Kingsley; Number and distribution of Delphinapteius leucas, in James, Hudson, and Ungava Bays, Canada 



739 



track-line is detected. Commonly, line- N 



transect analysis assumes that 1) g{0) 62 



is unity and 2) g(x) is never increasing 

 with X. An associated shape criterion, 

 which improves the behavior of esti- 

 mates obtained by line-transect survey 

 (Burnham et al., 1980; Buckland, 1985), 

 suggests that the sighting curve should 

 have a "shoulder" or plateau at small x. 



Richards' (1959) sigmoidal growth 61 



curve, reversed left-to-right, was chosen 

 for its flexibility to fit g(x). The ordinate 

 at the point of inflection was constrained 

 to be less than 0.9. Because of difficulty 

 in seeing straight down from a flat-win- 

 dowed aircraft, no animals could be seen 

 close to the transect line; therefore, close 

 to the transect line, an increase in g(x) 

 was modeled by an increasing sine- func- 

 tion (Fig. 4). It was assumed that^,,^^, = 1, 

 i.e. that all surface-visible beluga whales 

 situated at the best distance would be 

 detected. Detection bias would occur if 

 this assumption was incorrect. 



The data were truncated at 6000 ft 

 (1829 m> from the trackline; beyond 

 this distance, sightings were few, and 

 measured sighting angles and counts 

 of numbers were imprecise. Within this 

 range, the sighting curve was fitted 

 by maximum likelihood to the distri- 

 bution of distances from the trackline 

 to individual beluga whales, not to the ^g 



distribution of sighted groups (Hiby and 

 Hammond, 1989). A single sighting curve 

 was fitted, and a single estimate of k 

 was calculated, and for the survey of 

 James Bay and eastern Hudson Bay, 

 all three strata were pooled. It was 

 integrated numerically to calculate the 

 effective strip width. 57 



The transect counts were expanded to 

 an estimate of detectable numbers: 



M UDSON ST. 



59 



'^- 



f' Qillini^- 



Akoatok I. "^' 



Aupaluk *' !_ I I 



' LeafB. "^ 

 Tasiujaq ^ 



Koroc R. 

 Kangiqsualujjuaq 



KoksoakR. ^ "< 



Land observation points  



N 



J^N^^J^kTA, 



111 



71 70 69 68 67 66 65 64 W 



Figure 3 



Map of Ungava Bay with the survey design for aerial sui-veys in July and 

 August 199.3. 



where T^ 

 B 



= the transect spacing (km); 



= the total count of beluga whales in the s"' stra- 

 tum; and 



= the survey expansion factor (/km) i.e. the recip- 

 rocal of the two-sided effective strip width. 



X'^.-^B,.! 



V, =kT (kT -1) 



J.-1 



[21 



The uncertainty of N was estimated as the sum of V,,,, 

 the component from sampling the spatial distribution of 

 beluga whales in the stratum; and V^,, that was due to 

 uncertainty in the estimation of /;. V^j was estimated by 

 a serial difference method appropriate to systematic sam- 

 pling (Cochran, 1977): 



where B beluga whales were sighted on the/" of J, tran- 

 sects in stratum s. 



V,,,, the component of sampling error due to uncertainty 

 in the estimation of the effective strip width, was esti- 

 mated by 



