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Interrelationships and properties of parasite aggregation measures: a user's guide.

Aggregation of macroparasites among hosts is nearly universal among parasite-host associations. Researchers testing hypotheses on origins of parasite aggregation and its importance to parasite and host population ecology have used different measures of aggregation that are not necessarily measuring the same thing, potentially clouding our understanding of underlying epidemiological processes. We highlight these differences in meanings by exploring properties and interrelationships of six common measures of parasite aggregation, and provide a "user's guide" to inform researchers' decisions regarding their application. We compared the mathematical expressions of the different measures of aggregation, and ran two series of simulations and analyses. The first simulations tested the effect of random removals of parasites on aggregation levels under different conditions, while the second explored interrelationships between the measures, as well as between other individual parasitological sample measures (i.e. mean abundance, prevalence) and aggregation. Results of simulations and analyses showed that the six measures of aggregation could be separated readily into three groups: the variance-to-mean ratio (VMR) together with mean crowding, patchiness with k of the negative binomial, and Poulin's D with Hoover's index. These three pairs of measures showed differing responses to random parasite removals and differing relations with mean abundance and/or prevalence, highlighting that metrics capture different variation in other sample measures and different attributes of aggregation. We used results of our simulations and analyses, and a literature review, to list the properties, advantages, and disadvantages of each aggregation metric. We provide a comprehensive exploration of what is assessed by each metric, as a guide to metric choice. We implore researchers to provide enough information such that aggregation measures from each group are reported or can be readily calculated. Such steps are needed to allow large-scale analyses of variation in degrees of aggregation within and among parasite-host associations, to uncover epidemiological processes shaping parasite distributions.

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