Fast evaluation of study designs for spatially explicit capture-recapture

Spatially explicit capture-recapture methods use data from the detection of marked animals at known points in space to estimate animal population density without bias from edge effects. Detection is by means of stationary devices such as traps, automatic cameras or DNA hair snags. Data collection is often expensive, and it is not obvious how to optimize the frequency of sampling and the spatial layout of detectors. Results from a pilot study may be extrapolated by simulation to predict the effectiveness of different configurations of multiple detectors, but simulation is slow and requires technical expertise. Another approach for evaluating novel designs is to compute intermediate variables such as the expected number of detected individuals E(n) and expected number of recapture events E(r), and to seek relationships between these variables and quantities of interest such as precision and power. We present formulae for the expected counts and power. For many scenarios the relative standard error (RSE) of estimated density is close to 1/min{E(n),E(r)}, and for maximum precision E(n) approximate to E(r). We compare the approximation for RSE(D<^>) with more rigorous results from simulation. Computation of E(n) and E(r) is deterministic and much faster than simulation, so it is readily included in interactive software for designing studies with enough power to answer ecological questions. The related approximation for RSE(D<^>) is adequate for many purposes.