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

Abstract

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; 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. 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? 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. Users can further explore our results and sampling designs across a number of different scenarios using the RShiny app 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 inference and prediction, especially for those working in the fields of invasion ecology, disease emergence, and species conservation.

A practical guide to understanding and validating complex models using data simulations

“…The process for simulating data to determine statistical properties is identical to the process of simulating data for a basic validation above, except 100 s to 1000s of unique simulated datasets are generated using the estimated parameter values () rather than the single dataset (e.g. DiRenzo, Miller, et al, 2022; Rossman et al, 2016; Tingley et al, 2020).…”

“…However, it is also important to understand the effect of model misspecification, which occurs when the data generating model does not match the model used for statistical analysis (e.g. Dennis et al, 2019; Dey et al, 2022; DiRenzo, Miller, et al, 2022). Examples include cases where the dataset has extra sources of heterogeneity, there are distributional mismatches between the statistical model and the data generating model, or extra explanatory variables are not included in the statistical model.…”

“…A ‘full simulation study’ means that 100s to 1000s of simulations are performed, and Monte Carlo methods can be used to understand estimator properties of the simulated datasets, which ought to resemble the observed dataset in hand (e.g. DiRenzo, Miller, et al, 2022; Rossman et al, 2016; Tingley et al, 2020).…”

“…Typically, a finite set of values across the range of the parameters are chosen, and many datasets (from 100s to 1000s) are simulated at each of these values. Alternatively, ‘space‐filling’ designs can be used to sample across many combinations of parameter values (Carnell, 2022; DiRenzo, Miller, et al, 2022).…”

An operational workflow for producing periodic estimates of species occupancy at large scales

“…Our experience is that the parameters of this function are not mutually identifiable; hence, we have explored modelling phenology using a Gaussian distribution, in which the mean and standard deviation of detection dates are estimated. The Gaussian function is suitable for many species with annual life-cycles, but not for long-lived or multi-voltine species, in which case a different formulation is required, perhaps involving splines (Crainiceanu et al, 2005) or via additional levels of the hierarchy (Direnzo et al, 2021). Finally, detection is more likely on sites with abundant populations: ignoring this variation can lead to biased estimation in occupancy models (Royle and Nichols, 2003).…”