Large-Scale Model-Based Assessment of Deer-Vehicle Collision Risk

Ungulates, in particular the Central European roe deer Capreolus capreolus and the North American white-tailed deer Odocoileus virginianus, are economically and ecologically important. The two species are risk factors for deer–vehicle collisions and as browsers of palatable trees have implications for forest regeneration. However, no large-scale management systems for ungulates have been implemented, mainly because of the high efforts and costs associated with attempts to estimate population sizes of free-living ungulates living in a complex landscape. Attempts to directly estimate population sizes of deer are problematic owing to poor data quality and lack of spatial representation on larger scales. We used data on 74,000 deer–vehicle collisions observed in 2006 and 2009 in Bavaria, Germany, to model the local risk of deer–vehicle collisions and to investigate the relationship between deer–vehicle collisions and both environmental conditions and browsing intensities. An innovative modelling approach for the number of deer–vehicle collisions, which allows nonlinear environment–deer relationships and assessment of spatial heterogeneity, was the basis for estimating the local risk of collisions for specific road types on the scale of Bavarian municipalities. Based on this risk model, we propose a new “deer–vehicle collision index” for deer management. We show that the risk of deer–vehicle collisions is positively correlated to browsing intensity and to harvest numbers. Overall, our results demonstrate that the number of deer–vehicle collisions can be predicted with high precision on the scale of municipalities. In the densely populated and intensively used landscapes of Central Europe and North America, a model-based risk assessment for deer–vehicle collisions provides a cost-efficient instrument for deer management on the landscape scale. The measures derived from our model provide valuable information for planning road protection and defining hunting quota. Open-source software implementing the model can be used to transfer our modelling approach to wildlife–vehicle collisions elsewhere.

Deer-vehicle collisions. Data on wildlife-vehicle collisions in Bavaria are maintained in a central database by the Bavarian State Home Office. The database contains standardized information on all accidents caused by wildlife crossings that have been reported to the local police. Note that not only records of actual collisions with wildlife are contained in the database but also records of accidents induced by wildlife, such as collision with a tree while trying to avoid a collision with deer. The data are grouped according to the following species or groups of species: • hares and rabbits    • identifier of municipality in which the accident was reported • road type (motorway; primary, secondary, tertiary road; or residential street) • road number (for motorways, and primary, secondary, and tertiary roads) or name of the residential street • accident location as a chainage, i.e., distance in kilometers from a reference point, which is the point 0 for the particular road.
For all roads except residential streets, we computed Gauss-Krueger coordinates of the accident location based on the road number and chainage using the Bavarian Road Information System 1 . We first converted the chainages given in the database to the new station-based chainage system (i.e., a system with multiple reference points along one road, termed "OKSTRA"). In a second step, Gauss-Krueger coordinates were obtained 2 .
Using points in polygon algorithms implemented in the GRASS geographical information system 3 , the municipality in which each accident took place was determined.
Most accidents occurred in the municipality in which they were reported. However, accidents that took place in larger unpopulated areas (in German "gemeindefreie Gebiete") were usually reported in one of the neighboring municipalities. For our analyses, we assigned accidents to the municipality in which they actually occurred.
Our final data set consists of the number of accidents (those involving multiple vehicles were counted only once) for each municipality that is crossed by any road, grouped according to the road type (motorway primary, secondary, or tertiary roads; and residential streets) and year (2006 and 2009).
The usefulness of DVC data could be improved by better documentation of the accidents. The accident location can be more precisely recorded when the new chainage system (OKSTRA) is implemented in the DVC database. It would be additionally helpful if the species involved in an accident and ideally the sex of the animal could be recorded precisely. Continuous access to DVC databases will allow a constant data flow to be established and thus timely information about management success.
Overall, the number of accidents in 2009 was higher than in 2006. Figure S1 4 shows The total lengths of the different road types within each municipality was computed from the official road map using GRASS. The results were checked against Open-StreetMap 4 data. As expected, the results were virtually equivalent for larger roads but not for residential streets. Our reported results are based on the official road map.
Climate and land use data. Based on the merged forest areas within a municipality, we calculated the total length of forest edges using FRAGSTAT 3.3 [5]. Browsing data. The amount of ungulate browsing in Bavaria is monitored on a regular basis by the Bavarian Forest Administration [2,3]. The number of trees in each grouping surveyed is given in Table S1 1. For each game management district and group of tree species, the proportion of browsed trees is reported by the authorities as a measure of browsing intensity. Here, we used slightly smoothed estimates that take into account the status of trees in the neighboring game management districts.

Results
The following R code and data was used to fit models (1) and (2)  > rdata$offset <-predict(mod0, type = "link") > ### fit deviation from model (1) The selection frequencies obtained via the stability selection procedure are given in Table S1 2.
The contributions of climate, land use, browsing, and spatial heterogeneity to the DVC index index are shown in Figs. S1 9, S1 10, S1 11, and S1 12. shows the classification into seven risk classes based on the k-means classification method. Figure S1 10. Contribution of browsing intensity to the DVC index. The map shows the classification into seven risk classes based on the k-means classification method. Figure S1 11. Contribution of climate, land use, and browsing variables to the DVC index.
The map shows the classification into seven risk classes based on the k-means classification method. Figure S1 12. Spatial heterogeneity contributing to the DVC index. The map shows the classification into seven risk classes based on the k-means classification method.