14 



Fishery Bulletin 93fl), 1995 



Appendix 



"S =n m f(0)5. 



(5) 



To estimate the total fraction of trackline groups 

 missed owing to perception bias requires that the 

 survey be designed with two teams of completely in- 

 dependent observers. To be independent, both teams 

 would have to search simultaneously, not notifying 

 or cueing each other until a group of animals had 

 passed abeam of the vessel and were clearly missed 

 by the other team. This approach was deemed infea- 

 sible because of the need to approach groups to esti- 

 mate group size and species composition. If the ves- 

 sel was not turned until after all groups had passed 

 abeam, a very large percentage of those groups would 

 not be relocated. The probability of relocation would 

 depend on group size and species composition. These 

 factors would add considerably to the difficulty in 

 interpreting such survey data. 



Instead, the survey was designed to use a single, 

 conditionally independent observer who was aware 

 of sightings made by the primary team, but who did 

 not reveal the presence of a group until that group 

 was clearly missed by the primary team. Data from 

 the conditionally independent observer are used to 

 make an estimate of the probability that the primary 

 survey team detected a trackline group. 



The expected number of groups, n, seen very close 

 to the transect line, say within distance 8, can be 

 estimated as 



n a g(x)h(x)dx 







' (3) 



n 5 = 



g(x)h(x)dx 



where n m is the total number of groups seen within 

 the truncation distance co, g(x) is the probability of 

 seeing a group that is at perpendicular distance x, 

 and h(x) is the probability that a group will be at 

 perpendicular distance x (usually assumed to be 1.0 

 for primary observers at all x). As 5 approaches zero 

 distance, the above equation can be reexpressed as 



n s 



n a g(0)h{0)8 

 g{x)h(x)dx 



(4) 



which, from the line-transect definition of /TO) 

 (Burnham et al., 1980), can be simplified to 



The probability of a trackline group being seen by 

 the primary observers can be expressed as 



£l(0)= 



'1,S 



"is + n 2S I g 2 (0) 



(6) 



where the subscript 1 refers to sightings made by 

 the primary observers and subscript 2 refers to 

 sightings missed by the primary observers but seen 

 by the independent observer. Combining Equations 

 5 and 6 and simplifying results in 



Sl(0): 



l lca 



A<0) 



n lol k(0) + n 2l J 2 (0)/g 2 (0) 



(7) 



Because there were three primary observers and only 

 one independent observer, g x (0) should be greater 

 than or equal tog 2 (0). Thus 



Si(0)<l- 



n 2( o k (0) 

 n l( ofi(0) 



(8) 



This equation was applied (substituting = for <) to 

 the subset of data collected while an independent 

 observer was on duty to estimate the probability that 

 a group on the trackline would have been seen by 

 the primary observer team. This quantity will be bi- 

 ased and overestimated to the extent that g^O) is 

 greater thang 2 (0). 



The coefficient of variation forg^O) can be approxi- 

 mated as 



CV( gl iO)) = 



mCV(m) 

 1—m 



given 



and 



CV(m) 



m 



l 2oi 12 



k(0) 



na> 



fi(0) 



(9) 



(10) 



CV 2 (n 1 J + CV 2 (n 2(O ) + CV 2 {f 1 (0)) + CV 2 {k(0)). 



(11) 



