Forney et al.: Aerial surveys of Phocoena phocoena abundance trends 



369 



of poor sighting conditions. The pilot circled on por- 

 poise sightings if there was any question about species 

 identification or number of porpoise. Additional sight- 

 ings made while circling were recorded as "off effort" 

 sightings and were not included in the analyses. 



During the first survey year (1986), observers re- 

 ported all marine mammals sighted. However, the 

 large number of California sea lion sightings took a 

 disproportionate amount of time, so only harbor por- 

 poise were recorded in 1987-90. Following the surveys, 

 the data in the flight log or computer were checked for 

 accuracy and, if needed, compared with the tape 

 recordings. The data were transferred into micro- 

 computer databases for summary and analysis. 



Analytical methods 



Individual flight segments during which all sighting 

 conditions were constant were combined to measure 

 porpoise per kilometer in relation to each of the sight- 

 ing variables. These variables included Beaufort sea 

 state, cloud cover, viewing condition, individual ob- 

 servers, and an a posteriori geographic subdivision 

 chosen on the basis of apparent porpoise abundance: 

 south (low abundance) and north (high abundance) 

 (Fig. 2). This subdivision was created to correct for 

 slight interannual differences in survey effort for highl- 

 and low-density areas, caused by bad weather. 



Cloud cover was recorded as a percentage and later 

 coded into the categories "clear" (0-24%) and "cloudy" 

 (25-100%). Sighting efficiency and sample sizes de- 

 creased dramatically when Beaufort sea state was 

 higher than 3, so only segments with Beaufort 0-3 

 were used. Beaufort was combined with Beaufort 

 1 because there was very little survey effort at 

 Beaufort 0. 



The data were fitted to an analysis of covariance 

 (ANCOVA) model of the form: 



M + <*\ + <* 2 + 



+ <J(y-y) + £ 



(i) 



where P represents the log- transformed (log e ) value of 

 porpoise per kilometer, \i is the mean value of P, the 

 a represent qualitative factors influencing observed 

 porpoise abundance, 6 represents the coefficient for the 

 covariate year (y), y is the mean value of y, and e is 

 a random error term. Such an additive model for 

 logarithmic values is equivalent to a model describing 

 multiplicative effects on the untransformed number of 

 porpoise seen. This was deemed appropriate because 

 sighting conditions affect the fraction of porpoise seen 

 but not the absolute density of porpoise present. 

 Because of the logarithmic transformation, a linear 



* 012 



cc 



W 



2 010 



LU 



LU 



W OOB 



LU 



to 



O 06 



SOUTH (mean =0.025) 



mean = 0.056 



hull 



ii 



NORTH (mean =0.096) 



1 3 5 7/8 10 12 14 16 18 20 22 24 26 

 TRANSECT # 



Figure 2 



Porpoise seen per kilometer in transects 1 through 26 for 

 1986-90 surveys (including Beaufort sea states 0-3 and clear 

 skies only). For the analysis, transects were divided into two 

 areas at Point Pinos (between transects 14 and 15): south (low 

 abundance) and north (high abundance). 



increase or decrease in the covariate would be inter- 

 preted as an exponential increase or decrease in por- 

 poise abundance. The constant 0.001 was added to each 

 value before transformation to avoid trying to take the 

 logarithm of zero. This logarithmic transformation also 

 made the data more nearly normal (Fig. 3). 



It was not possible to include all potential variables 

 in the model selection procedure, because this would 

 have caused overstratification of the data. Individual 

 observer effects were excluded because not all ob- 

 servers collected data each year, resulting in a large 

 number of missing cell values. Viewing condition was 

 also excluded because it is somewhat redundant with 

 sea state and cloud cover and it is more subjective. 

 Previous nonparametric tests of individual observer 

 effects and viewing conditions with three years of data 

 (Forney et al. 1989) yielded no significant differences 

 in observed numbers of porpoise per kilometer. 



In the ANCOVA, the data were weighted by the 

 number of kilometers flown to correct for variability 

 due to unequal sample sizes. A stepwise selection pro- 

 cedure with the SAS procedure GLM (Joyner 1985) was 

 used to determine the best model for the observed data. 

 At each step, all appropriate parameters and inter- 

 action effects were tested individually. The most sig- 

 nificant parameter was added to the model, based on 

 a criterion level of a = 0.05. Each included variable was 

 retested for significance at each subsequent step of the 

 procedure. 



