Anganuzzi Detecting trends in dolphin abundance indices 



189 



comparison with <60% for the linear test. In the recov- 

 ery phase of the trajectory (starting when the tests 

 cover the period between years 12 and 22), the linear 

 test improves its performance relative to the smoothed 

 test. In absolute terms, the performance of both tests 

 seems to be poor between years 20 and 23, but this is 

 the result of the small difference between the first and 



last year of the period included in the moving time- 

 frame. After that, the 10 yr linear test performs al- 

 most as well as the smoothed test, as the result of an 

 underlying trend that can be approximated well by a 

 linear model. The 5yr linear test does not perform 

 well, although it detects the decline more frequently 

 than the 10 yr test. In spite of the improvement in the 

 last part of the trajectory, both 

 linear and smoothed tests reach 

 a maximum of only -70% of sig- 

 nificant trends. The performance 

 of all tests degrades quickly for 

 higher amounts of variability; the 

 maximum percentage of detec- 

 tions for the smoothed test falls 

 to around 40% for CV o =CV t =0.3. 

 In the case of the smoothed 

 test, the number of detections in- 

 creases when CV >CV E . This re- 

 sult seems to be a consequence 

 of higher Type-I error probabili- 

 ties, as suggested by the higher 

 number of detections in years 11 

 and 12. 



Steady decline The power of 

 both types of tests improves 

 under this scenario relative to 

 the previous one, due to the 

 smoother nature of the underly- 

 ing trend (Fig. 6). For CV =CV E 

 the smoothed test outperforms 

 the linear tests for all levels of 

 variability. The percentage of 

 significant trends detected by 

 the smoothed test ranges from 

 over 95% for CVs of 0.20 to -80% 

 for a CV of 0.30. The power of 

 the 10 yr linear test seems to be 

 more affected by increasing vari- 

 ability in the estimates, falling 

 to -50% detections for CV=0.40. 

 For CV a >CV E , the power of the 

 smoothed test seems to increase 

 although, as before, this is prob- 

 ably the result of greater Type-I 

 error rates. The 5 yr linear tests 

 show low power for all levels of 

 variability. 



Steady cycle The results of this 

 set of simulations are very simi- 

 lar to those from the 'rapid de- 

 cline' scenario (Fig. 7). Overall 

 performance for both tests im- 



