Estimates from non‐replicated population surveys rely on critical assumptions

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Modelling of species distributions, range dynamics and communities under imperfect detection: advances, challenges and opportunities (2017, background): “…assumptions (about numbers/types of covariates and shape of link functions), which has led to other authors warning that occupancy and detection are not truly identifiable with such data, and that estimation is not robust (Knape and KornerNievergelt 2015a, Knape and Korner-Nievergelt 2015b).”
Decomposing trends in Swedish bird populations using generalized additive mixed models (2016, background): “If observation errors are only due to missed detection of individuals (K ery et al. 2009), the cit may be interpreted as detection probabilities (see, e.g. Knape & Korner-Nievergelt 2015), but in general they give the proportions of the observed counts to the actual numbers of individuals.”
Hierarchical Species Distribution Models (2016, background): “There are alternative models that require only a single sample [17, 50, 90], but such models require stronger assumptions or structure in the process model and are a current topic of debate [63, 64, 91].”