32 
Fishery Bulletin 99(1) 
tance from the observer against the interval between ad- 
jacent radial sighting distances should have a slope of 
zero in the absence of rounding error. Following Barlow, 5 
we modeled the rounding error in radial sighting distanc- 
es with this regression method, where the slope of the re- 
gression represents the percentage of rounding error. As 
a result, we smeared radial sighting distances by a ran- 
dom factor between ±4%. Observers also showed a ten- 
dency to round bearing angles to the nearest 5 degrees; 
therefore we smeared angles by a random number be- 
tween ±5 degrees to further reduce the effects of round- 
ing (Buckland et al., 1993). 
We noted a problem in the recording of radial sighting 
distances when the ship was closer than 5.6 km (3 nmi) 
to shore. In these cases, the shoreline was closer than 
the true horizon and radial sighting distances were some- 
times recorded by using the shoreline as the horizon (doc- 
umented from database comments and inferred in other 
cases). The use of the shoreline as a false horizon intro- 
duces errors because resulting radial (and perpendicular) 
sighting distances are positively biased. Thirty sightings 
were identified for which shoreline bias probably resulted 
in positively biased distance readings. Frequency distribu- 
tions of “shoreline-biased” and “unbiased” perpendicular 
sighting distances were significantly different (Kolmogo- 
rov-Smirnov test, PcO.OOl) and the “shoreline-biased” dis- 
tribution revealed a higher proportion of sightings beyond 
400 m. To reduce this bias, we excluded the “shoreline- 
biased” sightings prior to data truncation and to fitting 
the detection function to the perpendicular distance data. 
Buckland et al. (1993) recommend truncation of 5% to 10% 
of the largest perpendicular distances prior to model fit- 
ting. We truncated all sightings beyond 1 km, which elim- 
inated 10% of all sightings. Three models (hazard rate, 
half-normal, and uniform) were fitted to the perpendicular 
distance data by using the program DISTANCE (Laake 
et al. 6 ) and the most parsimonious model was selected 
by DISTANCE based on minimizing Akaike’s Information 
Criterion (AIC: Akaike, 1973; Buckland et al., 1993). We 
also fitted the above models by using other truncation 
distances and bin intervals to examine the sensitivity of 
abundance estimates to these values. 
Because large porpoise groups are more likely to be de- 
tected at greater distances than single animals or pairs, it is 
possible to introduce bias into abundance estimates by over- 
estimating mean group size. Truncation of distance data 
will reduce potential overestimation of group size because 
the largest groups are eliminated, thus minimizing this 
bias. An additional step to reduce overestimation is to test 
for dependence between group size and detection distance 
5 Barlow, J. 1987. Abundance estimation for harbor porpoise 
( Phocoena phocoena ) based on ship surveys along the coasts 
of California, Oregon, and Washington. Administrative report 
LJ-87-05, National Marine Fisheries Service, Southwest Fisher- 
ies Center, 36 p. [Available from Southwest Fisheries Science 
Center, P.O. Box 271, La Jolla, CA 92038.] 
6 Laake, J. L., S. T. Buckland, D. R. Anderson, and K. R Burn- 
ham. 1996. DISTANCE user’s guide, 82 p. Colorado Coopera- 
tive Fish and Wildlife Research Unit, Colorado State University, 
Fort Collins, CO 80523. 
by regressing the log of the observed group size against 
the detection probability at distance x [log(s ; ) versus g(x)], 
as recommended by Buckland et al. (1993). If the regres- 
sion is significant at a = 0.15, the mean group size is re- 
placed with the regression-based estimate of mean group 
size at zero distance, where theoretically, group size bias 
should not occur. We used this regression method in the 
program DISTANCE to determine which group sizes to 
use for estimating abundance. 
We tested the null hypothesis that harbor porpoise are 
randomly distributed with respect to depth by comparing 
the proportion of porpoise sightings to the proportion of 
survey effort within 20-m depth intervals. We used depth 
soundings as a measure of survey effort because soundings 
were taken at regular 2-minute intervals while the ship 
was underway. If harbor porpoise are randomly distributed 
by depth, then the proportion of porpoise sightings to depth 
soundings should be relatively equal for a given depth in- 
terval. Distributions were compared by using a nonpara- 
metric Kolmogorov-Smirnov goodness-of-fit test. 
Precision of the abundance estimates was estimated 
with two methods. Log-normal confidence intervals were 
calculated analytically with formulae presented in Buck- 
land et al. (1993). Bootstrap confidence intervals and coef- 
ficients of variation (CV) were calculated as follows. Effort 
and sighting data from region i were divided into 5-km ef- 
fort segments (for Beaufort 0-2 sea states only). A TRUE- 
BASIC computer program (BOOTPORP) was written to 
randomly draw (with replacement) effort segments within 
each region until the number of kilometers drawn equaled 
the number of kilometers actually surveyed. A pseudo- 
abundance estimate was then calculated from this boot- 
strap sample and the process was repeated 2000 times. 
The CV of the point estimates were calculated as the stan- 
dard error of the 2000 bootstrap estimates divided by the 
original point estimate. Bootstrap 95% confidence inter- 
vals were determined by identifying the 2.5 th and 97.5 th 
percentiles of the 2000 bootstrap estimates. For each boot- 
strap sample, the effective half-strip width [ESW or 1//10)], 
was treated as a random variable drawn from a normal 
distribution with a mean and standard error equal to 
that obtained from the detection model fitted to the trun- 
cated perpendicular distances. The probability of detect- 
ing a trackline group of porpoise, g( 0), was estimated for 
each bootstrap as a random variable drawn from a bino- 
mial distribution with mean = 0.769 (SE=0.117). Thisg(O) 
value was calculated by Barlow 5 with independent observ- 
er methods, using a nearly identical vessel and the same 
observer configuration that we used. Owing to an insuf- 
ficient number of sightings by the independent observers 
during our survey, we could not independently estimate a 
value forg(0). 
We statistically compared abundance estimates obtained 
from the 1995 ship survey with estimates from aerial sur- 
veys conducted 1 to 2 months earlier (Forney, 1999), using 
the “confidence interval of differences” approach proposed 
by Lo (1994) and adopted by Forney and Barlow (1998) for 
bootstrap confidence intervals. Commonly used compara- 
tive methods, such as those based on whether confidence 
intervals overlap or whether one population mean is in- 
