Testing association patterns of social animals.

Indices of association among pairs of animals in a social population naturally vary. An important question in many studies of social structure is whether this variation can be accounted for purely by random association, or whether the data give evidence for preferred association, and/or avoidance of association (Whitehead 1997; Bejder et al. 1998; Whitehead & Dufault 1999). Probably the most appropriate way to carry out such tests is by using Monte-Carlo methods, in which association data are randomly permuted subject to certain constraints, and statistics of the original association data are compared with those from random data. Often the original data set consists of records of which individually identified animals were observed in which group, with group defined as an instantaneously observed spatial aggregation. In these cases it is usual to constrain the permutations so that the number of groups in which each individual was observed, and the number of animals in each group, are held constant (e.g. Slooten et al. 1993; Bejder et al. 1998). Bejder et al. (1998) permuted association matrices under these constraints by using a sequential routine developed by Manly (1995) for an analogous ecological problem (Table 1). This routine (unlike others that I have used for this task: Whitehead et al. 1982; Slooten et al. 1993) is straightforward, efficient and works with all appropriate data sets. Thus it represents a substantial development in our ability to test social structures for evidence of nonrandom associations. The core of the method of Manly (1995) and Bejder et al. (1998) (subsequently called MBFB) is the sequential alteration of a 1:0 group–individual matrix in such a way that row and column totals (number of animals in each group, and number of groups of each animal) are unaffected. This is achieved by randomly selecting, at each step, two individuals and two groups so that each individual is seen in only one of the groups, and each