Abstract: For some time now, social network analysis provides tools to describe concisely the social structure of animals. Nevertheless, the factors that shape the social network and determine the frequency of different types of affiliations are often unclear. For example, the effects of relatedness on social networks have been only studied on relatively few species. Both among social or sub-social species the effects ranged from no effect to a substantial effect. Here we test the hypothesis that relatedness has an effect on the social network of horses (Equus caballus) that live freely in semi-natural conditions, and specifically, that individuals with high values of relatedness to their neighbors in the network will have fewer links Wolf et al, 2011). This hypothesis is based on the notion that related individuals have common interests and are likely to assist each other, and may need less links to other, unrelated individuals. In addition, individuals of similar age and sex are likely to have common needs, and thus are more likely to be associated. We thus tested a second hypothesis: homophily to individuals with similar age and sex will have a role in determining the associations within the social network. The field study was conducted on 27 horses in the Blauwe Kamer reserve in the Netherlands (1.1 sq km). We videotaped horses and their groups and used the information from 22 horses, after excluding the five foals from the analysis. Relatedness was calculated from the pedigree, which was based on parentage, determined by DNA analysis. The social network was constructed based on spatial proximity data. We assessed the influence of relatedness, age-homophily and sex-homophily on the network structure with Multiple Regression Quadratic Assignment Procedure (MRQAP) (Krackhardt 1988), with the R package sna. The results show that there was no significant effect of relatedness on the network, nor an effect of age-homophily. Nevertheless, we found a significant effect of sex-homophily, the tendency of individuals to associate with individuals of the same sex. We argue that the lack of a relatedness effect is not likely to have been caused due to the inability to detect who is kin. The structured social system in horses includes strong associations between often unrelated individuals, alongside with young individuals leaving their natal harem as part of the inherent inbreeding avoidance (Linklater & Cameron 2009; Boyd et al. in press). The significant effect of sex-homophily could stem from the protection females get from associations with other females, e.g., in the reduction of harassment from males. Previous studies on feral horses showed that mares that were better connected with other females in their harem benefited from higher survival rates to their foals (Cameron et al. 2009). The associations among bachelor males could also contribute to the strength of the sex-homophily effect.
In order to generalize from our results, one needs to examine additional populations of horses, because the conditions in the Blauwe Kamer reserve may not be representative, mainly due to the limited opportunity for dispersal in a restricted area.
Keywords: Long-term affiliation; spatial proximity, kin detection
Boyd, L., Scorolli, A. L., Nowzari, H., & Bouskila, A. (2016). Chapter 2: Social organization. In J. I. Ransom, & P. Kaczensky (Eds.), Wild equids. Baltimore, Maryland (in press): The Johns Hopkins University Press.
Cameron, E. Z., Setsaas, T. H., & Linklater, W. L. (2009). Social bonds between unrelated females increase reproductive success in feral horses. Proceedings of the National Academy of Sciences, 106(33), 13850-13853
Krackhardt, D. (1988). Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social Networks, 10(4), 359-381.
Linklater, W. L., & Cameron, E. Z. (2009). Social dispersal but with philopatry reveals incest avoidance in a polygynous ungulate. Animal Behaviour, 77(5), 1085-1093.
Wolf, J. B., Traulsen, A., & James, R. (2011). Exploring the link between genetic relatedness r and social contact structure k in animal social networks. The American Naturalist, 177(1), 135-142.

Abstract: Abstract  We studied sex differences in the nature of aggression and dominance behaviour in two newly formed groups of 1-year-old Icelandic horses. One herd contained nine geldings, the other nine mares. The groups were matched with regard to dominance-determining traits such as age, weaning age, composition of native herd, social experience, genetic origin, body condition and maternal dominance status. High-ranking individuals of both sexes were more aggressive, high-ranking males were older, and high-ranking females had a better body condition. Frequencies of aggressions were similar in both groups. The mares reacted significantly more by showing submission upon an aggression rather than by not responding or by escalating the aggression. For the geldings, this difference was not observed due to a lower tendency to submit. A linear dominance hierarchy was found in both groups. David`s scores provided additional information regarding cardinal rank distances and were used to calculate steepness of hierarchies. The female hierarchy was somewhat steeper compared to the male hierarchy, suggesting somewhat lower despotism among males. This was mainly a consequence of the lower unidirectionality in male submission. Male contests occurred predominantly between dyads at top and mid positions, suggesting a low degree of acceptance of the hierarchy.

Abstract: Feral horses are social animals, which have to rely on survival strategies centered on the formation of cohesive social bonds within their bands. Many problems in the husbandry of social animals such as horses, are due to the fact that the limits of their adaptive abilities are exceeded. Evidence suggests that the fundamental social characteristics of domestic horses have remained relatively unchanged. The social structure, social strategies and social interactions were investigated (3 non-consecutive years, 24 hr per day for several weeks) in long term established groups of domestic horses (mares and geldings of all ages) and a few small introduced groups, kept in (semi)natural environments. The general aim was to investigate the social needs of domestic horses. The social life of domestic horses was characterised by long lasting bonds with preferred partners which were established and maintained by allogrooming, play, proximity and dominance behaviours. Bonding partners were mainly found within the same sex-age group, but adult geldings also bonded with sub-adult mares and geldings. Adult mares were clustered in a group, while the other animals formed a second group. Among the adult mares, subgroups according to reproductive state were formed. Individuals regulated their social network by interfering with interactions between other members of the herd, which in itself is complex. An intervention is a behavioural action of one animal that actively interferes with an ongoing interaction between a dyad with the apparent aim of altering that interaction. This was verified by post-hoc analyses of disturbed and undisturbed interactions. Interventions in allogrooming or play were performed significantly more often when at least one member of the initial dyad was a preferred partner of, or familiar to (within the small introduced bands) the intervener. The stronger the preferred association in allogrooming between the intervener and member(s) of the initial dyad, the higher the probability the intervener would displace one initial member and continue allogrooming with the other. Just five behaviours were extracted which reliably reflected the dominance relations among horses. Aggression with the hind quarters was used both offensively and defensively and therefore not suitable as a reliable parameter. Individual dominance relationships were related to social experience. The implications of these findings for horse husbandry were assessed. It is argued that the execution of affiliative behaviours may be rewarding in itself, and therefore always will be a highly motivated behaviour. It is shown that social positive physical interactions (allogrooming, play) with other horses is an ethological need and therefore indispensable in modern husbandry systems. Ethological needs are so important for the animal that husbandry systems that lack the possibilities to execute such behaviours will cause chronic stress. It is concluded that all horses need physical social contact, and that horses, which lack appropriate social learning experiences during ontogeny, may be hampered in their social functioning later in life. Solutions for problems, including dominance problems, in individual social housing and group housing are presented.

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.