M_tor not M_t: Temporal variation in detection probability in spatial capture-recapture and occupancy models

State variables such as abundance and occurrence of species are central to many questions in ecology and conservation, but our ability to detect and enumerate species is imperfect and often varies across space and time. Accounting for imperfect and variable detection is important for obtaining unbiased estimates of state variables. Here, I investigate whether closed spatial capture-recapture (SCR) and single season occupancy models are robust to ignoring temporal variation in detection probability. Ignoring temporal variation allows collapsing detection data across repeated sampling occasions, speeding up computations, which can be important when analyzing large datasets with complex models. I simulated data under different scenarios of temporal and spatio-temporal variation in detection, analyzed data with the data-generating model and an alternative model ignoring temporal variation in detection, and compared estimates between these two models with respect to relative bias, coefficient of variation (CV) and relative root mean squared error (RMSE). SCR model estimates of abundance, the density-covariate coefficient β and the movement-related scale parameter of the detection function σ were robust to ignoring temporal variation in detection, with relative bias, CV and RMSE of the two models generally being within 4% of each other. An SCR case study for brown tree snakes showed identical estimates of density and σ under models accounting for or ignoring temporal variation in detection. Occupancy model estimates of the occupancy-covariate coefficient β and average occupancy were also largely robust to ignoring temporal variation in detection, and differences in occupancy predictions were mostly <<0.1. But there was a slight tendency for bias in β under the alternative model to increase when detection varied more strongly over time. Thus, when temporal variation in detection is extreme, it may be necessary to model that variation to avoid bias in parameter estimates in occupancy models. An occupancy case study for ten bird species with a more complex model structure showed considerable differences in occupancy parameter estimates under models accounting for or ignoring temporal variation in detection; but estimates and predictions from the latter were always within 95% confidence intervals of the former. There are cases where we cannot or may not want to ignore temporal variation in detection: a behavioral response to detection and certain SCR observation models do not allow collapsing data across sampling occasions; and temporal variation in detection may be informative of species phenology/behavior or for future study planning. But this study shows that it can be safely ignored under a range of conditions when analyzing SCR or occupancy data.