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Chase, I. D., Tovey, C., Spangler-Martin, D., & Manfredonia, M. (2002). Individual differences versus social dynamics in the formation of animal dominance hierarchies. Proc. Natl. Acad. Sci. U.S.A., 99(8), 5744–5749.
Abstract: Linear hierarchies, the classical pecking-order structures, are formed readily in both nature and the laboratory in a great range of species including humans. However, the probability of getting linear structures by chance alone is quite low. In this paper we investigate the two hypotheses that are proposed most often to explain linear hierarchies: they are predetermined by differences in the attributes of animals, or they are produced by the dynamics of social interaction, i.e., they are self-organizing. We evaluate these hypotheses using cichlid fish as model animals, and although differences in attributes play a significant part, we find that social interaction is necessary for high proportions of groups with linear hierarchies. Our results suggest that dominance hierarchy formation is a much richer and more complex phenomenon than previously thought, and we explore the implications of these results for evolutionary biology, the social sciences, and the use of animal models in understanding human social organization.
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Hemelrijk, C. K., & Wantia, J. (2005). Individual variation by self-organisation. Neurosci Biobehav Rev, 29(1), 125–136.
Abstract: In this paper, we show that differences in dominance and spatial centrality of individuals in a group may arise through self-organisation. Our instrument is a model, called DomWorld, that represents two traits that are often found in animals, namely grouping and competing. In this model individual differences grow under the following conditions: (1) when the intensity of aggression increases and grouping becomes denser, (2) when the degree of sexual dimorphism in fighting power increases. In this case the differences among females compared to males grow too, (3) when, upon encountering another individual, the tendency to attack is 'obligate' and not conditional, namely 'sensitive to risks'. Results resemble phenomena described for societies of primates, mice, birds and pigs.
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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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Mesterton-Gibbons, M., & Dugatkin, L. A. (1995). Toward a theory of dominance hierarchies: effects of assessment, group size, and variation in fighting ability. Behav. Ecol., 6(4), 416–423.
Abstract: We introduce assessment to the analysis of dominance hierarchies by exploring the effect of an evolutionarily stable fighting rule when there is variation in resource holding potential (RHP) and RHP is not a perfectly reliable predictor of the outcome of a fight. With assessment, the probability of a linear hierarchy decreases with group size but can remain appreciable for groups of up to seven or eight individuals, whereas it decreases virtually to zero if there is no assessment. The probability of a hierarchy that correlates perfectly with RHP is low unless group size is small.
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Wittemyer, G., & Getz, W. M. (2007). Hierarchical dominance structure and social organization in African elephants, Loxodonta africana. Anim. Behav., 73(4), 671–681.
Abstract: According to the socioecological framework, transitivity (or linearity) in dominance relationships is related to competition over critical resources. When a population is structured into groups, the intensity of between- versus within-group competition influences the form and function of its social organization. Few studies have compared the type and relative intensity of competition at these two levels. African elephants have well-structured social relations, providing an exemplary system for such a study. We report on dominance hierarchies among free-ranging elephants and evaluate the factors that drive their socioecological structure to lie in a region of the three-dimensional nepotism/despotism/tolerance space rarely observed among social species; namely, where non-nepotistic, transitive dominance hierarchies within groups emerge despite kin-based philopatry and infrequent agonistic interactions over widely distributed resources. We found significant transitivity in dominance hierarchies between groups. Dominance relations among the matriarchs of different social groups were primarily age based, rather than driven by physical or group size, and group matriarch rank influenced the dominance relationships among nonmatriarchal females in the population. Our results suggest that between-group dominance relationships induce tolerance among group members, which in combination with high group relatedness, reduces the benefits of nepotism. We postulate that cognitive abilities and high risk of injury in contests enhance winner and loser effects, facilitating the formation of transitive dominance relationships, despite widely distributed resources over which infrequent competition occurs. The interplay of cognitive abilities, winner and loser effects, resource distribution, and within- and between-group dominance relationships may produce behaviour in other strongly social mammals that differs from that predicted by a superficial application of current socioecological models.
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Broom, M., & Cannings, C. (2002). Modelling Dominance Hierarchy formation as a Multi-player game. J. Theor. Biol., 219(3), 397–413.
Abstract: Animals who live in groups need to divide available resources amongst themselves. This is often achieved by means of a dominance hierarchy, where dominant individuals obtain a larger share of the resources than subordinate individuals. This paper introduces a model of dominance hierarchy formation using a multi-player extension of the classical Hawk-Dove game. Animals play non-independent pairwise games in a Swiss tournament which pairs opponents against those which have performed equally well in the conflict so far, for a fixed number of rounds. Resources are divided according to the number of contests won. The model, and its emergent properties, are discussed in the context of experimental observations.
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Adams, E. S. (2005). Bayesian analysis of linear dominance hierarchies. Anim. Behav., 69(5), 1191–1201.
Abstract: Studies on social animals often seek to identify dominance hierarchies, in which individuals are ranked according to competitive abilities based on counts of wins and losses in pairwise encounters. I illustrate Bayesian approaches, based on the method of paired comparisons, for determining ranks and for estimating relationships between dominance ability and other attributes. Bayesian inference combines prior probability distributions for each unknown parameter with likelihood functions to produce the joint posterior probability distribution for the quantities of interest. In contrast to nonparametric techniques for inferring ranks, Bayesian models yield measures of certainty for each inference and allow rigorous estimates of correlations between ranks and covariates even when there is considerable uncertainty as to the ranks themselves. A possible objection to the Bayesian approach is that it appears to entail more restrictive assumptions than do simpler methods. However, simulations show that Bayesian inferences are more robust to deviations from these assumptions than are the results of nonparametric methods.
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Jameson, K. A., Appleby, M. C., & Freeman, L. C. (1999). Finding an appropriate order for a hierarchy based on probabilistic dominance. Anim. Behav., 57(5), 991–998.
Abstract: Methods of ranking individuals in a dominance hierarchy that use transitivity of relationships may obscure irregularities. Furthermore, these methods use only a small proportion of the information available from dominance encounters. This paper presents an intuitively appealing and easily implemented alternative to existing methods for ordering dominance data, developed from the work of Batchelder et al. (1992Journal of Mathematical Psychology36, 185-212). The procedure presented here is based on a mathematical model of paired comparisons and it involves only simple estimation procedures. We illustrate its use with data on dominance among red deerCervus elaphus, stags. The results indicate that dominance relationships are well characterized by the scale values that the model provides, and, because the method provides predictions for all pairings of animals, dominance predictions also exist for pairs of animals that have yet to be observed. Moreover, the dominance outcomes predicted by the model using the order scale are highly correlated with actual dominance observations at all levels. Overall, the procedure described provides a solution to the problem of identifying an appropriate order for a near-linear 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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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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