Abstract: Research on reciprocity is impaired by confusing definitions and often wrongly used statistical tests. Here, two models of the mechanism on which reciprocity may be based are discussed and an initial step towards a new fremework for its analysis is presented. A distinction is made between reciprocity and interchange. In the case of reciprocity, for one kind of act the same kind is received in return. In interchange, however, two different kinds of acts are bartered. Three types of reciprocity/interchange in social actions among all pairs of group-members are distinguished ([`]qualitative', [`]relative' and [`]absolute') on the basis of the precision of the reciprocity/interchange. Permutation procedures for association between matrices (such as the Mantel Z and two other newly derived tests) are used as a statistical test for detecting reciprocity/interchange. A rough comparison of the power of the two new tests is included. The tests can be applied to all kinds of group-living animals and to all sorts of social behaviour. The distinction between the three types of reciprocity/interchange and the matching statistical methods are also useful for defining and detecting other patterns in social interactions, like unidirectionality and associations between different kinds of social behaviour. The influence on social interactions of variables like dominance rank, age and sex can be analysed in the three forms by testing correlations between invented matrices which represent the influence of these variables (the so-called hypothesis matrices) and social interaction matrices. These methods are extended for two categories of individuals, thus allowing the investigation of, for example, reciprocity between males and females. The methods are illustrated with examples of coalition formation and grooming behaviour among captive chimpanzees, Pan troglodytes.

Abstract: Aggressive herding of females is a frequent but not invariant response by male savannah baboons,Papio cynocephalus, to encounters with other troops. While males in some troops are consistently more likely to herd than those in others, not all inter-troop encounters result in herding, even within particular troops. This suggests that males assess the risk of male invasion posed by each encounter and respond accordingly. We used data from baboon troops in the Drakensberg mountains to determine the rules males follow in deciding whether to herd. Consistent differences between troops were explained only by the adult sex ratio. Males were more likely to herd if the sex ratio of their own troop was female biased, a finding that is concordant with the observation that males are more likely to immigrate into troops where the sex ratio is more female biased than the population average. Differences within troops were a consequence only of encounter distance, with herding being more likely at closer distances. We found a negative correlation between the angle of approach to the other troop and the subsequent angle of deflection. We interpret this to mean that herding functions to increase the distance between the interacting troops, thereby curtailing opportunities for strange males to inspect the troop and determine its sex ratio. In this way, possibly unlike those in other populations, the decision rules of these male baboons are geared to protecting longer-term reproductive prospects.