Variance Propagation for Density Surface Models

Abstract Spatially explicit estimates of population density, together with appropriate uncertainty, are required in many management contexts. Density surface models (DSMs) a two-stage approach for estimating spatially varying density from distance sampling data. First, detection probabilities—perhaps depending on covariates—are estimated based details individual encounters; next, local densities using GAM, by fitting encounter rates to location and/or covariates while allowing the detectabilities. One criticism DSMs has been that uncertainty two stages is not usually propagated correctly into final variance estimates. We show how reformulate DSM so probability stage (regardless its complexity) captured as an extra random effect GAM stage. In effect, we refit approximation function model at same time spatial model. This allows straightforward computation overall via exactly software already needed fit GAM. A further extension variation group size, which can be important covariate detectability well directly affecting abundance. illustrate these point transect survey data Island Scrub-Jays Santa Cruz Island, CA, and harbour porpoise SCANS-II line European waters. Supplementary materials accompanying this paper appear on-line.