180 



Fishery Bulletin 102(1) 



standing the processes affecting the probability of capture 

 and escape. 



The purpose of our study is to determine whether varia- 

 tions in the duration and timing of operations bias abun- 

 dance and mortality estimates derived from longline catch 

 rates. We present a theoretical model that is then related to 

 empirical observations of the effects of soak time on catch 

 rates. The strength in our approach is in applying a random 

 effects model to large data sets for over 60 target and non- 

 target species in six distinct fisheries. We also investigate 

 the survival of each species while hooked because prelimi- 

 nary analyses suggested that the effects of soak time on 

 catch rates might be linked to mortality caused by hooking 

 (referred to as "hooking mortality"). 



Factors affecting catch rates 



To aid interpretation of our statistical analysis of soak time 

 effects, we first developed a simple model to illustrate how 

 the probability of catching an animal may vary with soak 

 time. 



The probability of an animal being on a hook when the 

 branchline is retrieved is a product of two probability 

 density functions: first the probability of being hooked 

 and then the probability of being lost from the hook. 3 In- 

 fluencing the probability of being hooked are the species' 

 local abundance, vulnerability to the fishing gear, and the 

 availability of the gear. Catches will deplete the abundance 

 of animals within the gear's area of action, particularly for 

 species that have low rates of movement. Movement will 

 also result in variations in exposure of animals to the gear 

 over time — for instance, as they move vertically through 

 the water column in search of prey (Deriso and Parma, 

 1987). 



Other processes that will reduce the probability of be- 

 ing hooked include bait loss and reduced sensitivity to the 

 bait (Ferno and Huse, 1983). Longline baits may fall off 

 hooks during deployment, deteriorate over time and fall 

 off or they may lose their attractant qualities. They may be 

 removed by target species, nontarget species, or other ma- 

 rine life, such as squids. Hooked animals may also escape 

 by severing the branchline or breaking the hook. Sections 

 of the longline may become saturated when animals are 

 hooked, reducing the number of available baits (Murphy. 

 1960; Somerton and Kikkawa, 1995). After an animal has 

 been hooked, it may escape, fall off the hook, be removed by 

 scavengers, or it may remain hooked until the branchline 

 is retrieved. 



Some of the processes affecting the probability of an ani- 

 mal being on a hook when the the branchline is retrieved 



2 Campbell, R., W. Whitelaw, and G. McPherson. 1997. Do- 

 mestic longline fishing methods and the catch of tunas and non- 

 target species off north-eastern Queensland (2nd survey: May- 

 August 1996). Report to the Eastern Tuna and Billfish Fishery 

 MAC, 48 p. Australian Fisheries Management Authority, PC) 

 Box 7051, Canberra Business Centre, ACT 2610, Australia. 

 In discussing continuous variables we use the terms "proba- 

 bility" and "probability density function" interchangeably. 



are species-specific, whereas other processes may affect all 

 species. For example, bait loss during longline deployment 

 will reduce the catch rates of all species. In contrast, the 

 probability of a hooked animal escaping may be species-de- 

 pendent; some species are able to free themselves from the 

 hook whereas other species are rarely able to do this. 



Our simple model of the probability of an animal being 

 on a hook is based on a convolution of the two time-related 

 processes described above: 1) the decay in the probability 

 of capture with the decline in the number of baits that are 

 available; and 2) gains due to the increased exposure of 

 baits to animals and losses due to animals escaping, falling 

 off, or being removed by scavengers. 



The probability of an animal being on a hook when the 

 branchline is retrieved is the integral of the probability 

 density functions of capture and retention: 



rtT) = J P(t)P r lT-t)dt, 



(1) 



where jriT) = the "catch rate" or probability of an animal 



being on a hook when the branchline is 



retrieved at time T (T is the total soak time 



of the hook); 



P ( it) = the probability density function of an animal 



being captured at time t; and 

 P r (t) = the probability density function of a cap- 

 tured animal being retained on the hook for 

 a length of time f. 



The probability density function of capture can be approxi- 

 mated with an exponential function: 



Pit) = P e-", 



(2) 



where P = the probability of capture when the hook is 

 deployed (r=0); and 

 o = a parameter determining the rate of change in 

 capture probability over time. 



After the animal is hooked, the probability density function 

 of an animal being retained after capture can be approxi- 

 mated as 



PIt) = e- pw , 



(3) 



where /I = the "loss rate," a parameter determining the 

 rate of change in the probability of an animal 

 being retained after it has been captured. 



Substituting approximations 2 and 3 into Equation 1 

 gives 



7l(T)= \P e '"e <"' ' dt 



(4) 



/?-«' 



