reasonable for traps that attract fish because they 

 are baited, or because the trap acts as a refuge, or 

 some combination of both reasons. This rela- 

 tionship has been observed by Thomas (1973) in 

 the Maine (American lobster, Homarus 

 americanus) fishery and by Warner (pers. 

 commun.) and Simmons (pers. commun.) for 

 Florida Keys and Bahama spiny lobster trap 

 fishing. The distinction would be that the catch 

 curve for traps that are highly dependent on bait- 

 ing would presumably be relatively steeper than 

 for less bait-dependent traps reflecting the rela- 

 tive attracting power of the bait during the initial 

 soak time. 



In both cases it is expected that the total catch 

 per trap haul would peak and perhaps even de- 

 crease with very long soak times either because of 

 mortality in the trap (starvation, cannibalism, 

 predation) or escapement. Therefore, while it is 

 recognized that the catch per trap haul with re- 

 spect to the soak time is probably sigmoidal 

 shaped, the negatively sloped portion that would 

 be associated with long soak times is excluded 

 from the model on the assumption it is not within 

 the range of normal commercial fishing strategies. 



The number of times each trap is hauled in a 

 given time period (e.g., 1 mo) is the number of days 

 in the time period divided by the soak time (in 

 days). The total catch for the given fishing period 

 would be the catch per trap haul Equation (2) 

 times the number of times each trap is hauled 

 (D/S) times the number of traps (T). 



= Ls 



1-/3) 



aPT 



(5) 



where L = total catch in the fishing period 

 T = number of traps fished 

 D = number of days in the fishing period 

 S = soak time in days. 



FIGURE 3. — Total catch in the fishing period with respect to the 



soak time. 



respect to the soak time (Figure 3). This is because 

 a longer soak time increases the catch per trap 

 haul but decreases the number of hauls possible in 

 the fishing period. 



Holding the number of traps constant is a highly 

 restrictive condition. The advantage of increasing 

 the soak time would be to permit the individual 

 fisherman to operate more traps. The most rea- 

 sonable constraint measurement for fishing capa- 

 bilities is a maximum number of hauls in a fishing 

 period. 



It is assumed an individual vessel can make a 

 constant (maximum) number of hauls during the 

 fishing period. This maximum is predicated on 

 characteristics of the vessel, number in the crew, 

 distance traps are set from port, depth of water, 

 and weather conditions. 



» # 



H =K 



(8) 

 (9) 



Taking the first and second derivatives of Equa- 

 tion (5) with respect to the soak time: 



as 



-paDT 



S<l+/3> 



< 



d*L _ ()8 + ff 2 ) aDT 



ds 2 ' s«+jb> 



> o. 



(6) 



(7) 



Equations (6) and (7) imply that, holding the 

 number of traps constant, the total catch for the 

 fishing period decreases at a decreasing rate with 



where H = total number of trap hauls in P days 

 K = maximum number of trap hauls in P 

 days. 



Substituting Equation (9) into Equation (8) and 

 rearranging: 



T = 



P 



(10) 



Substituting Equation (10) into Equation (5) 

 results in a total catch equation where both the 

 soak time and number of traps vary in combi- 



214 



