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Summary    Models accounting for imperfect detection are important. Single‐visit ( SV ) methods have been proposed as an alternative to multiple‐visit methods to relax the assumption of closed population. Knape & Korner‐Nievergelt (Methods in Ecology and Evolution, 2015) showed that under certain models of probability of detection,  SV  methods are statistically non‐identifiable leading to biased population estimates.  There is a close relationship between estimation of the resource selection probability function ( RSPF ) using weighted distributions and  SV  methods for occupancy and abundance estimation. We explain the precise mathematical conditions needed for  RSPF  estimation as stated in Lele & Keim (Ecology, 87, 2006, 3021). The identical conditions that remained unstated in our papers on  SV  methodology are needed for  SV  methodology to work. We show that the class of admissible models is quite broad and does not excessively restrict the application of the  RSPF  or the  SV  methodology.  To complement the work by Knape and Korner‐Nievergelt, we study the performance of multiple‐visit methods under the scaled logistic detection function and a much wider set of situations. In general, under the scaled logistic detection function, multiple‐visit methods also lead to biased estimates.  As a solution to this problem, we extend the  SV  methodology to a class of models that allows use of scaled probability function. We propose a multinomial extension of  SV  methodology that can be used to check whether the detection function satisfies the  RSPF  condition or not. Furthermore, we show that if the scaling factor depends on covariates, then it can also be estimated.  We argue that the instances where the  RSPF  condition is not satisfied are rare in practice. Hence, we disagree with the implication in Knape & Korner‐Nievergelt (Methods in Ecology and Evolution, 2015) that the need for  RSPF  condition makes  SV  methodology irrelevant in practice.

Revisiting resource selection probability functions and single‐visit methods: clarification and extensions