Estimating Ixodes ricinus densities on the landscape scale
© Boehnke et al. 2015
Received: 21 April 2015
Accepted: 4 August 2015
Published: 14 August 2015
The study describes the estimation of the spatial distribution of questing nymphal tick densities by investigating Ixodes ricinus in Southwest Germany as an example. The production of high-resolution maps of questing tick densities is an important key to quantify the risk of tick-borne diseases. Previous I. ricinus maps were based on quantitative as well as semi-quantitative categorisations of the tick density observed at study sites with different vegetation types or indices, all compiled on local scales. Here, a quantitative approach on the landscape scale is introduced.
During 2 years, 2013 and 2014, host-seeking ticks were collected each month at 25 sampling sites by flagging an area of 100 square meters. All tick stages were identified to species level to select nymphal ticks of I. ricinus, which were used to develop and calibrate Poisson regression models. The environmental variables height above sea level, temperature, relative humidity, saturation deficit and land cover classification were used as explanatory variables.
The number of flagged nymphal tick densities range from zero (mountain site) to more than 1,000 nymphs/100 m2. Calibrating the Poisson regression models with these nymphal densities results in an explained variance of 72 % and a prediction error of 110 nymphs/100 m2 in 2013. Generally, nymphal densities (maximum 374 nymphs/100 m2), explained variance (46 %) and prediction error (61 nymphs/100 m2) were lower in 2014. The models were used to compile high-resolution maps with 0.5 km2 grid size for the study region of the German federal state Baden-Württemberg. The accuracy of the mapped tick densities was investigated by leave-one-out cross-validation resulting in root-mean-square-errors of 227 nymphs/100 m2 for 2013 and 104 nymphs/100 m2 for 2014.
The methodology introduced here may be applied to further tick species or extended to other study regions. Finally, the study is a first step towards the spatial estimation of tick-borne diseases in Central Europe.
The study describes the estimation of the spatial distribution of questing tick densities using the example of Ixodes ricinus in Southwest Germany. Ixodes ricinus is the most well-known and studied European tick species transmitting various arthropod-borne diseases [1, 2]. Suitable habitats are found all over in Germany . The knowledge of the spatial distribution of tick densities is a key factor in quantifying the risk of tick-borne diseases such as tick-borne encephalitis, Lyme borreliosis, anaplasmosis, rickettsiosis, and others.
Previous studies on the spatial distribution of ticks mainly comprise the determination of the presence and absence of single or multiple species. Frequently, these tick data were exclusively published for selected sites, but recently more and more models for spatial interpolation or analysis have been developed. These spatial distribution models, also known as ecological niche models, are generally applied on a continental scale. Therefore, various statistical models to describe species habitats have been developed. An overview on models as well as methodological caveats in the modelling with examples for I. ricinus was described by Estrada-Peña and co-authors . Several applications focus on the projection of climate niche models to estimate future scenarios. These studies provide maps of suitability indices and presence/absence maps of both the present and the future distribution of I. ricinus, covering Europe and Northern Africa [4, 5].
A total of 25 sampling sites in Southwest Germany, in the federal state Baden-Württemberg, were selected according to their vegetation cover and tick habitat suitability. Ixodes ricinus was flagged over an area of 100 m2 each month from March to October for each site. These field data were used to develop a generalised linear model (Poisson regression) describing the total number of nymphal ticks at the different sampling sites, which were collected during 1 year by monthly flagging an area of 100 m2. Air temperature, air humidity, height above sea level and land cover classification were used as explanatory variables. These were preselected according to their biological relevance. Air temperature was selected, since thermal conditions determine the rate of tick development from stage to stage and activity patterns, which in turn influence survival success and population density [10, 14, 15]. This, and potentially other synergetic processes, leads to decreasing tick densities with increasing altitude . Ticks and other terrestrial vertebrates must maintain their body water balance to survive. In a subsaturated atmosphere, unavoidable body water losses in ticks occur, e.g., by discharging faeces and urine, by gas exchange, and via the cuticle. Saturation deficit, the difference between the saturation vapour pressure at 100 % relative humidity (at a given temperature) and the given vapour pressure, is to a large extent a measure of the drying power of the atmosphere and as such largely responsible for the rate of body water loss of a given tick in a given situation . Unfed ticks and some engorged ticks are capable of compensating suffered body water losses by active water vapour uptake when the ambient relative humidity surpasses a certain threshold, the so-called critical equilibrium humidity . As a consequence, both saturation deficit and relative humidity must be taken in consideration when investigating the influence of humidity on ticks (Olaf Kahl 2015, personal communication). The habitat type influences not only the microclimatic conditions, but also the host spectrum and abundance. Ixodes ricinus prefers woodland habitats such as broadleaved, mixed or coniferous forests [10, 15].
As a result, predictive models were applied to extrapolate the tick densities to the entire region of Baden-Württemberg. A spatial resolution of 30 arc seconds, corresponding to about 0.5 km2, was selected to depict maximum features of the tick density taking into account simultaneously the resolution of the climate data. Although the tick density maps were exclusively developed for I. ricinus, the method may be applied for other tick species as well.
Tick sampling and in situ measurements
Specification of the 25 sampling sites in Baden-Württemberg, Germany
Gridded environmental data
The gridded data are variables available on a high-resolution raster covering the entire study area. They were used to predict the spatial distribution of the tick density. Exclusively variables with biological significance for the life cycle of ticks were used [15, 25–28]. Figure 2 depicts these explanatory variables comprising the height above sea level, the CORINE land cover classification as well as the air temperature, relative humidity and saturation deficit.
Tick densities and environmental variables for the 25 sampling sites
The spatial resolution of the density map was selected to be 30 arc seconds, which corresponds to grid lengths of about 0.9 km (latitude) and 0.6 km (longitude). Climate variables described above have slightly lower resolutions and were disaggregated using the bi-linear interpolation of the R package raster [31, 32]. Categorical CORINE data, however, were provided with the higher resolution of 3 arc seconds. Therefore, they were aggregated to the 30 arc sec grid by selecting the most frequent land class within each grid box.
Predictive statistical model
While the height and the climate variables were integrated in the model as numerical values, the land cover is considered as a categorical variable (classes A, B, C and M). For all other land cover classes the tick density is known to be very low or even zero. They comprise urban areas and water bodies for which no tick density was estimated. McFadden’s pseudo R p 2 (the coefficient of determination R2, adapted for additional categorical variables such as LC) and the root mean square error (RMSE) were selected as goodness-of-fit measures. The final model was evaluated by leave-one-out cross-validation (LOOCV).
Summary of regression models for 2013 and 2014
Model for 2013
Model for 2014
To verify the Poisson regression model leave-one-out cross-validation (LOOCV) was applied . It is a special case of the well-known p-out cross-validation with p = 1 as appropriate for the sampling size of n = 25 (flagging sites). LOOCV calculates all possible combinations of models calibrated with 24 sampling sites, which were validated with the remaining 1 site not used for calibration. Typically, LOOCV results were expressed by verification measures such as the prediction residual error sum of squares (PRESS) or the root mean square error (RMSE). For 2013, a value of RMSE = 227 nymphs/100 m2 was calculated providing a more realistic error measure than RMSE = 110 nymphs/100 m2 calculated with the whole set of sampling sites (Fig. 3). Due to generally lower observed nymphal densities, LOOCV results in lower errors of RMSE = 104 nymphs/100 m2 in 2014.
So far only few landscape scale tick density maps, such as those of the nymphal density of I. pacificus in California , were published. The I. ricinus maps presented here (Fig. 4, Additional file 1) contribute to the development of tick density maps compiled with statistical models. The nymphal densities are to be interpreted as the number of nymphs obtained by monthly flagging of an area of 100 m2. As a consequence of the flagging method only active questing ticks are sampled. Further, the proportion of questing ticks compared to the overall population depends on weather conditions . Therefore, the questing tick densities are naturally lower than the actual densities [34, 35] and variable to a certain extend. This has to be taken into account by interpreting the results of the modelled nymphal densities. However, investigating only forests and forest-like habitats has a positive effect on the comparability of the results, since forest habitats provide comparable microclimatic conditions in contrast to other habitats such as meadows or clearances. Since forests offer very good survival conditions for I. ricinus ticks in Baden-Württemberg, modelled nymphal densities have to be interpreted as the upper end of the population density scale. Therefore, lesser population densities are to be expected in other habitats.
Uncertainties appeared in the modelling process, especially in the selection of explanatory variables. As suggested by experts , only biologically meaningful variables were considered instead of the frequently applied approach of reducing significant variables from a large set of possible explanatory variables. As a side effect, collinearities (e.g. between altitude and temperature) were estimated, which should be avoided in generally applicable models . Due to the low number of explanatory variables used in the model, this is, however, not possible without reducing the model’s performance. Thus, the biological significance was higher valuated than statistical features and no generally applicable regression parameters were given. Instead, the regression parameters were separately fitted for each year and must be fitted again if further years will be investigated. In so doing, the model is demonstrably usable for mapping, i.e. spatial interpolation, but could not be used to predict future scenarios.
The model performance was expressed by explained variances of R p 2 = 71.7 % for the model fitted with the data of 2013 and R p 2 = 46.1 % for the model of 2014 (Fig. 3), indicating a high reliability of the I. ricinus density maps (Figs. 4, 5, Additional file 1). The results should be evaluated with regard to the uncertainties in observed tick densities as well as the low number of explanatory variables used for modelling. As a verification measure independent from observations used to calibrate the models, LOOCV errors of RMSE = 227 nymphs/100 m2 for 2013 and RMSE = 104 nymphs/100 m2 for 2014 were estimated. These errors are of the order of the mean nymphal density or 20 % of the maximum nymphal density, thus twice of the error estimated during the calibration process (RMSE = 110 nymphs/100 m2 for 2013 and RMSE = 61 nymphs/100 m2 for 2014). For high nymphal densities these errors are comparable to the observational error, i.e. the accuracy of flagging. It should be noted that it is also possible to fit the model with in situ measurements (Additional file 2), although gridded variables must be used to compile geographical maps.
Since the original research project was designed to estimate the density and distribution of ticks on the one hand, and to estimate the pathogen infestation on the other hand, the previous site selection had a focus on habitats and regions where ticks are likely to be found. Therefore, only a few sites with low and zero tick numbers were selected. This leads to uncertainties in observed and modelled nymphal densities, respectively. The inclusion of additional field data from land cover classes and altitudes with low tick densities would improve future model predictions. Varying abundance of several hosts, i.e. deer as the dominant host species for female ticks and small mammals as hosts for immature stages, are also likely to influence tick densities . Future model improvements are expected by incorporating these data.
Two years of I. ricinus observations from 25 sampling sites in the federal state Baden-Württemberg were used to develop a Poisson regression model. This predictive model was applied to compile very high-resolution maps depicting the spatial distribution of nymphal tick densities for the study area of 35,750 km2. The accuracy of the mapped tick densities was described by explained variances for the model calibration and prediction errors for the estimation of un-sampled sites. For the latter LOOCV was applied, indicating the reliability of the density maps. Although the methodology introduced here was shown to be suitable for compiling tick density maps, it may not be applied to other study regions without deriving new regression coefficients. For the same reason an application to predict climate change scenarios may not be recommended. Although field data were collected monthly (see the seasonal cycles in Additional file 3), only annually accumulated tick densities were considered to reduce the influence of observational errors and overdispersion , i.e. high nymphal densities due to local aggregation not resolved at the landscape scale (sub-grid scale effect).
Finally, the study is a first step towards a risk estimation for tick-borne diseases in Central Europe. Following the theory of the basic reproduction number for tick-borne diseases , this risk depends—beside other parameters—on the vector density or more exactly on the vector to host ratio. Mapping the risk of tick-borne diseases is therefore a challenge for the future. For other arthropod-borne diseases, however, vector density and disease risk maps are well established as described for Bluetongue  or Rift Valley Fever .
The project was designed by TP and SN, the field data were collected and determined by DB, MP, NL, PS, RG and RO, the statistical analysis and modelling was designed by FR, the model was implemented and tested by DB, KB, KL, JR, MW and FR, and the paper written by DB, KB, SN, TP, MP, NL, KL and FR. All authors read and approved the final manuscript.
The study was financed by the Ministry of the Environment, Climate Protection and the Energy Sector with their support programme BWPLUS under project numbers BWZ 11001, 11005, 11006 and 11007, and the Graduate School for Climate and Environment (GRACE). We are grateful to Florian Hogewind for technical assistance and to Sebastian Schmidtlein for institutional support.
Compliance with ethical guidelines
Competing interests The authors declare that they have no competing interests.
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