Assessing dominance hierarchies: validation and advantages of progressive evaluation with Elo-rating

TL;DR: In this article, an index to objectively assess the stability of a dominance hierarchy is proposed, which allows visualizing dominance relationships and the detection of rank dynamics, and it allows ranking hierarchies to be computed.

About: This article is published in Animal Behaviour.The article was published on 2011-10-01 and is currently open access. It has received 359 citations till now.

Summary

Study populations

• For their tests of Elo rating, the authors chose two species of macaques (crested, Macaca nigra, and rhesus macaques, M. mulatta).
• Even though their aim was not to test for species differences, the authors nevertheless aimed at gathering a broad data set including different, but comparable, species.

Data collection

• Groups comprised between 4 -18 adult males and 16 -24 adult females and were completely habituated to human observers and individually recognizable.
• The authors collected data on dyadic dominance interactions, i.e., agonistic interactions with unambiguous winner and loser, and displacement (approach / leave) interactions during all occurrence sampling on focal animals and during ad libitum sampling (Altmann 1974) .
• Overall, their data set comprised a total of 12,740 interactions involving 252 individuals.
• Dominance hierarchies were created separately for the different species, groups and sexes.

Data analysis

• The authors first aim was to investigate whether dominance rank orders calculated with Elo rating reflect rankings obtained with more established methods.
• To answer this, the authors assessed how similar rank orders generated with Elo rating are to those obtained with the I&SI method and David"s score.
• Please note that a sparse matrix is not necessarily a matrix with a higher proportion of unknown relationships.
• These additional matrices were again tested for linearity, resulting in 17 matrices retaining significant linearity and thus justifying the application of the I&SI algorithm.
• An increase in unknown relationships was generated as a consequence of the random deletion of 50% of all observed interactions (increase per period on average: 12.5%, inter-quartile range: 8 -17%, "reduced data set": Table 1 ).

Results

• The authors found that Elo ratings from the full data set correlated highly with Elo ratings from the randomly reduced data set (Table 2 ).
• The performance of Elo rating is virtually identical to the one of I&SI and slightly higher compared to David"s score (Table 2 ).
• Similarly, Elo rating produced strong correlations with slightly higher correlation coefficients compared to those obtained with David"s score from the remaining 49 time periods for which I&SI could not be applied (Table 2 ).
• In addition, results of their tests suggest that rankings from Elo rating and I&SI (given significant linearity test) remain stable in sparse data sets, whereas David"s score seems to create less reliable hierarchies in sparse data sets as a result of an increase in unknown relationships.

Discussion

• Even though there is abundant literature available that compares the concordance of different methods for the assessment of dominance ranks or scores (e.g., Bayly et al. 2006; Bang et al. 2010) , this is the first study to test the reliability of Elo rating with an extensive data set based on observations of free-ranging animals.
• The authors results on dominance interactions in crested and rhesus macaques show that Elo rating produces dominance rank orders which closely resemble rankings generated with David"s score and the I&SI method.
• Furthermore, their results indicate that Elo rating is very robust when data sets are limited in the number of interactions observed.
• Elo rating (and I&SI) even seems to produce more reliable dominance hierarchies than David"s score when the proportion of unknown relationships is high.
• One could argue that this effect is due to the initial proportion of unknown relationships, i.e., a relatively high proportion of unknown relationships in a "full" matrix leads to some uncertainty in the ranking which may make the scores from the further reduced matrix even less reliable.

General Discussion

• Unlike the I&SI method (given its application is feasible), Elo ratings do not necessarily reflect the rank order corresponding to a linear hierarchy in which an alpha individual is dominant (c.f., Drews 1993 ) over all other individuals and a beta individual is dominant over all other individuals except the alpha, and so on (de Vries 1998).
• Such a situation is found in the matrilineal rank organization of many Old World monkeys, which is characterized by a linear structure in which a daughter ranks below her mother, and among all daughters of one mother the youngest one ranks highest (Kawamura 1958; Missakian 1972 ; but see Silk et al. 1981 ).
• Ratings of the remaining individuals are scaled in between.
• Note that on March 10 th , the residing top ranking male (SJ) and another high ranking male (YJ) emigrated from the group and a new male (ZJ) joined the group on March 11 th , becoming the group"s new alpha male (see text for details).

Figures

Table 1. Robustness analysis. Correlation coefficients (rs) between rankings from full and reduced data sets. (Median and inter-quartile range)

Table 1. Robustness analysis. Correlation coefficients (rs) between rankings from full and reduced data sets. (Median and inter-quartile range)

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