256 



Fishery Bulletin 93(2), 1995 



within this strip were then used to calculate ratio- 

 to-size estimates of density ( D R ) for each survey by 

 using a single-stage, sampling approach in which 

 sampled transects were treated as clusters of unequal 

 sizes (i.e. transect lengths varied; Cochran, 1977; 

 Gates, 1979; Jolly and Watson, 1979): 



D - Y « 



""M- 



the density of turtles on the surface of the sound; and 



r* = 5>i. 



i=l 



the total number of turtles sighted during a survey, 



where y t = the number of turtles in the i th transect; 

 and 



n 



M R = 2_. m i> total area surveyed (km 2 ), 



1=1 



where m t - the area surveyed in the i th transect (km 2 ); 

 and 



inverse of one-half the effective strip width (Burnham 

 et al., 1980), mathematically equivalent to the value 

 of the pdf exactly on the flight line (perpendicular 

 distance=0). On the basis of the histograms of sight- 

 ing distances, data were censored such that the prob- 

 ability of sighting a turtle was not reduced by prox- 

 imity to the airplane. Distance data were rescaled 

 such that x=0 at the point data were censored (0.15 

 km from flight line). Simple, generalized, and non- 

 parametric models were examined with the program 

 TRANSECT (Laake et al., 1979) to derive density 

 estimators from the sighting distance data. Because 

 only small numbers of turtles were seen during most 

 sampling occasions, we could not conduct individual 

 analyses for each survey. Instead, sighting informa- 

 tion was combined for all Core Sound surveys and 

 for all Pamlico Sound surveys, and an overall flO)^ 

 was specified for each of the two water bodies (s). 

 Density for each survey ( D R ) then was estimated as 



D, 



fM s Y R 

 2L R 



where /10) is the overall /CO) for the water body, and 

 is obtained from the TRANSECT program, and L R 

 (km) is the total length of all transects (/.): 



n = the number of strip transects sampled. 



Variances of the density estimates, V( D R ), were 

 calculated as follows: 



it 



i_A 5>?(A-A?) 2 



V(D S ) = —Jt . i=l 



nM 2 n-1 



where N = the total number of strip transects pos- 

 sible; and 



y 



D ( = — - , the density of turtles in z'th transect; 

 m i and 



M 



M 



— , the average area of a single transect 



" (km 2 ). 



For line-transect analyses we used methods de- 

 scribed by Burnham et al. ( 1980). The essential prob- 

 lem in line-transect analysis is to construct a prob- 

 ability density function (pdf) from the set of perpen- 

 dicular distance observations of sighted organisms 

 to estimate fXO). The value of /10) is defined as the 



H 



■'R ~ ^t  



The estimated variance of the density estimate for 

 each survey was computed as 



V(D R ) = D R 



( V(Y R ) | V(f(0) s ) ) 

 Yr f(0f s 



The variance of the number of turtles sighted dur- 

 ing a survey V(Y R ) is 



V(Y R ) = fci- 



**1Mt-$ 



n-l 



and the variance of/l0) s is obtained from the pdf so- 

 lution (Burnham et al., 1980). 



Experiment to evaluate observer bias 



Four observers participated in the study. An experi- 

 ment was conducted on 29 August 1991 to evaluate 

 the accuracy and comparability of observer sightings 



