DOHL ET AL.: COMMON DOLPHIN DISTRIBUTION AND ABUNDANCE 



by the mean group size throughout the SCB ob- 

 tained for that season. The small sample size in any 

 cell and the very large variability in the size of 

 groups necessitated pooling of all sightings within 

 a season to calculate mean group size. The mean 

 group size in summer and autumn was 338 ± 38 SE 

 (n = 115), while that of winter and spring was 231 

 ± 73 SE (n = 36). While not significantly different 

 (^1,149 = 1-42, P > 0.25), we used separate mean 

 group size in calculations of seasonal abundance. We 

 tested the assumption that mean group size in each 

 season was constant throughout the SCB, using a 

 bootstrap procedure (Efron 1982). For a given 

 season, cell i contained n { observations of groups 

 of mean size s { . For each cell i, we randomly drew 

 10,000 sets of values of size n { from the group size 

 distribution based on all observations recorded in 

 that season, computed the mean of this subsample, 

 and formed a frequency distribution of these mean 

 values. If the percentile ranking of the observed 

 mean group size in cell i was >97.5% or <2.5%, 

 s, was assumed to be a nonrandom sample. For the 

 summer-autumn season, only 1 cell of the 26 cells 

 containing observations of common dolphins had 

 means which differed significantly from the rest of 

 the surveyed area. Similarly, for the winter-spring 

 season, only 1 cell in 10 showed a significant dif- 



N = 112 



.13 .27 .40 .67 .94 



DISTANCE IN KM 



1.22 1.48 



Figure 3.— Probability density function f(X) fit to histogram of 

 sighting frequency and perpendicular distance (rescaled; see text). 



ference from the overall group size distribution. 

 Therefore, group size homogeneity was assumed for 

 these data, and a single seasonal value of mean 

 group size (s) was used in all calculations of cell 

 density for each season. 



If f(0) and s may be assumed to be homogeneous, 

 the remaining source of between-cell variability is 

 the density of groups. We tested the hypothesis that 

 the density of groups is homogeneous through the 

 SCB as follows: taking the mean number of sight- 

 ings of common dolphin schools per kilometer of 

 transect for the entire surveyed area, A*. We com- 

 puted the expected number of cells containing a 

 specified number of sightings of groups, using the 

 formula: 



[Expected number of cells with k sightings] = 



1 e- rL . (A*L^ 



(2) 



i=i 



where m is the total number of cells sampled, k is 

 the specified number of sightings of groups, and L % 

 is the length of trackline surveyed in cell i. The ex- 

 pected number of cells containing k sightings were 

 compared with the observed number for all k using 

 a chi-square test. No significant spatial heteroge- 

 neity was evident for data collected in summer and 

 autumn (x 2 = 5.06, df = 5, P > 0.5). However, the 

 winter and spring distribution showed clear heter- 

 ogeneity in the density of groups by cell (x 2 = 

 12.85, df = 3, P < 0.005). 



We used the method of Chernoff and Moses (1959) 

 to place confidence limits on the estimate of the 

 number of groups per km of transect in cell i, A; 

 (see also Clopper and Pearson 1934). We used a com- 

 puter program which finds a density value, r 1( such 

 that the probability of observing n % or more groups 

 in a transect segment of length L { is 0.025; this is 

 the lower confidence bound on A,. Similarly, we find 

 a density value, r 2 , such that the probability of ob- 

 serving n { or fewer groups is 0.025; this forms the 

 upper bound on A^. T x and V 2 are defined as satis- 

 fying the equations: 



and 



k = n. 



k = n 



k\ 



= 0.025 



(3) 



2. \J_±L = o >02 5. 



*=o 



k\ 



(4) 

 337 



