Fishery Bulletin 93(1). 1995 



1993b). The basic equation for estimating abundance, 

 N, for grouped animals with line transect is given by 



N- 



AnSf(O) 

 2Lg(0) 



(1) 



where A = size of the study area; 



n = number of sightings; 



S = mean group size; 



fiO) = sighting probability density at zero per- 

 pendicular distance; 



L = length of transect line completed; and 



g(0) = probability of seeing a group directly 

 on the trackline. 



Ideally, S, /10), and g(0) would be estimated sepa- 

 rately for each species. However, the presence of 

 mixed-species groups and small sample sizes required 

 pooling for the estimation of/10) andg(O). The param- 

 eter /(0) was estimated with the Hazard rate model 

 (Buckland, 1985). This model was fitted by maximum 

 likelihood with ungrouped perpendicular distances. 

 Perpendicular distances were estimated from bearing 

 and radial distance estimates made by observers. 



Pooling and stratification for estimating f (0) 



Pooled /T0)'s were estimated for five species groups: 

 "small delphinids," "large delphinids," "small 

 whales," "large whales," and "cryptic species." The 

 five species groups were defined to include all of the 

 species seen on the survey (Table 1) and were based 

 on patterns of species cooccurrence in groups and on 

 similarities in the physical and behavioral attributes 

 that affect sightability from a ship. As an example, 

 bottlenose dolphins, Tursiops truncatus, were never 

 seen in a single-species group but were seen with 

 Risso's dolphins, Grampus griseus, 13 times, with 

 striped dolphins, Stenella coeruleoalba, one time, and 

 with sperm whales, Physeter macrocephalus , three 

 times. Bottlenose dolphins were pooled together with 

 Risso's dolphins because they were seen most fre- 

 quently with that species and because their sighting 

 characteristics are more similar to Risso's dolphins 

 (medium body size, prominent dorsal fin, occasional 

 low puffy blow, small to medium group size) than to 

 the other two species with which they were seen. 

 Because killer whales, Orcinus orca, were never seen 

 with other species but share the same sighting char- 

 acteristics, these were also included in the species 

 group "large delphinids." The other four groups are 

 "small delphinids" which are of small body size (2-3 

 m) and are found in medium to large groups; "small 

 whales" which are of medium body size (4-10 m), 



typically show no blow, often surface inconspicuously, 

 and are typically found in small groups; "large 

 whales" which are of large body size (10-30 m), al- 

 most always show a conspicuous blow, and are found 

 in small to medium groups; and "cryptic species" 

 which are small (1.5—4.0 m), show no blow, typically 

 surface inconspicuously, and are found in small 

 groups. The assignment of higher-than-species taxa 

 to species groups is given in Table 1. 



In estimating /10) for each species group, I explored 

 stratification by two factors that are likely to affect 

 sightability: sea state and group size. To avoid esti- 

 mating more parameters than are justified by the 

 data, I chose the most parsimonious stratification 

 model by minimizing Akaike's Information Criterion 

 (AIC) (Akaike, 1973), defined as 2 multiplied by the 

 number of parameters used to estimate f\ 0) minus 2 

 multiplied by the sum of the log-likelihoods of the 

 fitted values of/tO). Sea state was subjectively strati- 

 fied into calm (Beaufort 0-2) and rough ( Beaufort 3- 

 5), based on the obvious degradation in sighting con- 

 ditions that occurs with the presence of whitecaps at 

 Beaufort 3. I stratified by group size by first finding 

 the group size that divided the data into two samples 

 with approximately the same number of sightings in 

 each. If this stratification resulted in a lower AIC, I 

 explored further stratification into three samples of 

 approximately equal size. 



The above approach to stratification resulted in 

 different strata for each species group. For small 

 delphinids, AIC was minimized by stratifying group 

 size into the categories 1-20, 21-100, and >100. For 

 large delphinids, optimal stratification was with 

 group size categories of 1-20 and >20. For large 

 whales, AIC was minimized by using group size 

 strata of 1-3 and >3. Because "cryptic species" and 

 "small whales" were seldom seen in rough conditions, 

 I estimated abundance for these species by using only 

 data from calm conditions and did not explore strati- 

 fication by sea state. Group size stratification re- 

 sulted in higher AIC values for "cryptic species" and 

 "small whales," so these groups were not stratified 

 by group size. Sea-state stratification was not cho- 

 sen on the basis of AIC values for any species group. 



In stratification by group size, estimates of den- 

 sity in the various strata are added together to give 

 an overall density. The equation for estimating abun- 

 dance of each species k is therefore given by 



N t 



1 



7 = 1 



An hk S hk f hk (0) 

 2Lg jk (0) 



(2) 



where A = size of study area; 



