Abstract: Social dynamics and maintenance of social cohesion were studied by analysing social interventions in two groups of horses consisting of adult mares, their offspring, adult geldings and sub-adults. The animals were observed for a total of 1316 h. All relevant dyadic and triadic social interactions, including initial behaviour, possible intervention and outcome, were recorded. The main question was: do horses use interventions in affiliative interactions to safeguard their social network? Horses were significantly more likely to intervene in allogrooming or play interactions that involved a preferred partner. The stronger the preferred association in allogrooming, the higher the likelihood the intervener took over allogrooming with an initial dyad member. Interveners originating from two newly introduced groups (n = 3 and 5), intervened significantly more often when a member of their own group allogroomed with an unfamiliar horse. In play, no correlation with unfamiliarity was found. Overall, the intervening horses stopped more than half of the initial allogrooming interactions, and a third of all interactions. Therefore, social facilitation cannot sufficiently explain interference behaviour. This study shows that maintaining relationships with preferred partners is important to horses and has implications for equine husbandry and management.

Abstract: In the analysis of social dominance in groups of animals, linearity has been used by many researchers as the main structural characteristic of a dominance hierarchy. In this paper we propose, alongside linearity, a quantitative measure for another property of a dominance hierarchy, namely its steepness. Steepness of a hierarchy is defined here as the absolute slope of the straight line fitted to the normalized David's scores (calculated on the basis of a dyadic dominance index corrected for chance) plotted against the subjects' ranks. This correction for chance is an improvement of an earlier proposal by de Vries (appendix 2 in de Vries, Animal Behaviour, 1998, 55, 827-843). In addition, we present a randomization procedure for determining the statistical significance of a hierarchy's steepness, which can be used to test the observed steepness against the steepness expected under the null hypothesis of random win chances for all pairs of individuals. Whereas linearity depends on the number of established binary dominance relationships and the degree of transitivity in these relationships, steepness measures the degree to which individuals differ from each other in winning dominance encounters. Linearity and steepness are complementary measures to characterize a dominance hierarchy.

Abstract: Appleby (1983, Anim. Behav., 31, 600-608) described a statistical test, based on the work of Kendall (1962, Rank Correlation Methods), for the significance of linearity in dominance hierarchies. He suggested that unknown relationships should be assigned the value 1/2 and that subsequently the same test procedure can be used. In this paper it is shown that incorrect results are obtained by this method whenever there are unknown relationships. Values of the linearity index are systematically too low. P-values can be too high (underestimating the significance) or too low (overestimating), and seem to differ by not much more than a factor two (respectively a half) from the correct P-value. An improved method is developed for testing linearity in a set of dominance relationships containing unknown relationships. Furthermore, it is argued that, if one admits the possibility of tied dominance relationships, which should indeed be assigned the value 1/2, Landau's linearity index is to be preferred to Kendall's index. A randomization test is developed for assessing the significance of linearity or non-linearity in a set of dominance relationships containing unknown or tied relationships. The test statistic employed in this testing procedure is based on Landau's linearity index, but takes the unknown and tied relationships into account.