Fast evaluation of study designs for spatially explicit capture–recapture

1 1. Spatially explicit capture–recapture methods use data from the detection 2 of marked animals at known points in space to estimate animal population 3 density without bias from edge effects. Detection is by means of stationary 4 devices such as traps, automatic cameras or DNA hair snags. Data collec5 tion is often expensive, and it is not obvious how to optimise the frequency of 6 sampling and the spatial layout of detectors. Results from a pilot study may 7 be extrapolated by simulation to predict the effectiveness of different config8 urations of multiple detectors, but simulation is slow and requires technical 9 expertise. 10 2. Another approach for evaluating novel designs is to compute intermediate 11 variables such as the expected number of detected individuals E(n) and ex12 pected number of recapture events E(r), and to seek relationships between 13 these variables and quantities of interest such as precision and power. 14 3. We present formulae for the expected counts and power. For many sce15 narios the relative standard error (RSE) of estimated density is close to 16 1/ √ min{E(n),E(r)}, and for maximum precision E(n) ≈ E(r). We compare 17 the approximation for RSE(D̂) with more rigorous results from simulation. 18 4. Computation of E(n) and E(r) is deterministic and much faster than sim19