Measuring aggregation in parasite populations.

Aggregation, a fundamental feature of parasite distributions, has been measured using a variety of indices. We use the definition that parasite-host system A is more aggregated than parasite-host system B if any given proportion of the parasite population is concentrated in a smaller proportion of the host population A than of host population B. This leads to indices based on the Lorenz curve such as the Gini index (Poulin's D), coefficient of variation and the Hoover index, all of which measure departure from a uniform distribution. The Hoover index is particularly useful because it can be interpreted directly in terms of parasites and hosts. An alternative view of aggregation is degree of departure from a Poisson (or random) distribution, as used in the index of dispersion and the negative binomial k. These and Lloyd's mean crowding index are reinterpreted and connected back to Lorenz curves. Aggregation has occasionally been defined as the slope from Taylor's law, although the slope appears unrelated to other indices. The Hoover index may be the method of choice when data points are available, and the coefficient of variation when only variance and mean are given.