Occupancy modeling
We used program PRESENCE (2.12.33) to obtain the occupancy of leopards (MacKanzie et al., 2002). The naïve occupancy was calculated by dividing the no. of grids with species present/total number of grids surveyed in the block. The leopards can travel greater than the size of our replicate (2km) per day, hence the detection of the sign in successive spatial replicates violates the statistical independence required by the standard occupancy model (MacKenzie et al., 2017). The spatial correlation model (Hines et al., 2010) accounts for this correlation in the detection using the Markov spatial dependence approach. For the degree of dependence between the replicated samples, the model uses replicate level occupancy parameters ‘θ0’ and θ1, where ‘θ0’= Pr (leopard presence in a replicate/grid occupied and which was absent in the previous replicate) and ‘θ1’= Pr (leopard presence in a replicate/ grid occupied and was present in the previous replicate). We also checked the performance of the standard occupancy model (MacKenzie et al., 2002) and spatial correlation model (Hines et al., 2010) without adding any covariates in our data. We compared these models based on the Akaike Information Criterion (AIC) value as our no. of grids (>200) and replicates were adequate (replicate=16) (Burnham & Anderson, 2002). It clearly showed the correlation in sign detection on 2km long replicates. The AIC value for the spatial correlation model was less than the standard occupancy model indicating better performance by the former model (Supplementary file 1). Hence, all other analysis was performed using this model.
The sample covariates collected from the field survey included prey species, PS= (Barking Deer, Wild boar, Chital, and Rhesus), human disturbance (HD= looping, human encroachment), and livestock presence (L). We separated the wild boar (W) from other prey species because many studies reported leopards avoiding the wild boar (Karanth & Sunquist, 1995; Ramakrishnan et al., 1999) and we wanted to know how wild boar affects the presence of a leopard. Moreover, the occurrence of wild boar was the most widespread among the prey species.
The site covariates were management regime (IO = inside or outside of the national park), vegetation cover measured as NDVI- Normalized Difference Vegetation Index (N), terrain ruggedness index (R), and human population density (PD). If a grid falls more than half inside the national park or buffer zone, it was coded as ‘1’ and ‘0’ if it falls outside. The human population density was obtained from the Gridded Population of the World Version 4 (GPWv4) (CIESIN, 2018) and NDVI (2018) was obtained from the 250m resolution Medium Resolution Imaging Spectroradiometer (MODIS) satellite images of 2019 (Didan et al., 2015) available at https://earthexplorer.usgs.gov. Similarly, the terrain ruggedness index for each grid was calculated using 90m ASTER DEM (Fujusunda et al., 2005) in Arc GIS 10.1. We also included a sampling effort (SE) as a covariate that affects the detection probability. Before adding the covariates in our analysis, we tested the Spearman correlation coefficient (r) using PAST version (4.0) (Hammer et al., 2001). If /r/ >= 0.7 between covariates, one of the covariate is dropped off. Here, the correlation between the covariates of human disturbance (lopping and encroachment) and livestock were more than 0.7 (Supplementary file 3). Because of the contribution of livestock in leopard’s diet, we selected livestock and removed human disturbance to obtain the final model (Kshettry et al., 2018; Reynaert, 2018; Kandel et al. 2020).The data were prepared in an excel sheet via creating detection history for the leopard and their prey and livestock detection across all the grids, having 16 replicates each. On each replicate, the detection of the species was coded 1 and non-detection was coded 0. The site covariates were constant in each grid and we applied z-transformation to normalize the site covariate data. We defined the global model as follow:
Global [(Ψ) (IO, R, N, PD, PS, W, L), θ0 (.), θ1 (.), Pt (SE, IO, R, N, L)].
We identified the suitable covariates on the basis of ecological importance, a recommendation from previous studies, and simplest explanation of model (parsimony). We used a constant model for replicate level occupancy parameters (θ0 and θ1) (Karanth et al., 2011).
We also could not ignore the possibilities that some of the covariates or other unknown factors influencing the leopard presence contribute to variation in the leopard abundance and hence influence the replicate level detectability (Pt). To address this, our occupancy model focused on identifying the suitable covariate model structure for Pt from sample effort (SE), management type (IO), ruggedness (R), vegetation cover (N), and livestock (L). Then the suitable model structure of Pt was kept constant and Ψ was varied for the top covariate model structure on grid level occupancy. We identified top competitive models that fit the data well with delta AIC<2. From these top competitive models, we estimated the grid specific occupancy rate, the total fraction of Chure occupied by the leopard, replicate level occupancy parameters (‘θ0’ and θ1) and other parameters using the model averaging. We applied the parametric bootstrapping to the untransformed β parameter from the top models via simulating 1000 random deviate to obtain the standard deviation of the mean (MacKenzie et al., 2017, StatDisk 13: Triola Stats, https://www.triolastats.com/).