A unifying theoretical framework for tick-borne disease risk to explain conflicting results of exclosure experiments across scales

1 Abstract Disease ecology has focused greatly in recent decades on determining how changes to biodiversity may drive infectious disease risk for humans. Fencing off experimental areas (exclosures) has been a common experimental approach to assess how removing large-body size hosts may affect disease risk, especially with tick-borne pathogens (TBPs) such as those causing Lyme disease and tick-borne encephalitis. However, exclosure experiments have found conflicting results based on the scale of the experiment, with smaller exclosures tending to increase tick densities inside the exclosure (suggesting large incompetent mammal hosts produce a dilution effect) and larger exclosures tending to decrease tick densities inside (suggesting an amplification effect). Previously, we have lacked a unifying theoretical framework able to reconcile the results of exclosure experiments on multiple spatial scales. Here we present a spatially explicit model of TBP risk incorporating tick dispersal by small competent mammal hosts (rodents) which can enter the exclosure and by large incompetent mammal hosts (deer) which are excluded from the exclosure. Our model reproduces the scale-dependence observed in past exclosure experiments and neatly illustrates the mechanisms that cause it. Specifically, the modeled exclosure produces high densities of infected questing ticks near its boundary due to a dilution effect with deer, but the density drops off steeply moving into the exclosure’s center due to the limits of rodent-based tick dispersal. Though this contrasts with empirical results which have found lower tick densities at the exclosure’s edge than its center, we demonstrate that this contrasting pattern can also be produced if we additionally allow ticks in their free-living questing stage to disperse. We derive analytic expressions for our model’s resulting infected tick density gradients inside the exclosure, and encourage empiricists to test for such tick density gradients in future exclosure experiments rather than averaging measurements over the entire exclosure.