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Nelissen, M. H. J. (1986). The effect of tied rank numbers on the linearity of dominance hierarchies. Behav. Process., 12(2), 159–168.
Abstract: The occurence of tied rank numbers in dominance hierarchies is discussed, especially its effect on the linearity of the hierarchy. This linearity is measured with Landau's index, that is calculated for several hierarchies with tied ranks on one, two of three levels. Linearity is mostly affected by ties in small groups with many ties. A distinction is made between a hierarchy of individuals and hierarchical levels. The phenomenon of despotism is called an extreme case of tied ranks. It is proposed to regard hierarchies with a linearity in a continuous scale.
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Wittemyer, G., & Getz, W. M. (2006). A likely ranking interpolation for resolving dominance orders in systems with unknown relationships. Behaviour, 143(7), 909–930.
Abstract: n many animal systems agonistic interactions may be rare or not overt, particularly where such interactions are costly or of high risk as is common for large mammals. We present a technique developed specifically for resolving an optimized dominance order of individuals in systems with transitive (i.e. linear) dominance relationships, but where not all relationships are known. Our method augments the widely used I&SI method (de Vries, 1998) with an interpolation function for resolving the relative ranks of individuals with unknown relationships. Our method offers several advantages over other dominance methods by enabling the incorporation of any proportion of unknown relationships, resolving a unique solution to any dominance matrix, and calculating cardinal dominance strengths for each individual. As such, this method enables novel insight into difficult to study behavioural systems.
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Hewitt, S. E., Macdonald, D. W., & Dugdale, H. L. (2009). Context-dependent linear dominance hierarchies in social groups of European badgers, Meles meles. Anim. Behav., 77(1), 161–169.
Abstract: A social hierarchy is generally assumed to exist in those mammalian societies in which the costs and benefits of group living are distributed unevenly among group members. We analysed infrared closed-circuit television footage, collected over 3 years in Wytham Woods, Oxfordshire, to test whether social groups of European badgers have dominance hierarchies. Analysis of directed aggression between dyads revealed linear dominance hierarchies in three social-group-years, but patterns within social groups were not consistent across years. Dominance hierarchies were significantly steeper than random in five out of six social-group-years. In those social-group-years where a linear hierarchy was determined, there was an effect of sex on dominance rank, with females gaining significantly higher rank than males in two social-group-years. Overall, rank was not related to age, nor did it appear to affect the likelihood of an individual being wounded, or an individual's breeding status. The latter resulted from nonorthogonality between sex and breeding status, as there were only two breeding males. Overall, hierarchies were primarily dominated by breeding females, and may occur when breeding competition arises. Relatedness, unreciprocated allogrooming and sequential allomarking were not consistently related to levels of directed aggression across social-group-years. We suggest that dominance structures within European badger groups may be context dependent, with future study required to complete our understanding of where, and when, they arise.
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Bang, A., Deshpande, S., Sumana, A., & Gadagkar, R. (2010). Choosing an appropriate index to construct dominance hierarchies in animal societies: a comparison of three indices. Animal Behaviour, 79(3), 631–636.
Abstract: A plethora of indices have been proposed and used to construct dominance hierarchies in a variety of vertebrate and invertebrate societies, although the rationale for choosing a particular index for a particular species is seldom explained. In this study, we analysed and compared three such indices, viz Clutton-Brock et al.'s index (CBI), originally developed for red deer, Cervus elaphus, David's score (DS) originally proposed by the statistician H. A. David and the frequency-based index of dominance (FDI) developed and routinely used by our group for the primitively eusocial wasps Ropalidia marginata and Ropalidia cyathiformis. Dominance ranks attributed by all three indices were strongly and positively correlated for both natural data sets from the wasp colonies and for artificial data sets generated for the purpose. However, the indices differed in their ability to yield unique (untied) ranks in the natural data sets. This appears to be caused by the presence of noninteracting individuals and reversals in the direction of dominance in some of the pairs in the natural data sets. This was confirmed by creating additional artificial data sets with noninteracting individuals and with reversals. Based on the criterion of yielding the largest proportion of unique ranks, we found that FDI is best suited for societies such as the wasps belonging to Ropalidia, DS is best suited for societies with reversals and CBI remains a suitable index for societies such as red deer in which multiple interactions are uncommon.
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Neumann, C., Duboscq, J., Dubuc, C., Ginting, A., Irwan, A. M., Agil, M., et al. (2011). Assessing dominance hierarchies: validation and advantages of progressive evaluation with Elo-rating. Animal Behaviour, 82(4), 911–921.
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Hartmann, E., Christensen, J. W., & McGreevy, P. D. (2017). Dominance and Leadership: Useful Concepts in Human-Horse Interactions? Proceedings of the 2017 Equine Science Symposium, 52, 1–9.
Abstract: Dominance hierarchies in horses primarily influence priority access to limited resources of any kind, resulting in predictable contest outcomes that potentially minimize aggressive encounters and associated risk of injury. Levels of aggression in group-kept horses under domestic conditions have been reported to be higher than in their feral counterparts but can often be attributed to suboptimal management. Horse owners often express concerns about the risk of injuries occurring in group-kept horses, but these concerns have not been substantiated by empirical investigations. What has not yet been sufficiently addressed are human safety aspects related to approaching and handling group-kept horses. Given horse's natural tendency to synchronize activity to promote group cohesion, questions remain about how group dynamics influence human-horse interactions. Group dynamics influence a variety of management scenarios, ranging from taking a horse out of its social group to the prospect of humans mimicking the horse's social system by taking a putative leadership role and seeking after an alpha position in the dominance hierarchy to achieve compliance. Yet, there is considerable debate about whether the roles horses attain in their social group are of any relevance in their reactions to humans. This article reviews the empirical data on social dynamics in horses, focusing on dominance and leadership theories and the merits of incorporating those concepts into the human-horse context. This will provide a constructive framework for informed debate and valuable guidance for owners managing group-kept horses and for optimizing human-horse interactions.
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