Joint species distribution models (JSDMs) are a recent development in biogeography and enable the spatial modelling of multiple species and their interactions and dependencies. However, most models do not consider imperfect detection, which can significantly bias estimates. This is one of the first papers to account for imperfect detection when fitting data with JSDMs and to explore the complications that may arise.

A multivariate probit JSDM that explicitly accounts for imperfect detection is proposed, and implemented using a Bayesian hierarchical approach. We investigate the performance of the JSDM in the presence of imperfect detection for a range of factors, including varied levels of detection and species occupancy, and varied numbers of survey sites and replications. To understand how effective this JSDM is in practice, we also compare results to those from a JSDM that does not explicitly model detection but instead makes use of  "collapsed data". A case study of owls and gliders in Victoria Australia is also illustrated.

Using simulations, we found that the JSDMs explicitly accounting for detection can accurately estimate intrinsic correlation between species with enough survey sites and replications. Reducing the number of survey sites decreases the precision of estimates, while reducing the number of survey replications can lead to biased estimates. For low probabilities of detection, the model may require a large number of survey replications to remove bias from estimates. However, JSDMs not explicitly accounting for detection may have a limited ability to disentangle detection from occupancy, which substantially reduces their ability to accurately infer the species distribution spatially. Our case study showed positive correlation between Sooty Owls and Greater Gliders, despite a low number of survey replications.

To avoid biased estimates of inter-species correlations and species distributions, imperfect detection needs to be considered. However, for low probability of detection, the JSDMs explicitly accounting for detection is data hungry. Estimates from such models may still be subject to bias. To overcome the bias, researchers need to carefully design surveys and choose appropriate modelling approaches. The survey design should ensure sufficient survey replications for unbiased inferences on species inter-dependencies and occupancy.

We gratefully acknowledge the assistance of Dr. Matt White and the Arthur Rylah Institute, Department of Environment, Land, Water and Planning (Victoria) for providing their field data for the Victorian Central Highland Owl and Glider Study.  

The species data was collected over 202 sites in the Central Highland area of Gippsland in Victoria, using call playback and spotlighting with a visual search along a 100m transect, by teams from the former Victorian Department of Environment, Land, Water and Planning (DEPI) \autocite{Lumsden2013}.  Surveys took place from March to August 2012 with two to three survey replications at each site. 

OwlGlider_SurveyData: 

Site occupancy data. The archive contains the values of the covariates at the survey sites used in the analysis of the 4 species (Powerful Owls, Sooty Owls, Greater Gliders and Yelow bellied gliders.),  (so_occupancy_cov.csv and so_detection_cov.csv) and contains the results of the 2 to 3 surveys and observations for 4 species (so_species_data.csv).  All data is in csv format.

SurveyDataProcessing:

R code and instructions to extra data to format required for analysis as described in the associated paper.