Statistical analysis
We assessed the effect of the accessibility to agricultural crop fields from the location of deer killed on the δ15N values of bone collagens (i.e., the relative dietary contribution of crops). We aggregated the area (m2) of agricultural crop fields by the ‘1 × 1 km mesh (the third mesh)’, a national grid system of Japan with a unit cell size of 30″ in latitude and 45″ in longitude (c. 1 × 1 km) using GIS software (ArcGIS Desktop 10.4.1). The classification of landscape elements in the study area was based on the most recent vegetation/land use map available on J-IBIS (Ministry of the Environment, 1999). As mentioned above, we classified both crop fields and sown grasslands as agricultural crop fields because deer consume vegetables and pasture grasses in the area (Tsukada et al., 2012; Nagano Prefecture, 2016; Hata et al., 2019).
Accessibility to agricultural crop fields was expressed using an accessibility index defined by the incidence function model (IFM, Hanski, 1994). The IFM is a useful measure of connectivity that incorporates both areas of potentially accessible patches (i.e., crop field in 1 × 1 km grid cells) and the distance to these patches. We considered that the IFM would be more suitable than simpler indices such as the distance to nearest agricultural crop fields and per cent agricultural crop fields within a buffer radius because the IFM is based on a realistic assumption that deer individuals can access agricultural crop fields at multiple grid cells within their home ranges, and incorporates smooth distance decay in accessibility. Because the migratory behavior and dispersal pattern can vary according to sex (Takii et al., 2012b), separate models were generated for males and females. The following model was constructed to evaluate the effect of the accessibility to crop fields on the δ15N values in female deer:
yi = β 0 +β 1Σj exp(−αdij )Aj+β 2C +ei
where yi is the i th δ15N value of bone collagen, reflecting the feeding history over several years or the lifespan of the individual (Stenhouse & Baxter, 1979; Hedges et al., 2007; Koch, 2007). This parameter was used as the relative dietary contribution of crop of each deer individual. The accessibility index was defined by Σj exp(−αdij )Aj, where α is a parameter controlling for mobilization ability with respect to distance (i.e., small α meaning slow distance decay). It is a special case of the original IFM (Hanski, 1994), Σj exp(−αdij )Ajβ, when β = 1, assuming linearity between the area of the crop field and the amount of accessible resource (i.e. agricultural crop) in the field. The straight-line distance between the i th location of deer killed and mesh j was denoted by dij , and the crop field area of the j th grid cell was denoted byAj . Because agricultural crops are often used for baits (Kilpatrick et al., 2010; Ikeda et al., 2018), crop-foraging deer may be more familiar with trapping baits and more likely to consume them; that is, the δ15N values may be higher for deer killed by trapping than by shooting. Therefore, we added the method of culling (C ) as a confounding factor (set to 1 for shooting and 0 for trapping) to the female model. β 0,β 1, and β 2 are the intercept, the coefficient for Σj exp(−αdij )Aj and the coefficient for C , respectively.ei is an error term following a normal distribution. The values of ln(α), β 0,β 1, and β 2 were estimated using the maximum likelihood method. We estimated log-transformed α to ensure that α > 0. Because male deer were killed by trapping only, C was excluded in the male model. All statistical analyses were performed using R for Windows 3.5.2 (R Development Core Team, 2018).