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Plant and animal survey detection rates are important for ecological surveys, environmental impact assessment, invasive species monitoring, and modeling species distributions. Species can be difficult to detect when rare but, in general, how detection probabilities vary with abundance is unknown. We developed a new detectability model based on the time to detection of the first individual of a species. Based on this model, the predicted detection rate is proportional to a power function of abundance with a scaling exponent between zero and one that depends on clustering of individuals. We estimated the model parameters with data from three independent datasets: searches for chenopod shrub species and coins, experimental searches for planted seedlings, and frog surveys at multiple sites in sub‐tropical forests of eastern Australia. Analyses based on the detection time and detection probability suggest that …