Efficient Bayesian analysis of occupancy models with logit link functions

Melding wildlife surveys to improve conservation inference

Integrated models are a popular tool for analyzing species of conservation concern. Species of conservation concern are often monitored by multiple entities that generate several datasets. Individually, these datasets may be insufficient for guiding management due to low spatio-temporal resolution, biased sampling, or large observational uncertainty. Integrated models provide an approach for assimilating multiple datasets in a coherent framework that can compensate for these deficiencies. While conventional integrated models have been used to assimilate count data with surveys of survival, fecundity, and harvest, they can also assimilate ecological surveys that have differing spatio-temporal regions and observational uncertainties. Motivated by independent aerial and ground surveys of lesser prairie-chicken, we developed an integrated modeling approach that assimilates density estimates derived from surveys with distinct sources of observational error into a joint framework that provides shared inference on spatio-temporal trends. We model these data using a Bayesian Markov melding approach and apply several data augmentation strategies for efficient sampling. In a simulation study, we show that our integrated model improved predictive performance relative to models for analyzing the surveys independently. We use the integrated model to facilitate prediction of lesser prairie-chicken density at unsampled regions and perform a sensitivity analysis to quantify the inferential cost associated with reduced survey effort.

Fast Bayesian inference for large occupancy datasets

In recent years, the study of species' occurrence has benefited from the increased availability of large-scale citizen-science data. While abundance data from standardized monitoring schemes are biased toward well-studied taxa and locations, opportunistic data are available for many taxonomic groups, from a large number of locations and across long timescales. Hence, these data provide opportunities to measure species' changes in occurrence, particularly through the use of occupancy models, which account for imperfect detection. These opportunistic datasets can be substantially large, numbering hundreds of thousands of sites, and hence present a challenge from a computational perspective, especially within a Bayesian framework. In this paper, we develop a unifying framework for Bayesian inference in occupancy models that account for both spatial and temporal autocorrelation. We make use of the Pólya-Gamma scheme, which allows for fast inference, and incorporate spatio-temporal random effects using Gaussian processes (GPs), for which we consider two efficient approximations: subset of regressors and nearest neighbor GPs. We apply our model to data on two UK butterfly species, one common and widespread and one rare, using records from the Butterflies for the New Millennium database, producing occupancy indices spanning 45 years. Our framework can be applied to a wide range of taxa, providing measures of variation in species' occurrence, which are used to assess biodiversity change.

Model selection in occupancy models: Inference versus prediction

Occupancy models are a vital tool for ecologists studying the patterns and drivers of species occurrence, but their use often involves selecting among models with different sets of occupancy and detection covariates. The information-theoretic approach, which employs information criteria such as Akaike's information criterion (AIC) is arguably the most popular approach for model selection in ecology and is often used for selecting occupancy models. However, the information-theoretic approach risks selecting models that produce inaccurate parameter estimates due to a phenomenon called collider bias, a type of confounding that can arise when adding explanatory variables to a model. Using simulations, we investigated the consequences of collider bias (using an illustrative example called M-bias) in the occupancy and detection processes of an occupancy model, and explored the implications for model selection using AIC and a common alternative, the Schwarz criterion (or Bayesian information criterion, BIC). We found that when M-bias was present in the occupancy process, AIC and BIC selected models that inaccurately estimated the effect of the focal occupancy covariate, while simultaneously producing more accurate predictions of the site-level occupancy probability than other models in the candidate set. In contrast, M-bias in the detection process did not impact the focal estimate; all models made accurate inferences, while the site-level predictions of the AIC/BIC-best model were slightly more accurate. Our results show that information criteria can be used to select occupancy covariates if the sole purpose of the model is prediction, but must be treated with more caution if the purpose is to understand how environmental variables affect occupancy. By contrast, detection covariates can usually be selected using information criteria regardless of the model's purpose. These findings illustrate the importance of distinguishing between the tasks of parameter inference and prediction in ecological modeling. Furthermore, our results underline concerns about the use of information criteria to compare different biological hypotheses in observational studies.

Community confounding in joint species distribution models

Joint species distribution models have become ubiquitous for studying species-environment relationships and dependence among species. Accounting for community structure often improves predictive power, but can also affect inference on species-environment relationships. Specifically, some parameterizations of joint species distribution models allow interspecies dependence and environmental effects to explain the same sources of variability in species distributions, a phenomenon we call community confounding. We present a method for measuring community confounding and show how to orthogonalize the environmental and random species effects in suite of joint species distribution models. In a simulation study, we show that community confounding can lead to computational difficulties and that orthogonalizing the environmental and random species effects can alleviate these difficulties. We also discuss the inferential implications of community confounding and orthogonalizing the environmental and random species effects in a case study of mammalian responses to the Colorado bark beetle epidemic in the subalpine forest by comparing the outputs from occupancy models that treat species independently or account for interspecies dependence. We illustrate how joint species distribution models that restrict the random species effects to be orthogonal to the fixed effects can have computational benefits and still recover the inference provided by an unrestricted joint species distribution model.