Ixodid (hard) ticks play important ecosystem roles and have significant impacts on animal and human health via tick-borne diseases and physiological stress from parasitism. Tick occurrence, abundance, behavior, and key life-history traits are highly influenced by host availability, weather, microclimate, and landscape features. As such, changes in the environment can have profound impacts on ticks, their hosts, and the spread of diseases. Researchers interested in enumerating questing ticks attempt to integrate this heterogeneity by conducting replicate sampling bouts spread over the tick questing period as common field methods notoriously underestimate ticks. However, it is unclear how (or if) tick studies account for this heterogeneity in the modeling process. This step is critical as unaccounted variance in detection can lead to biased estimates of occurrence and abundance. We performed a descriptive review to evaluate the extent to which studies account for the detection process while modeling tick data. We also categorized the types of analyses that are commonly used to model tick data. We used hierarchical models (HMs) that account for imperfect detection to analyze simulated and empirical tick data, demonstrating that inference is muddled when detection probability is not accounted for in the modeling process. Our review indicates that only 5 of 412 (1%) papers explicitly accounted for imperfect detection while modeling ticks. By comparing HMs with the most common approaches used for modeling tick data (e.g., ANOVA), we show that population estimates are biased low for simulated and empirical data when using non-HMs, and that confounding occurs due to not explicitly modeling factors that influenced both detection and abundance. Our review and analysis of simulated and empirical data shows that it is important to account for our ability to detect ticks using field methods with imperfect detection. Not doing so leads to biased estimates of occurrence and abundance which could complicate our understanding of parasite-host relationships and the spread of tick-borne diseases. We highlight the resources available for learning HM approaches and applying them to analyzing tick data.

Methods

To illustrate the problems that arise from not accounting for the detection process while estimating tick abundance, we performed two simulations that mirrored tick dragging studies and used common statistical frameworks for modeling tick data. For both simulations, we chose 5 temporal replicate surveys of 100 plots and specified a positive relationship of temperature on abundance and detection probability; average abundance (λ) was arbitrarily set to 20 ticks. Our choice of replicate surveys is a common field design for studying ticks (Dobson, 2013), and environmental factors such as temperature influence tick abundance and activity (Gilbert, 2021; Klarenberg and Wisely, 2019) and are often used to model tick abundance. For our first simulation, we specified low detection probability (ρ = 0.2) as tick dragging surveys often only collect ~10–20% of questing ticks (Drew and Samuel, 1985; Nyrhilä et al., 2020). We assumed perfect detection (ρ = 1) for our second simulation, meaning that all ticks would be captured by dragging or flagging surveys if they were present.

We simulated count data arising from a negative binomial distribution using the 'simNmix' function from AHMbook R package (Kéry et al., 2022) as tick abundance data often have a high variance-to-mean ratio due to aggregated and high counts (Elston et al., 2001). Following simulations, we estimated abundance and evaluated relationships between average seasonal temperature and tick abundance using 3 common approaches for modeling tick count data (linear models [LM], generalized linear models [GLM], and generalized linear mixed-effects models [GLMM]). For the LM analysis, we added 1 to the tick counts and log-transformed counts to meet assumptions of normality. This approach, although problematic, is a standard method to force count data into a linear modeling framework (O’Hara and Kotze, 2010) and common in tick studies (e.g., Allen et al., 2019). For the GLM and GLMM analyses, we used the raw counts and specified models with negative binomial errors. We used the ‘lm’ and ‘glm’ functions in the base R package for the LM and GLM analyses, respectively, and the ‘glmmTMB’ function in the glmmTMB R package (Brooks et al., 2017) for the GLMM analysis.

To highlight the shortcomings of the preceding analytical approaches, we compared inference with an N-mixture or binomial mixture model – a type of HM that is often used for estimating abundance when count data are imperfectly detected (Kéry and Royle, 2015). We fit the N-mixture model using the ‘pcount’ function in the unmarked R package (Fiske and Chandler, 2011) and specified average temperature across all sampling occasions as a covariate on abundance (λ) and temperature during each sampling occasion as a covariate on detection probability (ρ).

We then evaluated how well each statistical approach recovered average abundance (λ = 20) and relationships between average seasonal temperature and abundance when detection is assumed to be imperfect (ρ = 0.2) and perfect (ρ = 1). All simulations and statistical analyses were performed using R software (R Core Team, 2022), and predictive plots were created using the ggplot2 R package (Wickham, 2016).

References

Allen, D., Borgmann-Winter, B., Bashor, L., Ward, J., 2019. The density of the Lyme disease vector Ixodes scapularis (blacklegged tick) differs between the Champlain Valley and Green Mountains, Vermont. Northeast. Nat. 26, 545–560. https://doi.org/10.1656/045.026.0307

Brooks, M.E., Kristensen, K., van Benthem, K.J., Magnusson, A., Berg, C.W., Nielsen, A., Skaug, H.J., Mächler, M., Bolker, B.M., 2017. glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. R J. 9, 378–400. https://doi.org/10.32614/rj-2017-066

Dobson, A.D.M., 2013. Ticks in the wrong boxes: Assessing error in blanket-drag studies due to occasional sampling. Parasites and Vectors 6, 1–6. https://doi.org/10.1186/1756-3305-6-344

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Gilbert, L., 2021. The impacts of climate change on ticks and tick-borne disease risk. Annu. Rev. Entomol. 66, 273–288. https://doi.org/10.1146/annurev-ento-052720-094533

Kéry, Marc, Royle, J.A., Meredith, M., 2022. AHMbook: Functions and Data for the Book “Applied Hierarchical Modeling in Ecology” Vols 1 and 2.

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Klarenberg, G., Wisely, S.M., 2019. Evaluation of NEON data to model spatio-temporal tick dynamics in Florida. Insects 10. https://doi.org/10.3390/insects10100321

Nyrhilä, S., Sormunen, J.J., Mäkelä, S., Sippola, E., Vesterinen, E.J., Klemola, T., 2020. One out of ten: low sampling efficiency of cloth dragging challenges abundance estimates of questing ticks. Exp. Appl. Acarol. 82, 571–585. https://doi.org/10.1007/s10493-020-00564-5

O’Hara, R.B., Kotze, D.J., 2010. Do not log-transform count data. Methods Ecol. Evol. 1, 118–122. https://doi.org/10.1111/j.2041-210x.2010.00021.x

R Core Team, 2022. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/. R Found. Stat. Comput. Vienna, Austria. URL http//www.R-project.org/.

Wickham, H., 2016. ggplot2: Elegant graphics for data analysis, First Ed. ed. Springer, New York, NY. https://doi.org/https://doi.org/10.1007/978-0-387-98141-3