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VanDierendonck, M. C., de Vries, H., & Schilder, M. B. H. (1995). An Analysis of Dominance, Its Behavioural Parameters and Possible Determinants in a Herd of Icelandic orses in Captivity. Netherl. J. Zool., 45(3-4), 362–385.
Abstract: Th e applicability of the concept of dominance was investigated in a captive herd of  Icelandic
horses and  ponies of diff erent breeds. Eight out of  behaviours possibly related
to dominance occurred frequently enough to be investigated in detail. For these eight agonistic
behaviours the coverage, the unidirectionality in the exchange, and the degree of
transitivity (Landau`s linearity index) were calculated. Four off ensive behaviours, together
with avoidance, were suitable for further analysis with regard to dominance. Th e patterns
of asymmetries with which these behaviours were exchanged were suffi ciently similar as to
justify the application of the dominance concept and to construct a (nearly) linear dominance
hierarchy. Th e rank order of the castrated stallions was completely linear, the hierarchy
of the mares was almost completely linear. Th e results suggest that off ensive and defensive
aggressive behaviours should be treated separately and that the concept of dominance
is applicable. However, ritualized formal dominance signals between adult horses appear to
be (almost) absent. Th e rank positions of the individuals were correlated with age and residency
in the herd but not with height. Middle ranking horses tended to be more frequently
in the close vicinity of another horse than high ranking or low ranking horses. Over and
above this correlation at the individual level, it was found that pairs of horses close in rank
to each other were more often also spatially close to each other. Being in oestrus did not infl
uence the dominance relationships between mares. For castrated stallions the rank positions
were correlated with the age at which they were castrated. Th is suggests that in male
horses experience prior to neutering infl uences the behaviour afterwards.
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Gammell, M. P., de Vries, H., Jennings, D. J., Carlin, C. M., & Hayden, T. J. (2003). David's score: a more appropriate dominance ranking method than Clutton-Brock et al.'s index. Anim. Behav., 66(3), 601–605.
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de Vries, H., Stevens, J. M. G., & Vervaecke, H. (2006). Measuring and testing the steepness of dominance hierarchies. Anim. Behav., 71(3), 585–592.
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.
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de VRIES, H. A. N. (1998). Finding a dominance order most consistent with a linear hierarchy: a new procedure and review. Anim. Behav., 55(4), 827–843.
Abstract: A procedure for ordering a set of individuals into a linear or near-linear dominance hierarchy is presented. Two criteria are used in a prioritized way in reorganizing the dominance matrix to find an order that is most consistent with a linear hierarchy: first, minimization of the numbers of inconsistencies and, second, minimization of the total strength of the inconsistencies. The linear ordering procedure, which involves an iterative algorithm based on a generalized swapping rule, is feasible for matrices of up to 80 individuals. The procedure can be applied to any dominance matrix, since it does not make any assumptions about the form of the probabilities of winning and losing. The only assumption is the existence of a linear or near-linear hierarchy which can be verified by means of a linearity test. A review of existing ranking methods is presented and these are compared with the proposed method.
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Albers, P. C. H., & de Vries, H. (2001). Elo-rating as a tool in the sequential estimation of dominance strengths. Anim. Behav., 61(2), 489–495.
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De Vries, H., & Appleby, M. C. (2000). Finding an appropriate order for a hierarchy: a comparison of the I&SI and the BBS methods. Anim. Behav., 59(1), 239–245.
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Vervaecke, H., Stevens, J., Vandemoortele, H., Sigurjönsdöttir, H., & De Vries, H. (2007). Aggression and dominance in matched groups of subadult Icelandic horses (Equus caballus). J. Ethol., 25(3), 239–248.
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.
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Stevens, J., Vervaecke, H., De Vries, H., & Van Elsacker, L. (2006). Social structures in Pan paniscus: testing the female bonding hypothesis. Primates, 47(3), 210–217.
Abstract: Abstract Based on previous research in captivity, bonobos, Pan paniscus, have been called a female-bonded species. However, genetic and behavioural data indicate that wild females migrate. Bonding between these unrelated females would then be in contradiction with socio-ecological models. It has been argued that female bonding has been overemphasized in captive bonobos. We examine patterns of proximity, grooming and support behaviour in six well established captive groups of bonobos. We find that female bonding was not a typical characteristic of all captive bonobo groups. In only two groups there was a trend for females to prefer proximity with other females over association with males. We found no evidence that following or grooming between females was more frequent than between males and unrelated females or between males. Only in coalitions, females supported each other more than male-female or male-male dyads. We also investigated five mother-son pairs. Grooming was more frequent among mothers and sons than in any other dyad, but sons did not groom their mothers more than males groomed unrelated females. Mothers groomed their sons, or provided more support to them than females groomed or supported unrelated males. Thus, while bonds between females were clearly present, intersexual relations between males and either unrelated females or their mothers are of more, or equal importance.
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Stevens, J., Vervaecke, H., de Vries, H., & Van Elsacker, L. (2005). The influence of the steepness of dominance hierarchies on reciprocity and interchange in captive groups of bonobos (Pan paniscus). Behaviour, 142(7), 941–960.
Abstract: Biological market models explain variability in reciprocity and interchange between groups. In groups with a shallow dominance gradient, grooming will be mostly exchanged for itself (i.e. exchange will occur). In groups with steep dominance hierarchies, interchange is expected: individuals will groom higher ranking individuals to get access to limited resources or commodities such as support in conflicts, and grooming will be traded for these commodities. We examine patterns of reciprocity in grooming and support, and of interchange of grooming for support or for tolerance in six captive groups of bonobos. We test whether differences between groups in patterns of reciprocity and interchange can be attributed to differences in a measure of steepness of dominance hierarchies, which is based on dyadic agonistic interactions. We found that grooming was reciprocal in some, but not all groups. Support was highly reciprocal, but this was a side effect of dominance in most groups. Interchange between grooming and support was observed in some groups. Corroborating earlier findings, this was a side effect of individuals preferring high ranking individuals as grooming and support partners, possibly because these high-ranking individuals provide more efficient support in conflicts. There was no evidence for interchange of grooming for tolerance. Variability in grooming reciprocity was explained by differences in steepness of dominance hierarchies, as predicted by the biological market models. In groups with a shallow dominance hierarchy, grooming was more reciprocal. This was not true for reciprocity in support. There was some evidence that individuals groomed dominants more frequently in groups with a steep dominance hierarchy. The variation in interchange relations between grooming and support did not depend on the steepness of dominance hierarchies. We suggest that grooming in itself is a valuable commodity in bonobos, especially under captive conditions, which can be exchanged reciprocally. Bonobos may interchange grooming for another value equivalent, with food sharing as a very likely candidate. This interchange effects seem more dependent on potential to monopolise food than on steepness of dominance hierarchies per se.
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Vervaecke, H., de Vries, H., & van Elsacker, L. (2000). The Pivotal Role Of Rank In Grooming And Support Behavior In A Captive Group Of Bonobos (Pan Paniscus). Behaviour, 137(11), 1463–1485.
Abstract: We investigated dyadic grooming relationships in a captive group of bonobos (Pan paniscus) and questioned what social function grooming fulfils in the 'market of services and favors'. Hereto we examined which of two theoretical models – grooming for support (Seyfarth, 1977, 1980) or grooming according to the similarity principle (de Waal & Luttrell, 1986) – best accounted for the observed grooming distribution. Similarity in traits did not correlate with increased grooming or close proximity among the individuals. Therefore, the similarity hypothesis was rejected. Seyfarth's model of rank-related grooming was largely confirmed. The animals distributed their grooming according to the rank of the receivers. We found an exchange between grooming and receipt of support. There was more grooming up than down the hierarchy. However, not all predictions about rank-related competition over grooming were confirmed. We found that dyadic grooming reciprocity indeed increased with decreasing rank distance. Yet, there was no increase of grooming within the dyad with decreasing rank distance and high ranking individuals were not competed over at the highest rates. The observed correlation between grooming and support received represents an important fit with Seyfarth's prediction, but does not allow for conclusions about underlying causal processes. Other causal explanations, besides the 'groom to receive support' hypothesis, that could explain a similar correlation are discussed.
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