Somerton and Kobayash': Robustness of Wetherall length-based method to population disequilibria 



313 



selection, and selection bias is small (3%). 

 But when F = 0.6, the initial l e (47cm) is 

 considerably less than the size at 95% selec- 

 tion, and selection bias is consequently 

 larger (15%). 



Since selection bias asymptotically ap- 

 proaches zero with increasing value of the 

 initial l c (Fig. 4a), one logical way of reduc- 

 ing equilibrium bias would be to choose a 

 larger initial l c . This strategy, however, 

 would increase the second type of equilib- 

 rium bias (herein referred to as Type II or 

 residual bias), because residual bias in- 

 creases with initial l c (Fig. 4b). For exam- 

 ple, when F = 0.6 and the initial l c = 47cm, 

 residual bias is about 16%. But when F = 0.3 

 and l c = 51cm, residual bias is 34%. 

 Although the causes of residual bias are 

 unknown, it could be related to either of two 

 factors. First, as Wetherall et al. (1987) 

 demonstrate, the estimates of Z/K and L^ 

 are asymptotically unbiased as the sample 

 size increases. Since increasing the size of 

 the initial l c reduces sample size, it follows 

 that bias will increase. Second, as Laurec 

 and Mesnil (1987) demonstrate, individual 

 variability in growth, which has been incor- 

 porated into our simulation model, leads to 

 bias in length-based estimates of mortality. 



In the foregoing, we have demonstrated 

 that disequilibrium bias in the Wetherall 

 estimates of Z/K and L M can be large and 

 that time averaging does not remove such 



