Measuring and using skew in the study of social behavior and evolution

Unequal distribution of benefits from cooperation is a fundamental feature of social behavior, and many quantitative measures of this skew have been proposed. Overall group size and productivity affect each of the measures somewhat differently depending on their formulation. Some of the differences are due to whether the index is intended to measure skew relative to a random distribution or relative to the maximum possible skew. Sampling errors, however, will tend to make smaller and less productive groups seem more skewed than they actually are. Differential survival or residence times of group members add a second factor that can result in skew independent of behavioral mechanisms. Thus, significant biases can result in indices that do not account for random processes or differential survival within groups. Seven published skew indices plus a new index (B) that combines observed variance with the expected binomial variance were tested across simulations that compared groups varying in resource distribution probabilities, size, or productivity. Only the B index always avoided error through correctly adjusting for group size, productivity, and differential residence times. Thus, the B index has the best potential to be a benchmark value that can be used for identifying evolutionary patterns in social behavior, both across and especially within species. Although skew indices have been applied mostly to shared reproduction, the B index is suitable to any situation where group members divide benefits. Skew indices potentially can identify and test evolutionary scenarios across a wide range of behavioral interactions, such as dominance hierarchies, information exchange, and parental care.