A graphical exploration of the relationship between parasite aggregation indices.

The level of aggregation in parasite populations is frequently incorporated into ecological studies. It is measured in various ways including variance-to-mean ratio, mean crowding, the k parameter of the negative binomial distribution and indices based on the Lorenz curve such as the Gini index (Poulin's D) and the Hoover index. Assuming the frequency distributions follow a negative binomial, we use contour plots to clarify the relationships between aggregation indices, mean abundance and prevalence.

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 is more aggregated than parasite-host system if any given proportion of the parasite population is concentrated in a smaller proportion of the host population than of host population . This leads to indices based on the Lorenz curve such as the Gini index (Poulin's ), coefficient of variation and the Hoover index, all of which measure departure from a uniform distribution.

Local approximation of a metapopulation's equilibrium.

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed.

A metapopulation model with Markovian landscape dynamics.

We study a variant of Hanski's incidence function model that allows habitat patch characteristics to vary over time following a Markov process. The widely studied case where patches are classified as either suitable or unsuitable is included as a special case. For large metapopulations, we determine a recursion for the probability that a given habitat patch is occupied.

Does moving up a food chain increase aggregation in parasites?

General laws in ecological parasitology are scarce. Here, we evaluate data on numbers of fish parasites published by over 200 authors to determine whether acquiring parasites via prey is associated with an increase in parasite aggregation. Parasite species were grouped taxonomically to produce 20 or more data points per group as far as possible.