FISHERY BULLETIN: VOL. 84, NO. 2 



Such confidence limits are asymmetric about X x and 

 decrease in size with increasing transect coverage. 

 They have the important properties that r 2 , the up- 

 per limit, tends to be large when the transect length 

 L; is small, even when the number of groups ob- 

 served is zero, and the lower limit r 1 is bounded by 

 zero. 



Population size estimates were made for each cell 

 i in each season from the relationship N { = D { • s 

 • A { , where N { is the cell population, D t is the 

 estimated density of groups based on Equation (1) 

 (groups/km 2 ), s is the seasonal mean group size, 

 and A { is the open-water area of cell i. Total 

 population size in each season, (N), was estimated 

 as from the sum of populations in each cell, and from 

 the theoretical formula: 



- T w/(0) _ . 

 N = J -s-A 



2L 



(5) 



where n is the total number of groups observed, L 

 is the total transect length, s is the seasonal mean 



group size, and A is the areal extent of the study 

 area. The variance of N was estimated from the rela- 

 tionship (K. Burnham 4 ). 



var (N) = A 2  var 0,) 



(6) 



where var t ) = 0,) 2 



var(s) 

 (E(i)f 



var(n) var(/"(0)) 



(E(n)f (£(A0))) 2 



+ 



. The variance of n was calculated assum- 



ing that n had a Poisson distribution; if this assump- 

 tion holds, var(n) = n (Burnham et al. 1980). 

 The variance of /(0) was calculated by program 

 TRANSECT, using the method of Burnham et al. 

 (1980). Variance of s was estimated as the standard 

 error of the mean group size. The formula for 

 variance requires that/(0) and s be independent, an 

 assumption that may be violated due to the diff eren- 



4 K. Burnham, Department of Statistics, School of Physical and 

 Mathematical Sciences, North Carolina State University, Raleigh, 

 NC 27650-5457, pers. coramun. 



Figure 4.— Common dolphin distribution in the Southern California Bight, winter and spring, 1975-78. Density contours show 



animals/km 2 . 



338 



