A covariate‐augmented mixed gamma‐exponential time‐to‐detection occupancy model

Abstract Occupancy models traditionally use repeated detection/non‐detection data to estimate the probability that a species occupies a site when detection is imperfect. Time‐to‐detection (TTD) data provide an alternative source of information on detectability, and the mixed gamma–exponential model with a shared‐detectability parameter () represents a flexible TTD framework for accommodating unobserved detection heterogeneity and dependence across repeated visits. However, existing applications of the model do not incorporate habitat or temporal covariates, limiting ecological interpretability and potentially biasing inference. We extend the framework by incorporating covariates into both the occupancy and detection components. A key challenge is that, in the original formulation, the marginal detection rate enters directly into the latent gamma structure, complicating the inclusion of visit‐level covariates. Using a reformulated latent structure, the proposed model allows site‐level habitat features and visit‐level temporal variables to jointly influence occupancy probabilities and detection rates. The detection process is decomposed into persistent and occasion‐specific latent components, with the shared‐detectability parameter describing the degree of shared detectability across repeated visits. Choosing between model structures cannot easily be done using traditional model selection methods because boundary parameters are involved. We develop likelihood‐based model comparison procedures that solve this problem. Simulation studies comparing the full model with reduced alternatives show that incorporating covariates substantially improves estimation accuracy. For occupancy, the covariate‐augmented model reduces bias relative to all reduced models (by 1%–17%) and achieves the lowest total estimation error in most settings, with reductions of 40%–75%. For detection rates, it avoids the severe negative bias observed in simpler models (often exceeding 40%) and yields markedly higher precision, reducing total estimation error by 60%–80%. An application to avian TTD data from South Africa's Fynbos biome reveals clear effects of vegetation, elevation and survey‐level covariates on both occupancy and detectability. The proposed covariate‐augmented model extends the practical utility of TTD data by enabling more realistic and interpretable ecological inference. By accommodating spatial and temporal heterogeneity while retaining computational tractability, this framework provides a flexible tool for analysing TTD data in the presence of structured detection heterogeneity.