Elsevier

Animal Behaviour

Volume 69, Issue 5, May 2005, Pages 1191-1201
Animal Behaviour

Bayesian analysis of linear dominance hierarchies

https://doi.org/10.1016/j.anbehav.2004.08.011Get rights and content

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.

Section snippets

Advantages of Bayesian approaches

Methods based on probability models offer a number of benefits relative to nonparametric techniques. In addition to inferring which estimate of ranks has the greatest support, probability-based models yield measures of certainty about the inferences, such as 95% confidence intervals. They also allow analysis of deviations between model assumptions and data, and comparison of alternative models, such as those assuming transitive or intransitive dominance relationships (Tufto et al. 1998). In

The method of paired comparisons

The method of paired comparisons (David 1988) can be interpreted as a method to reveal underlying dominance abilities given data on the outcome of contests (Leonard, 1977, Boyd and Silk, 1983). ‘Dominance ability’ is understood here as a measure of ability to prevail in a particular type of encounter due to fighting ability, motivation and past experiences. Physical strength and learning through fighting and observation are among the possible determinants of dominance ability.

Let di represent

Simulation methods

Use of nonparametric method to assign ranks is sometimes recommended when it is not clear that the assumptions of more specific models are met (de Vries 1998). To determine if this advice is warranted, I simulated data sets under a variety of rules, described below, governing relative dominance abilities and sample sizes, including cases in which the assumptions of the Bradley–Terry model are violated. I analysed each data set by the I&SI method and by Bayesian estimation of the Bradley–Terry

Discussion

Bayesian analysis of dominance hierarchies offers significant advantages over methods that identify ranks by nonparametric criteria, such as the I&SI method (de Vries, 1998, de Vries and Appleby, 2000). Simulations showed that the inferences of Bayesian versions of the Bradley–Terry model are more accurate than those of the I&SI method under a variety of circumstances, even when the assumptions of the Bradley–Terry model are violated (Table 4, Table 5). Bayesian analyses are also more

Acknowledgments

I thank Ming-Hui Chen, Dipak Dey, Kent Holsinger and Paul Lewis for advice about Bayesian methods and Kent Holsinger for helpful comments on the manuscript.

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