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/).