Joint species distribution models with species correlations and imperfect detection

Abstract

Spatiotemporal patterns in biological communities are typically driven by envi-ronmental factors and species interactions. Spatial data from communities are naturallydescribed by stacking models for all species in the community. Two important considerationsin such multispecies or joint species distribution models (JSDMs) are measurement errors andcorrelations between species. Up to now, virtually all JSDMs have included either one or theother, but not both features simultaneously, even though both measurement errors and speciescorrelations may be essential for achieving unbiased inferences about the distribution of com-munities and species co-occurrence patterns. We developed two presence–absence JSDMs formodeling pairwise species correlations while accommodating imperfect detection: one using alatent variable and the other using a multivariate probit approach. We conducted three simula-tion studies to assess the performance of our new models and to compare them to earlier latentvariable JSDMs that did not consider imperfect detection. We illustrate our models with alarge Atlas data set of 62 passerine bird species in Switzerland. Under a wide range of condi-tions, our new latent variable JSDM with imperfect detection and species correlations yieldedestimates with little or no bias for occupancy, occupancy regression coefficients, and the speciescorrelation matrix. In contrast, with the multivariate probit model we saw convergence issueswith 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 thatwere consistently negatively biased, that is, underestimated. We found that the number of latentvariables required to represent the species correlation matrix adequately may be much greaterthan previously suggested, namely aroundn/2, wherenis community size. The analysis of theSwiss passerine data set exemplifies how not accounting for imperfect detection will lead tonegative bias in occupancy estimates and to attenuation in the estimated covariate coefficientsin a JSDM. Furthermore, spatial heterogeneity in detection may cause spurious patterns in theestimated species correlation matrix if not accounted for. Our new JSDMs represent an impor-tant extension of current approaches to community modeling to the common case where spe-cies presence–absence cannot be detected with certainty.