312 



Fishery Bulletin 89(2). 1991 



140 

 120 

 100 



-40 



80 



60 



»-> 40 



< 20 



M 



U. 



o o 



< 



m -20 



-40 



-60 



F=0.6 



1 



3 4 5 6 7 8 9 10 11 12 13 14 15 16 

 YEARS SINCE INITIATION OF FISHING 



OBSERVED 

 SMOOTHED 



90 

 80 

 70 

 60 

 50 

 40 

 30 

 20 

 10 

 

 -10 



OBSERVED 

 SMOOTHED 



1 



3 4 5 6 7 8 9 10 11 12 13 14 15 16 

 YEARS SINCE RECRUITMENT PULSE 



2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 

 YEARS SINCE RECRUITMENT FAILURE 



Figure 3 



Effect of time-averaging catch length-frequencies, with a 3-year running average, on the bias in Z/K. (a) For the fishing-up experi- 

 ment at F = 0.3 and F = 0.6, Z/K estimates based on averaged data and those based on unaveraged data are plotted against years 

 since the initiation of the fishery. For the recruitment perturbation experiment at F = 0.6, Z/K estimates from averaged and unaver- 

 aged data are plotted against the number of years since (b) a 1-year doubling of recruitment and (c) a 1-year absence of recruitment. 



If a population is found to be in disequilibrium, one 

 can either discard the parameter estimates or find some 

 means to reduce or eliminate the disequilibrium bias. 

 Following the second approach, we have examined the 

 utility of a technique often used with such age-based 

 procedures as catch curve analysis to reduce the effects 

 of year class variability. This technique consists of 

 averaging the catch length frequencies over time. The 

 effectiveness of time-averaging depends on the type 

 of perturbation that creates the disequilibrium. In the 

 fishing-up experiment, time averaging has essentially 

 no effect when F = 0.3 and only a slight effect when 

 F = 0.6 (Fig. 3a). In the recruitment variation experi- 

 ment, time averaging has a somewhat greater effect, 

 especially during the periods of maximum bias when 

 reductions in bias are as much as 30% (Fig. 3b). Time 

 averaging, however, also increases bias during some 

 periods. Although time averaging is somewhat more 

 effective when disequilibrium is due torecruitment per- 



turbation, the 3-year time averaging employed in our 

 study appears to be an ineffective way of reducing dis- 

 equilibrium bias. 



Besides disequilibrium bias, the Wetherall method is 

 subject to two types of biases that may occur even when 

 the population is in equilibrium. The first type of 

 equilibrium bias (herein referred to as Type I or selec- 

 tion bias) is always negative and occurs when fish, equal 

 in length to the smallest l c values used in the regres- 

 sion, are not fully vulnerable to the fishery (Fig. 4a). 

 Since, in practice, the exact form of the fishery selec- 

 tion curve will rarely be known, choice of the initial 

 l c value is somewhat arbitrarily based on the shape of 

 a catch length-frequency histogram. Our approach 

 follows Polovina (1989) in choosing the initial l c to be 

 one size-interval greater than the rightmost mode on 

 a length-frequency histogram. This choice, however, 

 can result in selection bias. For example, when F = 0.3, 

 the initial l c (51cm) is identical to the length of 95% 



