Figure 3 - available via license: Creative Commons Attribution 4.0 International
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Elo-based steepness and classic steepness. Classic steepness (right column) is calculated with P ij David's scores and represents a point estimate. Two individuals have the same David's score and hence have a tied rank and therefore are slightly jittered vertically for visual purposes. Elo-based steepness carries over uncertainty deriving from, amongst others, data density. The lower panel has twice the number of interactions observed compared to the top panel, which informs the Bayesian Elo steepness, but has no effect on classic David's score steepness.
Source publication
The steepness of dominance hierarchies provides information about the degree of competition within animal social groups and is thus an important concept in socioecology. The currently most widely-used metrics to quantify steepness are based on David's scores (DS) derived from dominance interaction networks. One serious drawback of these DS-based me...
Contexts in source publication
Context 1
... the next step, David's scores are then normalized such that the scores of all individuals range between 0 and n − 1, where n is group size. To derive the steepness metric, a simple linear regression is fit between scores and ordinal ranks of the scores (figure 1 in de Vries et al. (2006), see also figure 3). The absolute value of the slope coefficient of this model then is the steepness metric. ...
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... these cumulative winning probabilities at hand, we fit a regression model analogously to de Vries et al. (2006) with cumulative winning probabilities as a function of ordinal ranks of cumulative winning probabilities. The absolute value of the regression slope then is the steepness index (see also figure 3). ...
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... a result, their cumulative winning probability distributions overlap to a very large extent. In summary, our new steepness measure follows an analogous approach as classic steepness by using standardized scores of individuals as the source to estimate the steepness slope ( figure 3). In contrast to classic steepness though, these individual scores represent probability distributions of cumulative winning probabilities derived from Elo-ratings. ...
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... we investigated how well the different methods dealt with sparse data. Here, we performed a removal experiment, in which we increased the proportion of unknown relationships incrementally in a given data set by removing interactions, and subsequently quantified the relationship between steepness and the proportion of unknown relationships in each data set (see figure A3). This approach provided insights into the robustness of the different methods with respect to data density. ...
Citations
The steepness of dominance hierarchies provides information about the degree of competition within animal social groups and is thus an important concept in socioecology. The currently most widely used metrics to quantify steepness are based on David's scores (DS) derived from dominance interaction networks. One serious drawback of these DS‐based metrics is that they are biased, that is, network density systematically decreases steepness values.
We provide a novel approach to estimate steepness based on Elo‐ratings, implemented in a Bayesian framework (STEER: Steepness estimation with Elo‐rating). We evaluate and validate its performance by means of experimentation on empirical and artificial datasets and compare its performance to that of several other steepness estimators.
STEER has two key advantages. First, it is unbiased, precise and more robust to data density than DS‐based steepness. Second, it provides explicit probability distributions of the estimated steepness coefficient, which allows uncertainty assessment. In addition, it relies on the same underlying concept and is on the same scale as the original measure, and thus allows comparison to existing published results.
STEER provides a considerable improvement over existing methods to estimate dominance hierarchy steepness. We demonstrate its application with an example comparing within‐ and between species variation in steepness in a comparative analysis and present guidelines on how to use it. The R package EloSteepness allows convenient numeric and graphical assessment of the new steepness measure.
