A matrix partial correlation test used in investigations of reciprocity and other social interaction patterns at group level

Abstract

Reciprocity and other social interaction patterns can be studied at two levels, within pairs (i.e. at dyadic level) and among pairs (i.e. at group level). In this paper advantages of the latter approach are emphasized. However, an analysis at group level implies the correlation of interaction matrices and because such data are statistically dependent, the significance of a correlation has to be calculated in a special way. This is done by means of Mantel's permutation procedure. In order to reckon with individual variation, Mantel's permutation procedure is used in combination with the so-called Kr statistic, whereby correlations are calculated simultaneously for each separate row. With the aid of the Kr test, the correlation for interchange of grooming for the receipt of “support” in conflicts in baboons and vervet monkeys [data from Seyfarth (1976, Anim. Behav. 24 , 917–938, 1980, Anim. Behav. 28 , 798–813)] was reconfirmed. However, this result may have arisen as a by-product of correlations with other variables. Therefore, the partial form of the Kr test is derived and applied to Seyfarth's data and it appears that the interchange of grooming for the receipt of “support” in conflicts, is indeed a spurious correlation in vervets but not in baboons. Direct tuning of grooming to the amount of received “support” seems therefore unlikely in case of the vervets but may exist in the baboons. Some further suggestions are given about the way in which reciprocity/interchange may emerge as a by-product of simple (behavioural) rules. In certain behaviours (like for instance “reconciliation”) missing values occur “conditionally”, i.e. when the preceding behaviour (a fight in case of “reconciliation”) was absent. The same Kr partial correlation test can be used in order to make efficient use of the existing data. This is illustrated with an example of a test for reciprocity of “tolerance” during food sharing among captive female chimpanzees.