Data from: Improving inferences and predictions of species environmental responses with occupancy data

Occupancy models represent a useful tool to estimate species distribution
throughout the landscape. Among them, MacKenzie et al.’s model (2002, MC),
is frequently used to infer species environmental responses. However, the
assumption that detection probability is homogeneous or fully explained by
covariates may limit its performance. Species should be more easily
observed at sites with a higher number of individuals. We simulated data
following Royle and Nichols (2003) occupancy model (RN) that accounts for
abundance-driven heterogeneous detection and two variants with
overdispersion in the detection probability and local abundances. Then, we
compared the performance of the MC model against that of RN.  In
addition to model misspecifications, insufficient information in data
(i.e. infrequent detections) can limit our ability to detect existing
effects with affordable sampling designs. To deal with this source of
error, we extended RN approach to a community-level joint species model
(RN-JSM), where species responses and detectability depended on their
traits and phylogeny. Then, we tested RN-JSM performance in simulated and
out-of-sample field data. High abundance-driven heterogeneity in detection
(i.e. common and secretive species) limited the ability of the MC model to
quantify covariate effects; especially, when the number of visits was low.
Both models (MC and RN), often failed to detect existing effects when data
were overdispersed. Moreover, the RN model consistently lacked sufficient
power when analyzing data from uncommon species (even when simulations and
model specifications perfectly matched). This problem was solved by our
RN-JSM, which yielded more precise and accurate estimates of species
environmental responses. Increased accuracy in rare species held when the
RN-JSM was tested with real and out-of-sample datasets. In the light of
our results, we propose: (i) for common and secretive species analyze
occupancy data with the RN model and prioritize revisiting sites; (ii) for
species that may have overdispersed detectability or local abundances
(e.g. with correlated behaviors or occurring in clusters), apply RN
extensions that account for this extra variation (e.g. Poisson-beta or
zero-inflated models). Finally, (iii) for uncommon species (mean
abundances < 1), whenever possible, gather data at the community
level and apply joint-species modeling techniques.