Ignoring species availability biases occupancy estimates in single-scale occupancy models

1. Most applications of single-scale occupancy models do not differentiate
between availability and detectability, even though species availability
is rarely equal to one. Species availability can be estimated using
multi-scale occupancy models, and the availability process includes
elements of species movement, behavior, and phenology. However, for the
practical application of multi-scale occupancy models, it can be unclear
what a robust sampling design looks like and what the statistical
properties of the multi-scale and single-scale occupancy models are when
availability is less than one. 2. Using simulations, we explore the
following common questions asked by ecologists during the design phase of
a field study: (Q1) what is a robust sampling design for the multi-scale
occupancy model when there are a priori expectations of parameter
estimates?, (Q2) what is a robust sampling design when we have no
expectations of parameter estimates?, and (Q3) can a single-scale
occupancy model with a random effects term adequately absorb the extra
heterogeneity produced when availability is less than one and provide
reliable estimates of occupancy probability?. 3. Our results show that
there is a tradeoff between the number of sites and surveys needed to
achieve a specified level of acceptable error for occupancy estimates
using the multi-scale occupancy model. We also document that when species
availability is low (< 0.40 on the probability scale), then
single-scale occupancy models underestimate occupancy by as much as 0.40
on the probability scale, produce overly precise estimates, and provide
poor parameter coverage. This pattern was observed when a random effects
term was and was not included in the single-scale occupancy model,
suggesting that adding a random-effects term does not adequately absorb
the extra heterogeneity produced by the availability process. In contrast,
when species availability was high (> 0.60), single-scale occupancy
models performed similarly to the multi-scale occupancy model. 4. As a
companion, we provide an RShiny app that allows users to further explore
our results and sampling designs across a number of different scenarios
https://gdirenzo.shinyapps.io/multi-scale-occ/. Our results suggest that
unaccounted for availability can lead to underestimating species
distributions when using single-scale occupancy models, which can have
large implications on ecological inference and predictions for
practitioners, such as those working at the front lines of invasion
ecology, disease emergence, and species conservation.