Reliable variance propagation for spatial density surface models
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Density Surface Models (DSMs) are two-stage models for estimating animal density from line-transect data. First, detectability is estimated by distance sampling, and then a Generalized Additive Model (GAM) is used to estimate animal density as a function of location and/or other spatially-varying environmental covariates. One criticism of DSMs has been that uncertainty from the two stages is not usually propagated correctly into the final variance estimates. Here we show how to reformulate a DSM so that the uncertainty in detection probability from the distance sampling stage (regardless of its complexity) is captured as a random effect in the GAM stage. This allows straightforward computation of the overall variance via standard GAM machinery. We further extend the formulation to allow for spatial variation in group size, which can be an important covariate for detectability. We illustrate these models using line transect survey data of minke whales and harbour porpoise from the SCANS-II survey in northern Europe.
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