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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Feh, C. (1999). Alliances and reproductive success in Camargue stallions. Anim. Behav., 57(3), 705–713.
Abstract: A study of a herd of Camargue horsesEquus caballus, showed that while the majority of high-ranking stallions held single-male harems, some sons of low-ranking mares, being low ranking themselves, formed alliances that could last a lifetime. The two stallions were each other's closest associate and preferential grooming partner. Alliances were based on coalitions in which either both partners confronted an intruder synchronously or the dominant of the pair tended the female(s) while the subordinate simultaneously displayed towards the rival. Alliance partners were of similar age but were not more closely related to each other than to other stallions in the herd. Long-term paternity data revealed that subordinates sired close to a quarter of the foals born into the alliance group, and significantly more foals than low-ranking stallions in the herd adopting a `sneak'-mating strategy. The dominant appeared to benefit from the presence of his subordinate partner. Fights occurred all year round, and the subordinate stallion of each alliance pair fought outside competitors more than twice as often as the dominant. Forming short-term alliances before defending mares on their own may enhance long-term reproductive success for both partners. Other benefits to both partners include higher survivorship of their foals and increased access to proven reproductive mares. These results suggest that the relationship between alliance partners is based on mutualism, but several conditions for reciprocity seem to be fulfilled: the benefit to the dominant (assistance in fights), and the benefit to the subordinate (access to reproduction), are both costly to the other partner and delayed in time.
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Feh, C. (2005). Relationships and Communication in Socially Natural Horse Herds. In D. S. Mills, & S. M. McDonnell (Eds.), The domestic horse : the origins, development, and management of its behaviour. Cambridge: Cambridge University Press 2005.
Abstract: Horses are quite unique. In most mammals, sexes segregate and maintain bonds only during the breeding season (Clutton-Brock, 1989). Some canids, a few rodents and primate species such as gorillas, hamadryas baboons and red howler monkeys are the exception, where the same males stay with the same females all year round and over many breeding seasons. Typically, both sexes disperse at puberty in these species. In horses, it was clearly shown that the causes for female dispersal were incest avoidance and not intra-specific competition (Monard, 1996). As a rule, this is confirmed for mammal species where tenure length by males exceeds the age at first reproduction in females (Clutton-Brock, 1989). When horses are allowed to choose their mating partner freely, the inbreeding coefficient of the offspring is lower than expected should they mate randomly (Duncan et al, 1984).
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Wilson, D. S., & Dugatkin, L. A. (1996). A reply to Lombardi & Hurlbert. Anim. Behav., 52(2), 423–425.
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