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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Poisbleau, M., Fritz, H., Valeix, M., Perroi, P. - Y., Dalloyau, S., & Lambrechts, M. M. (2006). Social dominance correlates and family status in wintering dark-bellied brent geese, Branta bernicla bernicla. Anim. Behav., 71(6), 1351–1358.
Abstract: In many gregarious species, including ducks and geese, being dominant provides more benefits than costs, because dominants have better access to resources essential for survival or reproduction. In geese, being in better body condition during migration towards the breeding grounds positively influences reproductive success. However, underlying proximate mechanisms linking prebreeding body condition on the wintering grounds to breeding success remain poorly understood. We investigated social dominance correlates and family status, in three consecutive winters, in a free-ranging, migrating, dark-bellied brent goose population. Families with juveniles dominated pairs, and pairs dominated singletons. Dominance rank did not increase with the number of juveniles per family. Males were dominant over females. Social dominance and reproductive status for a given winter were significantly correlated with body mass, body size and body condition during the previous winter, suggesting that body condition in winter also affects subsequent breeding success and hence also dominance. Levels of testosterone and triiodothyronine were not correlated with immediate or later dominance or reproductive status. We discuss the role of family status as a signal of social status in determining reproductive strategies.
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Poisbleau, M., Jenouvrier, S., & Fritz, H. (2006). Assessing the reliability of dominance scores for assigning individual ranks in a hierarchy. Anim. Behav., 72(4), 835–842.
Abstract: The dominance score (number of wins divided by the total number of interactions) is the most widely used procedure in field studies to rank individuals. Its reliability depends on the number of interactions on which it is calculated. However, most authors use it without any estimate of the associated error. We describe the precision associated with a dominance score estimate as a function of the number of interactions on which it is based, and hence provide a tool to plan field protocols and effort. The precision error decreases according to a power function with increasing number of interactions, but with more precision for extreme scores for any given number of interactions. We discuss the fact that the minimum number of interactions should be based on the precision associated with the 50% score, the least precise of all scores. We also emphasize the trade-off between recording effort and precision of the estimator, and give an example of our choice of 26 interactions for fieldwork on ducks and geese. When comparing individual ranks based on dominance scores with ranks given by the dominance matrix, we found a good correlation, with more mismatches around the middle of the hierarchy. This was consistent with the precision calculated with our model. We conclude that dominance score is a reliable tool, but conclusions must take into account the number of interactions on which the calculations are done. We also discuss the importance of initial assumptions and sources of bias in field studies.
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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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Cameron, E. Z.,, Linklater, W. L.,, Stafford, K. J.,, & Minot, E. O.,. (2003). Social grouping and maternal behaviour in feral horses (Equus caballus): the influence of males on maternal protectiveness. Behav. Ecol. Sociobiol., 53(2), 92–101.
Abstract: The risk of infant injury or mortality influences maternal behaviour, particularly protectiveness. Mares are found in bands with a single stallion or bands with more than one stallion in which paternity is less certain. We investigated maternal behaviour in relation to band type. Mares in bands with more than one stallion were more protective of their foals, particularly when stallions and foals approached one another. The rate of aggression between the stallion and foal was a significant predictor of maternal protectiveness, and mare protectiveness was significantly correlated with reduced reproductive success in the subsequent year. Mares that changed band types with a foal at foot, or had their band type experimentally altered, were more protective of their foal in multi-stallion bands than they were in single-stallion bands. Equids are unusual amongst ungulates in that infanticide and feticide have been reported. Both occur where paternity has been uncertain, and equid social structure is similar to other species in which infanticide has been reported. Stallions benefit from infanticide as the mare has greater reproductive success in the subsequent year. Stallion aggression is a significant modifier of mare behaviour and maternal effort, probably due to the risk of infanticide.
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RHO, J. R., SRYGLEY, R. B., & CHOE, J. C. (2004). Behavioral ecology of the Jeju pony (Equus caballus): Effects of maternal age, maternal dominance hierarchy and foal age on mare aggression. Ecol. Res., 19(1), 55–63.
Abstract: On Jeju Island, Korea, dominance hierarchy and maternal care according to maternal age were studied in a herd of Jeju ponies (Equus caballus), consisting of 73 mares, their foals and one stallion. Dominance ranks were nearly linear and increased significantly with the age of mares. Most aggressive encounters involved mares under 5 years old. Mares under the age of 5 years have apparently not established their rank. The mean frequency of aggressive actions of mares per hour increased significantly as the day of parturition approached. Aggressive actions of mares with foals decreased significantly as their foals aged. The overall frequency of aggression of mares with foals also decreased significantly with the age of the mares. Our results suggest that the cost of maternal care is lower for older, more dominant mares than for subordinate ones.
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