Temporal changes in aggregation: a laboratory study

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Abstract
Changes in the variance to mean ratio and the parameter k of the negative binomial distribution were used to study temporal changes in the degree of aggregation of the monogenean parasite, Gyrodactylus turnbulli in free-running laboratory populations of the guppy, Poecilia reticulata. The parasite undergoes recurrent epidemic cycles in the host population under conditions of regular immigration of uninfected guppies. During the early phase of the epidemic, heterogeneity among fish together with direct reproduction are thought to contribute to the increasing degree of aggregation. During the increasing phase of the epidemic cycle, parasites become increasingly aggregated in the host population, presumably because of the direct reproduction of the parasite on the surface of a single host. As the peak prevalance and abundance are approached, the parasites become less aggregated with lowest clumping occurring during the declining phase of the cycle. This is thought to be a function of density-dependent death of infected hosts, and density-dependent reduction in parasite survival and reproduction on hosts that recover from infection. This study clearly indicates that the variance to mean ratio and the parameter k of the negative binomial distribution do not quantify the same aspect of the frequency distribution. It is suggested that the variance to mean ratio is a better measure when the prevalence and−or mean burden are changing and when the tail of the distribution is of particular interest, and that k may be a preferred parameter when the zero class or the lightly infected hosts are of primary interest.