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).