Multi-Species Occupancy Model (MSOM)
Species occupancy and detection were estimated using Multi-Species
Occupancy Models (MSOM; Iknayan et al. , 2014). Similarly to
single-species occupancy models (MacKenzie et al. , 2002), MSOM
uses repeated surveys (Winkler extractions) to tease apart the real
absences of species from detection errors (false zeroes), and therefore
estimates species presence even in those patches where they went
undetected. By estimating detection and occupancy rates for each
species, the model provides unbiased estimates of species presence in
each patch (unlike naïve/raw observations of presence; Tingley et
al. , 2020). MSOM also combines the detection and occupancy of all
species into a single model and, similarly to mixed-effects models,
estimates the variability among species (random effects) in their
detection, occupancy, and the effect of covariates on these rates. By
estimating the overall parameters (fixed effects; hyperparameters) and
the variability in model coefficients across species in the community
(random effects) in a single model, MSOMs provide (1) more precise
estimates of species detection and occupancy of individual species
compared to simpler single-species models (rare species borrow strength
from common species), (2) high-precision estimates of the number of
missing species in each patch and regionally (alpha and gamma richness
estimators; Tingley et al. , 2020), and (3) correct measures of
similarity in species composition (Jaccard) while taking into account
imperfect detection (beta-diversity estimator; see Chao et al. 2005 for
the implications of imperfect detection on beta-diversity).
To estimate the number of missing species across the landscape (gamma
richness estimator), we used a data augmentation approach by adding 300
species with zero occurrences in the data (Iknayan et al. 2014). These
represent species potentially present at the landscape that went
completely missing in the study due to detection errors. As the number
of missing species estimated by the model was much lower than the 300
additional species included (see Results), the inclusion of more than
300 species did not change the results.
In addition to using the MSOM, we also conducted Mixed-Effects Models
using species presences/absences within patches as the response
variable. These models used raw data assuming no detection errors. The
predictor variables included patch size, landscape area, connectivity,
and cattle presence. Species were included as random factors for
intercepts and all slopes. Most of the model results were qualitatively
similar to the MSOMs, with species consistently showing positive
associations with habitat patch area. For a few species that exhibited
distinct patterns in the mixed-effects models, we ran single-species
occupancy models. However, we did not find significant and distinct
results from the MSOM, which indicates that differences among occupancy
models (including MSOM) and raw-data models (Mixed-Effects models) arise
primarily from changes in detectability among patches rather than true
changes in occupancy. Given that the MSOM provides corrected estimates
of diversity and occupancy, even for rare and unobserved species, we
only present results from this model in the main text (see Fig. S1 for
results of mixed-effects models).