interval can be more accurately 

 estimated by: 



= t ± y — 



s 



S=4 



T*D = T ± Z^ D 



(28) 



(29) 



S=4 



v BT 

 where x >4=>2,^q < ^ 



S=4 ^ 



v P T 



x < 4 => 2, q > °- 



S=4 ° 



Utilizing Equations (28) and (29) and 1962 

 parameters, Table 2 indicates how the number of 

 traps, trap days, adjusted traps, and adjusted trap 

 days would compare with alternative soak times. 

 The interpretation of Table 2 is that the ad- 

 justed number of traps (column 5) reflects the 

 relative fishing power of a trap at different soak 

 times. Utilizing a 4-day soak time as a base, a trap 

 hauled every day has 2.75 the fishing power of a 

 trap hauled every 4 days. In the other direction, a 

 trap hauled every 7 days has 0.54 the fishing 

 power of a trap hauled every 4 days. 



Equation (24) represents the relationship 

 between soak time and number of traps that will 

 result in the same total catch. This relationship 

 can be utilized to weight trap days according to 

 soak time. The first step is to choose a base soak 

 time (e.g., S = 4). When the soak time is 4 days, 

 then the number of "adjusted traps" is equal to the 

 number of traps and the number of "adjusted trap 

 days" is equal to the number of trap days. 



T* =T - j 4 X ^- (dS) (25) 



T* = T + BT (In 4 - lnjc) (26) 



T*D = [T + BT (In 4 - In x)] D (27) 



TABLE 2. — Traps, trap days, adjusted traps, adjusted trap days 

 according to alternative soak times (base: S = 4). 



Adjustment of Catch Per Trap Day 

 to a Standardized Soak Time 



Once the catch per trap day has been empiri- 

 cally estimated with respect to the soak time 



217 



