Model selection
To investigate potential factors influencing activity patterns
associated with the lunar cycle, we developed two models: a mixed
effects model to explore factors that might influence activity during
the lunar month, and a logistic mixed effects model to examine whether
the lunar cycle influences habitat preference or avoidance by leopard
and prey during the lunar cycle.
For the first model that explored lunar cycle activity, we examined
which factors were associated with an increase or decrease in activity
closer to the full moon phase (e.g., lunar phobic versus lunar philic).
To investigate this hypothesis, we used a Generalized Linear Mixed
Effects Model (GLMM) using only nocturnal data (activity predominantly
between 1 h after the sunset and 1 h before the sunrise), with temporal
activity events occurring during the full moon’ as the response variable
to check lunar phase influences on animals’ activities (Norris et al.,
2010). Wed also categorized seasons as either summer or winter as we
suspected that predators and prey may shift their activity in the
different seasons (Yang et al. 2019). In addition, there is an
ecologically significant factor which positively influences an animal’s
night and day activity called ‘Moonlight Risk Index’ (MRI) (Gigliotti
and Diefenbach, 2018, Searle et al., 2021). We calculated this index of
nocturnal luminosity by multiplying together the amount of the moon
illuminated, the proportion of time between sunset and sunrise that the
moon was above the horizon and their information taken from moonrise
software for each moon phase data stamped on camera trap images and the
inverse proportion of the sky covered in clouds between 0 (overcast) and
1 (clear) as an explanatory variable; clouds cover information data for
each capture event was taken from a free online data source in the
Heshun county in tieqiaoshan provincial nature reserve (TPNR) in Shanxi
province China (https://m.tianqi.com/lishi/heshun/201601.html) see
for more details in Table 1.
First, for all global models used in model 1 or 2, we checked for
multi-collinearity using the variance inflation factor (VIF), with
covariates eliminated from our model at VIF > 3, and using
Pearson correlation test, a variable was excluded when correlation
|r| > 0.7 with other covariates (Yang et
al., 2019). Second, we used super-ranked correlation test to check
leopard and prey temporal co-occurrence or avoidance. Third, the GLMMs
were fitted using the R package lme 4 and MuMIn (Yang et al., 2019).We
used stepAIC to select the most parsimonious model at delta AICc ≤ 2
(Zaman et al., 2019, Zaman et al., 2020b).
For the second model which explored circadian activity events during the
four different lunar phases for leopard and prey linked to habitat
factors, we considered four moon phase activity occurrence events of the
leopards and their prey species during the night and daytime into the
following three categories: (1) nocturnal, as defined above; (2)
diurnal, activity predominantly between 1 h after sunrise and 1 h before
sunset, and; crepuscular, 1 h before sunrise to 1 h after sunrise and 1
h before sunset to 1 h after sunset (Zhao et al., 2020). For example, if
a species was less active during the full moon or other lunar phase at
the nighttime (lunar phobic), we examined whether that species shifted
to being more active during daylight (full moon day or other moon
phases) hours to compensate for the time ‘lost’ by being less active at
night during the full moon phase. For each activity during night vs day
events, ROC was used to define the accuracy of a classification model at
the user-defined threshold value of 0.5 (Zaman et al., 2020b), and area
under the curve (AUC) score of ≤ 0.7 (Jiang et al., 2015) and also ran a
Shapiro–Wilk’s test and graphic examination of histograms were made to
confirm that the data were normally distributed. We used a Logistic
Generalized Linear Mixed Effects Model (GLMM) with the designation of
day or night activity capturing events during four moon phases only set
as the binary response variable (0 all moon phases of day, 1 all moon
phases of night, i.e., day vs. night ). Habitat factors were included as
explanatory variables and the camera trap identity was considered a
random effect in our model to differentiate between the effects of
non-dependent variables, removing when not a random effect (Yang et al.,
2019, Zaman et al., 2019, Zaman et al., 2020b) and packages rocr,
lmtest, car and package lme 4 and MuMIn were used for Logistic
Generalized Linear Mixed Effects Model (GLMM) and all the analysis were
computed in R statistical software V.3.5.1 package (www.r-project.org, R
Core Development Team 2018).