902 



Fishery Bulletin 97(4), 1999 



First whale 



Present Absent Total 



Second whale present a b a + b 



absent c d c + d 



total a + c b + d n 



where (a + c) and ia + b) denote the total number of 

 occurrences of the first and second individuals re- 

 spectively, a the number of joint occurrences, and d 

 the total number of frames in which neither whale 

 occurred in years in which both were photographed. 

 First, the degree of association between all indi- 

 viduals was measured by using Coles (1949j asso- 

 ciation index (CAI): 



CAI 



SE = 



CAI 



SE = 



ad — be 



(a + b)(b + d) 



(a + c){c + d) 



n(a + b)(b + d) 



ad -be 



{a + b){a + c) 

 ib + d)ic + d) 

 n{a + b)(a + c) 



for ad > be. 



for be > ad and d > i 



propriate for an analysis of patterns of association 

 between individuals because not all individuals were 

 equally identifiable (see Bigg et al., 1990) as was es- 

 pecially the case for cow-calf pairs, in which the of- 

 ten well-marked mother was generally identified in 

 more photographs than her usually indistinct young 

 calves even though they always traveled together. 



Only CAI values for all years' combined were used 

 to determine intrapod groups. CAI values were later 

 calculated for the periods 1984-88 and 1989-95 and 

 used to examine changes in bond strength between 

 mothers and female offspring as the offspring ma- 

 tured and produced their own calves. The relation- 

 ship between age of males and the bond strength with 

 their mothers was also examined with these CAI 

 values. 



Groupings of individuals were identified from den- 

 drograms constructed with an agglomerative aver- 

 age single-link algorithm (Johnson, 1967; see Fig. 1 ) 

 In this procedure, CAI values for all possible pairs of 

 individuals were compared and the pair with the 

 highest CAI was linked. Then the pair of unlinked 

 individuals with the highest CAI was linked, or an 

 unlinked individual with a higher mean CAI value 

 with previously linked individuals was linked to that 

 pair, and so on until the mean CAI dropped to 20''r. 

 By this point, the vast majority of individuals had 

 been linked into intrapod groups and we switched to 

 an analysis with the point correlation coefficient 

 (PCC): 



CAI 



SE = 



ad -be 



~ i.b + d){e + d) 



(a + b){a + e) 



n{b + d){e + a) 



for be > ad and a > d. 



PCC 



ad - be 



The index was expressed as a percentage ranging 

 from 100 to -100, with lOO'/r indicating that the joint 

 number of occurrences of each whale equaled the 

 number of occurrences of the least-photographed in- 

 dividual. Zero percent indicated that the individu- 

 als were randomly distributed among photographs, 

 and -1009^ indicated that the two individuals were 

 never photographed together. The statistical signifi- 

 cance of CAI values was evaluated according to their 

 standard errors using Student's t test (Cole, 1949). 

 The CAI provides a measure of complete associa- 

 tion ( rather than absolute association ) in that a value 

 of 1009f occurs only when the'joint number of occur- 

 rences equals the number of occurrences of the less 

 frequently photographed individual (see Cole, 1949, 

 for details and a review of association indices). An 

 index of complete association was deemed more ap- 



[(a + b)(a + e)ib + d)(c + d)] 



where a represents the number of photographs con- 

 taining one or more members of both groups, b and e 

 represent the numbers containing members of only 

 one or the other of the groups, and d represents the 

 number containing no members of either group. 



The PCC index, a measure of absolute association, 

 was used to examine associations among intrapod 

 groups determined by CAI analysis because each 

 group was considered equally identifiable. The PCC 

 index varies from 1009f to -1009r, with indicating 

 a random distribution. An index of absolute associa- 

 tion was deemed to be more appropriate for intrapod 

 groups because all groups contained readily identi- 

 fiable animals; therefore observation of one group in 

 the absence of another group indicated that each 

 group was traveling independently of one another. 

 The relationship.s among intrapod groups were ex- 

 amined from dendrograms constructed from PCC 

 values with an agglomerative average single-link 

 algorithm (see Fig. 2). Linkages with a positive PCC 



