Forney et aL Aerial surveys of Phocoena phocoena abundance trends 



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-0 3 -0.2 -0 1 1 0.2 0.3 4 



COVARIATE 



Figure 7 



Distribution of covariate estimates (6) representing yearly 

 change in abundance (from ANCOVA) for 500 simulations 

 each of (A) 10% annual decrease, (B) no change, and (C) 10% 

 annual increase in abundance over five survey years. Shaded 

 area under curves A and C which lies on the incorrect side 

 of zero represents the y-error when a = 1.0. Dashed line marks 

 location along the x-axis of the covariate estimate for actual 

 1986-90 harbor porpoise data. 



The choice of adding the constant 0.001 in the log- 

 transform may at first seem a bit odd, but in fact would 

 be the same as the more familiar transformation 

 ln(x + 1) if relative abundance had been defined as por- 

 poise per thousand kilometers, rather than porpoise per 

 kilometer. Several other constants were tested to 

 determine if the choice of transformation might in- 

 fluence the analysis. The stepwise procedure yielded 

 the same model in each case. The value 0.001 was 

 chosen because it yielded the most normal distribution 

 of porpoise per kilometer values (Fig. 3B). 



This approach to trend analysis also assumes that the 

 fraction of animals visible from the air does not change 

 over time. The probability of detection can be influ- 

 enced by many factors, particularly sighting conditions, 

 porpoise behavior and group sizes, and observer dif- 



ferences. In our analysis, we controlled for sighting 

 conditions by eliminating poor conditions and stratify- 

 ing by the remaining ones. Changes in observers be- 

 tween years prevented tests of observer differences. 

 However, based on previous tests with three years of 

 data, they are not believed to be significant (Forney 

 et al. 1989). 



Harbor porpoise behavior, including frequencies of 

 active versus inactive behaviors and mean group sizes, 

 has been shown to vary by area and season (Calam- 

 bokidis et al. 1990, Taylor and Dawson 1984, Sekiguchi 

 1987). To control for these potential differences, the 

 surveys followed the same transect lines during the 

 same season (autumn) each year. Nevertheless, group 

 sizes in 1989 were significantly different than those in 

 1987 and 1988 (Kolmogorov-Smirnov test of cumulative 

 distributions, P = 0.02 for both tests). The difference 

 appears to be due to a larger percentage of groups con- 

 taining three or more animals. 



If group size affects harbor porpoise sightability, a 

 substantial change in group size distribution could bias 

 the trend analysis, either obscuring a present trend or 

 creating a false one. To test for this possibility, the 

 ANCOVA was repeated excluding the data for 1989. 

 The overall results were similar, with the same final 

 model, similar parameters, and no significant yearly 

 trend (P = 0.98). We conclude that this slight difference 

 in group sizes is not likely to have affected our analysis. 



Conclusion 



The use of simulations allows researchers to estimate 

 appropriate error levels for the analysis of surveys 

 of animal populations. The ANCOVA model we used 

 suggests that no trend in harbor porpoise abundance 

 occurred between 1986 and 1990. However, our simula- 

 tions show that the power of this model to detect trends 

 using conventional a-levels of 0.05 or 0.10 is poor. 

 Therefore, it is more correct to say that we could not 

 reject the null hypothesis of no trend due to insufficient 

 power. 



Power can be increased by raising the acceptable 

 level of a. If only the sign of the coefficient for the 

 covariate year is used to determine the direction of a 

 trend, regardless of significance level, then the 

 ANCOVA has a high probability of detecting trends 

 correctly, particularly with eight or more annual sur- 

 veys. However, at higher a levels, the probability of 

 detecting a change in the wrong direction (y-error) 

 increases. 



When making decisions, there are distinct trade-offs 

 between the error types which must be evaluated. In 

 trend analysis, power should be defined as 1 - (/? + y) 

 to include only detection of a trend in the correct direc- 



