Simple epidemiological model predicts the relationships between prevalence and abundance in ixodid ticks

We tested whether the prevalence of ticks can be predicted reliably from a simple epidemiological model that takes into account only mean abundance and its variance. We used data on the abundance and distribution of larvae and nymphs of 2 ixodid ticks parasitic on small mammals (Apodemus agrarius, Apodemus flavicollis, Apodemus uralensis, Clethrionomys glareolus and Microtus arvalis) in central Europe. Ixodes trianguliceps is active all year round, occurs in the study area in the mountain and sub-mountain habitats only and inhabits mainly host burrows and nests, whereas Ixodes ricinus occurs mainly during the warmer seasons, occupies a large variety of habitats and quests for hosts outside their shelters. In I. ricinus, the models with k values calculated from Taylor's power law overestimated prevalences. However, if moment estimates of k corrected for host number were used instead, expected prevalences of both larvae and nymphs I. ricinus in either host did not differ significantly from observed prevalences. In contrast, prevalences of larvae and nymphs of I. trianguliceps predicted by models using parameters of Taylor's power law did not differ significantly from observed prevalences, whereas the models with moment estimates of k corrected for host number in some cases under-estimated relatively lower larval prevalences and over-estimated relatively higher larval prevalences, but predicted nymphal prevalences well.