Anganuzzi: Detecting trends in dolphin abundance indices 



187 



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Figure 3 



Example of a simulated series of relative abundance estimates for each of four scenarios. Solid line represents true underlying trend in 

 the population. Dashed line connects simulated point estimates. Distribution of simulated bootstrap estimates is represented by the 

 distribution of dots. 



Ratio between estimates As a way of assessing how 

 well each method describes the underlying trend in 

 the population, an estimated rate of change was ob- 

 tained. For the smoothed test, this is the ratio of two 

 smoothed estimates separated by 10 yr. For the linear 

 test, it is the ratio of the corresponding estimates cal- 

 culated from the linear regression. These estimated 

 rates of change were then compared with the true rates 

 of change and the discrepancies summarized as aver- 

 age absolute error. 



Correlation in the smoothed estimates 



One of the problems of the smoothed test is that the 

 smoothing procedure induces a correlation between es- 

 timates. This lack of independence affects the results 

 of the comparison between estimates close in time, 

 and it is therefore important to assess the magnitude 

 of this correlation and how it is reduced as the separa- 



tion in time between estimates increases. To investi- 

 gate this, the following Monte Carlo procedure was 

 carried out on the series of relative abundance esti- 

 mates for dolphin stocks in the EPO reported by 

 Anganuzzi et al. (1992). 



1 For each year, 79 estimates were sampled with 

 replacement from the distribution of bootstrap esti- 

 mates of relative abundance. The 79 estimates were 

 available from the standard bootstrap procedure used 

 to estimate confidence bounds in the relative abun- 

 dance estimation (Anganuzzi & Buckland 1989). 



2 Each of the 79 trajectories obtained in the previ- 

 ous step were smoothed, and 85^ confidence limits for 

 the resulting smoothed estimates were obtained based 

 on the percentile method. This step is essentially the 

 application of the smoothed test. 



3 Steps 1 and 2 were repeated 100 times, therefore 

 obtaining 100 estimates of the lower and upper confi- 

 dence bounds for the smoothed estimates for each year. 



