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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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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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Hemelrijk, C. K., Wantia, J., & Gygax, L. (2005). The construction of dominance order: comparing performance of five methods using an individual-based model. Behaviour, 142(8), 1043–1064.
Abstract: In studies of animal behaviour investigators correlate dominance with all kinds of behavioural
variables, such as reproductive success and foraging success. Many methods are used to
produce a dominance hierarchy from a matrix reflecting the frequency of winning dominance
interactions. These different methods produce different hierarchies. However, it is difficult to
decide which ranking method is best. In this paper, we offer a new procedure for this decision:
we use an individual-based model, called DomWorld, as a test-environment. We choose this
model, because it provides access to both the internal dominance values of artificial agents
(which reflects their fighting power) and the matrix of winning and losing among them and,
in addition, because its behavioural rules are biologically inspired and its group-level patterns
resemble those of real primates. We compare statistically the dominance hierarchy based on
the internal dominance values of the artificial agents with the dominance hierarchy produced
by ranking individuals by (a) their total frequency of winning, (b) their average dominance
index, (c) a refined dominance index, the David`s score, (d) the number of subordinates each
individual has and (e) a ranking method based on maximizing the linear order of the hierarchy.
Because dominance hierarchies may differ depending on group size, type of society, and the
interval of study, we compare these ranking methods for these conditions.We study complete
samples as well as samples randomly chosen to resemble the limitations of observing real
animals. It appears that two methods of medium complexity (the average dominance index
and David`s score) lead to hierarchical orders that come closest to the hierarchy based on
internal dominance values of the agents. We advocate usage of the average dominance index,
because of its computational simplicity.
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Weeks, J. W., Crowell-Davis, S. L., Caudle, A. B., & Heusner, G. L. (2000). Aggression and social spacing in light horse (Equus caballus) mares and foals. Appl. Anim. Behav. Sci., 68(4), 319–337.
Abstract: Aggression and social spacing were studied in 14 light horse mares and their foals living at pasture. Focal samples were collected on each mare-foal dyad for 6 to 10.5 h from 2 months of foal age until weaning at approximately 4 months of age. Observations on foals continued until approximately 6 months of age for 7.5 to 10.5 h per foal. Every 2 min the identities of all individuals within 5 m were recorded. All occurrences of agonistic behavior, and the participants, were recorded during the focal samples. In addition, during feeding of supplemental grain, all occurrences of agonistic behavior by all subjects were recorded. Significant correlations were found between mare rank and the rank of foals both prior to and after weaning. Before weaning, the rank of the foal was significantly correlated with birth order. No significant correlation between birth order and foal rank was found for the post-weaning hierarchy. An animal's gender had no significant effect on foal rank or the choice of preferred associate. Both prior to and after weaning, foals associated preferentially with the foal of their dam's most preferred associate. In addition, significant positive correlations were found between rank of mares and foals and the rate at which they directed aggression to other herd members. (C) 2000 Elsevier Science B.V.
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Langbein, J., & Puppe, B. (2004). Analysing dominance relationships by sociometric methods--a plea for a more standardised and precise approach in farm animals. Appl. Anim. Behav. Sci., 87(3-4), 293–315.
Abstract: Social dominance is a multidimensional phenomenon occurring in all gregarious farm animals and finds its reflection in a dominance hierarchy. Hence, numerous studies have tried to analyse dominance relationships as well as to correlate outcoming results (mostly individual ranks) with other behavioural and/or physiological features of the animals. Although the concept of dominance, once established, has been developed continuously and several sociometric measures were cumulatively introduced, a consistent analysing approach has not been achieved, especially in farm animals. Thus, considerable inconsistencies in the used methodology may impair obtained results and interpretations. The present paper is a plea for a more standardised and complex approach when analysing dominance relationships, not only in farm animals. First, derived from a structural definition of dominance, we suggest in detail the preferably consistent use of appropriate sociometric measures at all social levels of analysis: the dyad as the starting level, the group as the highest level, and the individual as the basic level. Second, we applied this procedures in a case study to analyse social dominance in a group of dwarf goats (n=12) and pigs (n=10), respectively, to comparatively demonstrate benefits and problems of such an approach in two different farm animal species. It is concluded that the use of individual ranks is actually only reasonable when fundamental sociometric measures both at the dyadic level (e.g. percentage of dyads which have a significant asymmetric outcome) and at the group level (e.g. the strength of hierarchy) are successfully tested by statistical methods as also presented in this paper. The calculated sociometric measures deliver not only a more comprehensive “picture” of the social relationships within a group as simple ranks do, but also indicate possible reasons of differences in the behavioural development. For instance, whereas the dwarf goats maintained a quasi-linear dominance hierarchy over time with a high rate of overt agonistic behaviour, pigs after the establishment of their hierarchy showed a reduced agonistic behaviour which makes it questionable to calculate reliable sociometric measures. These species-dependent variations may be primarily caused by different kinds of the fighting behaviour in goats (i.e. ritualised, low costs) and pigs (i.e. more seriously, high costs). Overall, a more consistent and standardised approach of analysing social dominance in (farm) animals may improve the scientific value of single studies and makes it easier to compare various studies within a species and between species.
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Schooening, B. (1998). Ethology of the horse. Prakt. Tierarzt, 79(6 Suppl.), 25–28.
Abstract: The paper starts with a short introduction/definition about ethology and the used methods in this scientific field, giving special examples for horses and about how their “normal behaviour” is measured. The behaviour repertoire of horses is described in a brief outline with special emphasis on their social systems and hierarchies and the problem of dominance, especially in interaction with humans. Schlütersche GmbH & Co. KG, Verlag und Druckerei.
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Beaugrand, J. P. (1997). Relative importance of initial individual differences, agonistic experience, and assessment accuracy during hierarchy formation: a simulation study. Behav. Process., 41, 177–192.
Abstract: This simulation study explores some conditions leading to transitivity within dominance orders. Combinations of three parameters were varied to study their consequences upon hierarchy formation and upon the degree of linearity of resultant structures. The factors studied were: (1) the importance of initial resource holding potentials (RHPs); (2) changes brought in RHPs by successive victories and defeats; and (3) accuracy of RHP assessment made by opponents. Results show that initial differences in RHP always lead to perfectly transitive chains whose rank order reflects the importance of initial differences. Even when simulated animals make important errors while assessing each other during round robin tournaments, emerging dominance structures are perfectly linear and ranks obtained in the structure are highly correlated with initial values in RHPs. Moreover, accumulated experiences of victory and/or defeat alone always lead to perfectly linear hierarchies. Their combination with initial individual differences in RHP led to the same conclusion. Even when assessment was far from being perfect, not only perfect chains were formed but initial values in RHPs significantly influenced rank order when the contribution of victory and defeat to RHP was relatively unimportant. The higher the importance of victory and defeat to RHP as compared to that of initial RHP values, the lower was the correlation between initial RHP values and the ranks order reached by individuals in the resultant hierarchies. In general also, the lower the variation within initial RHPs, the lower was the correlation between initial RHPs and ranks in the hierarchy. At a given level of initial RHP dispersion, increasing the contribution of victory and defeat to RHP diminished the correlation between initial RHP values and obtained ranks. In addition, inaccurate assessment reduced the overall correlation, especially when dispersion of initial RHP values was low and the contribution of victory and defeat relatively unimportant. These results shed some light on the controversy about the respective roles of initial individual attributes and that of patterns of resolution in the formation of animal hierarchies. We present the emergence of social order within closed systems as those simulated here as a case of self-organization.
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Beaugrand, J. P. (1997). Relative importance of initial individual differences, victory and defeat experiences, and assessment accuracy during hierarchy formation: A simulation study (Vol. 41). Elsevier.
Abstract: This simulation study explores some conditions leading to transitivity within dominance orders. Combinations of three parameters were varied to study their consequences upon hierarchy formation and upon the degree of linearity of resultant structures. The factors studied were (i) the importance of initial Resource Holding Potentials (RHPs) , (ii) changes brought in RHPs by successive victories and defeats, and (iii) accuracy of RHP assessment made by opponents. Results show that initial differences in RHP always lead to perfectly transitive chains whose rank order reflects the importance of initial differences. Even when simulated animals make important errors while assessing each other during round robin tournaments, emerging dominance structures are perfectly linear and ranks obtained in the structure are highly correlated with initial values in RHPs. Moreover, accumulated experiences of victory and/or defeat alone always lead to perfectly linear hierarchies. Their combination with initial individual differences in RHP led to the same conclusion. Even when assessment was far from being perfect, not only perfect chains were formed but initial values in RHPs significantly influenced rank order when the contribution of victory and defeat to RHP was relatively unimportant. The higher the importance of victory and defeat to RHP as compared to that of initial RHP values, the lower was the correlation between initial RHP values and the ranks order reached by individuals in the resultant hierarchies. In general also, the lower the variation within initial RHPs, the lower was the correlation between initial RHPs and ranks in the hierarchy. At a given level of initial RHP dispersion, increasing the contribution of victory and defeat to RHP diminished the correlation between initial RHP values and obtained ranks. In addition, inaccurate assessment reduced the overall correlation, especially when dispersion of initial RHP values was low and the contribution of victory and defeat was high. These results shed some light on the controversy about the respective roles of initial individual attributes and that of patterns of resolution in the formation of animal hierarchies. We present the emergence of social order within closed systems as those simulated here as a case of self-organization.
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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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