Assessing the reliability of dominance scores for assigning individual ranks in a hierarchy

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.