2.3 MaxEnt modelling

We used the open source software package MaxEnt v.3.4.4, which can be downloaded from http://biodiversity informatics.amnh.org/open_source/maxent/ (Sun et al., 2020). Francois’ langur occurrence records and environmental variables were imported into MaxEnt. All models were set random seeds and used 75% of the record data as the training set and the remaining 25% as the test set with 10 replicates and bootstrap as replicated run type (Wang et al., 2020), while the number of modelling iterations was set at 10000 to allow the models to have adequate time for convergence (Young et al., 2011). The jackknife test procedure was used to evaluate the relative importance of each environmental variable. The response curves of environmental variables were used to test the correlation between the variables and the occurrence probability of Francois’ langur. Logistic was selected to output results. The default options were used for the other parameters.

2.4 Model evaluation and validation

Receiver operating characteristic (ROC) curve analysis is an effective method for evaluating the accuracy of species distribution models (Liu et al., 2022; Wang et al., 2007). We used the area under the ROC curve (AUC), which is a threshold-independent discrimination metric that represents the probability that a random presence or absence is correctly assigned by the model (Phillips et al., 2006). The AUC values range from 0.5 to 1.0, with AUC > 0.9 indicating excellent performance (Janitza et al., 2013).

The mean value of the 10 replicates from the model was taken as the distribution result, and the value represent habitat suitability index (HSI), which was between 0 and 1. The ASCII output file from MaxEnt was transformed into a raster layer, which was reclassified using the Spatial Analyst tool. At present, the classification of suitable habitat areas is largely based on experience, and there is no unified standard (Sun et al., 2020). We used the Jenks’ natural breaks classification in ArcGIS combined with maximum training sensitivity plus specificity (Max TSS), balance training omission, predicted area and threshold value (average TPT) in the MaxEnt output to reclassify the data into four suitability areas for Francois’ langur: high habitat suitability, moderate habitat suitability, low habitat suitability, and unsuitable habitat. The spatial analysis tool in ArcGIS 10.2 was used to calculate the areas and proportions of each suitability area.

2.5 Changes in potential distribution and centroid shifts

To construct the core distribution shifts and potential area changes under each future climate model, binary suitable or unsuitable maps were produced using ArcGIS 10.2 to analyse the changes in centroid and potential distributions based on the threshold of unsuitable area. By comparing the suitable/unsuitable potential distributions in different time periods, a total of four types of distribution changes were determined, namely, contraction, expansion, no change and no occupancy (Jose & Po, 2020; Liu et al., 2022). Moreover, because the potential distribution of Francois’ langur was scattered and its outline was irregular, centroid shift analysis was conducted based on the potential distribution under different time periods using SDMtoolbox v2.4 (Brown, 2014) to visually show the changing trends of the potential core distribution of Francois’ langur.