310 



Fishery Bulletin 89[2), 1991 



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Figure 1 



Temporal patterns of disequilibrium bias in the estimates of Z/K and L„ , expressed as percentage differences relative to the equilibrium 

 values. For the fishing-up experiment at two fishing mortality rates (F = 0.3 and 0.6), biases of (a) Z/K and (b) L„ are plotted against 

 the number of years since the initiation of the fishery. For the recruitment perturbation experiment at F = 0.6, biases of (c) Z/K and 

 (d) L„ are shown plotted against the number of years since a 1-year doubling of recruitment (pulse) and a 1-year absence of recruit- 

 ment (failure). 



population adjusts from one equilibrium to the next, 

 and (2) bias in Z/K estimates is considerably larger than 

 bias in L^ estimates. 



Even though the simulated changes in fishing mor- 

 tality and recruitment may be more abrupt than those 

 typically experienced by the population, the simulations 

 clearly demonstrate that the Wetherall estimates of 

 Z/K and L^ can be quite biased when the population 

 is not in equilibrium. As a consequence, the method ap- 

 parently can be used with confidence only when popula- 

 tion equilibrium can be demonstrated. Such a demon- 

 stration of equilibrium, or lack thereof, can be achieved 

 by comparing successive catch length-frequencies with 

 a chi-square test of independence. The utility of the chi- 

 square test can best be judged by examining its 

 statistical power to detect the disequilibrium conditions 

 that lead to biased parameter estimates. Since the 

 statistical power of the proposed test will increase as 

 between-year differences in catch length-frequencies 



increase, it will tend to vary positively with the magni- 

 tude of parameter bias. Provided that sample sizes are 

 sufficiently large, the test can therefore be used as a 

 data screening device to detect when parameter bias 

 is likely. One important consideration, then, is the rela- 

 tionship between sample size and the undetectable level 

 of disequilibrium bias. This relationship can be seen by 

 comparing the time trajectories of power (Fig. 2) with 

 those of bias (Fig. 1). 



Consider first the fishing-up experiment and bias in 

 estimates of Z/K. For F = 0.3 and a sample size of 5000 

 fish, the statistical power of detecting disequilibria is 

 high (i.e., ^0.75) from years 3 to 7 (Fig. 2a). Although 

 this interval includes most of the period in which bias 

 is high (Fig. la), it does not include the first 2 years 

 after the initiation of the fishery when bias is also high, 

 because the proposed test requires 3 successive years 

 of data. Furthermore, the interval of high statistical 

 power does not include years 8-10 when bias is nearly 



