Fishery Bulletin 9 1(2). 1993 



4 A correlation matrix between years for both up- 

 per and lower limits of the confidence bounds was esti- 

 mated on the basis of results of the previous step. 



5 Estimates of correlation as a function of the dis- 

 tance in time between estimates were obtained. This 

 was done by averaging over all correlation coefficients 

 between estimates separated by a given number 

 of years, that is, by taking the 



average of elements in the 

 subdiagonals of the correlation 

 matrix obtained in step 4. 



beginning of the period both the linear and smoothed 

 tests have similar proportions of detected trends, close 

 to the nominal significance level. As the underlying 

 trend in the period included in the tests departs from 

 linearity, the smoothed test tends to outperform both 

 linear tests. For CV n =CV ( =0.2, the smoothed test indi- 

 cates a maximum of almost 80% significant trends in 



Results 



Number of detected trends 



The results of this analysis are 

 shown in Figs. 4-7, as the num- 

 ber of detected trends each year 

 in 100 simulations for the differ- 

 ent scenarios. The underlying 

 trends are shown on an arbitrary 

 scale to relate changes in perfor- 

 mance of the tests to changes in 

 population trajectory. 



Stable population This sce- 

 nario can be used to assess the 

 actual level of significance of the 

 tests. An ideal procedure for de- 

 tecting trends would indicate sig- 

 nificant trends in -5% of the 

 tests under this scenario, given 

 that the significance level is set 

 at 5%. Results from the simula- 

 tions are shown in Fig. 4. Both 

 linear tests show an actual sig- 

 nificance level close to the ex- 

 pected value. These results were 

 relatively robust to the different 

 values of CVs tested. The 

 smoothed test also performs well 

 in all cases, except when 

 interannual variation exceeds the 

 precision of the estimate. For ex- 

 ample, for CV„=0.2 and CV E =0.3, 

 the percentage of detected trends 

 was -10''. 



Rapid decline In this scenario, 

 different trade-offs of the tests 

 are illustrated by their perfor- 

 mance along the simulated pe- 

 riod (Fig. 5). For CV =CV £ , at the 



Smoothed test 

 10 yf linear led 

 6 yf linear lest 



cvO.3 



cv € :0.2 



cv, : 0.2 -0.3 



I 

 15 



Year 



20 



Smoothed tesl 

 10 yr linear lest 

 S yr linear test 



Figure 4 



Percentage of trends detected in 100 simulations of the 'stable population' scenario 

 for two levels of precision: (top) CV„=0.2, and (bottom) CV„=0.3. The two lines for 

 each smoothed test represent different levels of interannual variation, CV,. Broken line 

 ( ) represents underlying trend in the population on an arbitrary scale. 



