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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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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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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. 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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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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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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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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