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).