Joint species distribution models with species correlations and imperfect detection.

Spatiotemporal patterns in biological communities are typically driven by environmental factors and species interactions. Spatial data from communities are naturally described by stacking models for all species in the community. Two important considerations in such multispecies or joint species distribution models (JSDMs) are measurement errors and correlations between species. Up to now, virtually all JSDMs have included either one or the other, but not both features simultaneously, even though both measurement errors and species correlations may be essential for achieving unbiased inferences about the distribution of communities and species co-occurrence patterns. We developed two presence-absence JSDMs for modeling pairwise species correlations while accommodating imperfect detection: one using a latent variable and the other using a multivariate probit approach. We conducted three simulation studies to assess the performance of our new models and to compare them to earlier latent variable JSDMs that did not consider imperfect detection. We illustrate our models with a large Atlas data set of 62 passerine bird species in Switzerland. Under a wide range of conditions, our new latent variable JSDM with imperfect detection and species correlations yielded estimates with little or no bias for occupancy, occupancy regression coefficients, and the species correlation matrix. In contrast, with the multivariate probit model we saw convergence issues with large data sets (many species and sites) resulting in very long run times and larger errors. A latent variable model that ignores imperfect detection produced correlation estimates that were consistently negatively biased, that is, underestimated. We found that the number of latent variables required to represent the species correlation matrix adequately may be much greater than previously suggested, namely around n/2, where n is community size. The analysis of the Swiss passerine data set exemplifies how not accounting for imperfect detection will lead to negative bias in occupancy estimates and to attenuation in the estimated covariate coefficients in a JSDM. Furthermore, spatial heterogeneity in detection may cause spurious patterns in the estimated species correlation matrix if not accounted for. Our new JSDMs represent an important extension of current approaches to community modeling to the common case where species presence-absence cannot be detected with certainty.