Measures of Inequality Are Not Equal

Abstract

Inequalities in reproductive success or resource acquisition are fundamental to evolution and population ecology. There is, however, no unique way to measure inequality. We review 21 measures used to quantify it and clarify the conceptual difference between inequality and skewness. In two very different families of distributions, all indices except three give higher values for more unequal distributions of resources, although some of them are poor at distinguishing between similar inequality values. When applied correctly by testing against a null hypothesis of no inequality among individuals, most indices can therefore be used to detect deviations from randomness, but with varying ease as most lack statistical tables and rely on resampling techniques instead. As an example to test the performance of the 21 indices, we used each index to analyze 71 data sets of unequal mating success in leks. In pairwise comparisons, 24% of the indices fail to show a positive intercorrelation. This reflects differences in how indices incorporate variation in the number of competitors and mean acquisition of the resource. All indices are sensitive to these aspects if inequality is measured in data arising from different distributions. These results illustrate the general conclusion that a unique "best" solution is not available; each measure presents its own definition of inequality. The choice of an inequality index requires specifying the null expectations and interpreting deviating values in relation to the biological question being addressed. This means, for example, considering individual male mating success in the context of lekking or relating the mass distribution of individual plants to alternative hypotheses about competition in plant population ecology. When sample sizes vary, testing robustness by using several measures is advisable.

Keywords: leks; reproductive skew; resource acquisition; sampling error; statistical power; variance in fitness.