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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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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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VanDierendonck, M. C., de Vries, H., Schilder, M. B. H., Colenbrander, B., & Þorhallsdóttir, A. G. and S., H. (2009). Interventions in social behaviour in a herd of mares and geldings. Appl. Anim. Behav. Sci., 116(1), 67–73.
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.
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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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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. (1995). An improved test of linearity in dominance hierarchies containing unknown or tied relationships. Anim. Behav., 50(5), 1375–1389.
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.
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