190 



Fishery Bulletin 91|2). 1993 



proves relative to that scenario, 

 due to the smoother underlying 

 trend, reaching a maximum of 

 90% for the smoothed test for 

 CV=0.2. This performance falls 

 rapidly, as the amount of variabil- 

 ity increases, to a maximum of 

 slightly over 20% when CV=0.40. 

 For CV„>CV E , the smoothed test 

 again shows an apparent increase 

 in power related to high Type-I 

 error probabilities. Once more, the 

 5yr linear test shows very low 

 power throughout the series. 



Ratio between estimates 



The purpose of this analysis is to 

 assess sensitivity of the estimated 

 rates of change, obtained by 

 smoothing or linear procedures, 

 to departures from linearity of the 

 underlying trend. It also mea- 

 sures the ability of the procedures 

 to reconstruct the true underly- 

 ing population trajectory. The re- 

 sults of this analysis are shown 

 for each of the simulated trajec- 

 tories in Fig. 8. Results indicate 

 that the estimated rates of change 

 obtained through the smoothing 

 procedures are better, in terms of 

 the average absolute error, than 

 estimates obtained by any of the 

 linear methods, even when the 

 simulated trend is linear ('stable' 

 scenario, Fig. 8, page 192). Esti- 

 mates from the 5 yr linear regres- 

 sions are consistently worse than 

 estimates from the 10 yr regres- 

 sions, as expected due to the 

 greater number of points on which 

 the latter is based. The only ex- 

 ception is for the scenario with 

 cyclic fluctuations, where the 

 10 yr linear estimates are poorer 

 than the 5 yr estimates. This is a 

 consequence of the period of the 

 sinusoidal cycle in the underlying population that 

 can be better approximated by a linear model over a 

 short period of time. For longer periods in the cycle, 

 10 yr linear estimate should improve, as suggested 

 by its performance in the scenario with an expo- 

 nential decline. Results for the smoothed procedure 

 are consistent over the sets of scenarios, indicating its 



robustness to departures from linearity in the popula- 

 tion trajectory. 



Correlation between smoothed estimates 



Results from this analysis are shown in Figs. 9 and 10 

 (pages 193, 194), which indicate that the correlation 



