2.4 Data analysis
The percentages of the different plant species in the diet of each study group were calculated using the total feeding records. Similarly, the percentages of the different plant parts in the monthly diet of each study group were calculated using the monthly total feeding records. The Shannon-Wiener index was used to compare the food diversity index (FDI) of the langurs. The formula was as follows:
\(FDI=H^{\prime}=\sum_{i\ =\ 1}^{n}P_{i}\text{Ln}P_{i}\)
where H’ is the Shannon-Wiener diversity index, and \(P_{i}\) is the percentage of the feeding records of the plant species i . Similarly, the diet composition was expressed as the percentage of the feeding time spent on specific food items or food species.
Generalized linear mixed models (GLMMs) were used to examine the influence of season on the diet. Specifically, the number of food species per month and diversity index were tested as the response variables, the seasons were set as fixed factors, and the sample size was set as a random factor. Season was considered a key factor when it influenced the goodness-of-fit of the model and the p-value was lower than 0.05, which indicated a significant difference in the diet between the dry and rainy seasons.
Then, generalized linear models were constructed to examine the influence of ecological factors on the FAI, diet, and dietary diversity. The monthly food availability (including young leaves, flowers, fruits, and mature leaves) was set as the response variable, and climatic factors (including rainfall and temperature) were set as explanatory variables to test the impact of climatic factors on food provision. Similarly, the monthly food species and diversity index was set as the response variable, and food availability (including young leaves, flowers, fruits, and mature leaves), climatic factors (including rainfall and temperature), and diet composition (including young leaves, flowers, fruits, and mature leaves) were set as explanatory variables to examine the influences of diet composition and ecological factors on the langurs’ diet. The models considered all possible combinations of all the predictors (total ranked according to their Akaike information criterion [AIC] values). The relative importance of each predictor (Wip) was obtained by summing the Akaike weights for each model. The models with the lowest AIC values were considered to be the top models, and the models within two AIC units (ΔAIC ≤ 2) of the top models were considered to be highly supported (Burnham & Anderson, 2002). Model-averaged regression coefficients (β) with 95% confidence intervals were used to estimate the effect of each predictor in the models, and the predictors in the highly supported models were determined to be the most important factors affecting the response variables when their 95% confidence intervals for the β-values did not overlap with zero (Xu et al., 2017).
To improve linearity and normality, the numeric variables, such as food availability, were log10(X + 1)-transformed (Xu et al., 2017), and the variables expressed in percentages, such as the feeding time, were log (X + 0.00001)-transformed because the raw data for the nonfood species were zero (Warton & Hui, 2011). In addition, Spearman’s rank correlation was used to estimate the relationship among the variables. The normality of all the variables was examined using a one-sample Kolmogorov-Smirnov test. The GLMMs were performed using the lime4 package in R version 4.0.4 (R Core Team, 2021). The model averaging was performed using the dredge and model.avg function in the MuMIn package (Bartoń, 2019). All the analyses were conducted using R version 4.2.1. All the tests were two-tailed, with significance levels of 0.05 (R Core Team, 2023).