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these models has not been tested thoroughly, and prior (unpublished)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.