Scripts from: Performance of generalized distance sampling models with temporary emigration: a simulation study

Generalized distance sampling (GDS) models are the distance sampling equivalent of temporary emigration N-mixture models. In addition to density and the perceptibility component of detection, both contain an additional parameter for availability for detection which becomes estimable when data from repeated 'visits' are available. GDS models thus account for open populations. This makes them more robust, since natural populations are hardly ever perfectly closed, arguably even over the course of a single breeding season. However, the performance of these models has not been tested thoroughly, and prior (unpublished) analyses suggested that biased estimates, especially for density (high) and availability (low), may typically occur under certain conditions. We conducted three simulation studies and found that bias arises in low-information scenarios, particularly with low sample sizes and low parameter values. Our simulations enable us to determine "estimation frontiers", which separate satisfactory from unsatisfactory estimation performance. Typically, 4-5 replicates, 100-200 sites, and specific combinations of parameter values - particularly those linked to availability and detection probability - are required for reliable estimates. We found that inclusion of covariates in the models could improve estimates in some situations by reducing the incidence of extreme estimates. One novel result from our simulations is that while density and availability may be non-identifiable under some combinations of sample size and for certain parameter values, their product (i.e., the density of the available population) may be more reliably inferred. Our findings provide important insights for study design and for obtaining and interpreting abundance estimates in models with temporary emigration, all with important implications for ecology and wildlife management.