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

Abstract

SummaryModels 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,SVmethods 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 andSVmethods for occupancy and abundance estimation. We explain the precise mathematical conditions needed forRSPFestimation as stated in Lele & Keim (Ecology, 87, 2006, 3021). The identical conditions that remained unstated in our papers onSVmethodology are needed forSVmethodology to work. We show that the class of admissible models is quite broad and does not excessively restrict the application of theRSPFor theSVmethodology.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 theSVmethodology to a class of models that allows use of scaled probability function. We propose a multinomial extension ofSVmethodology that can be used to check whether the detection function satisfies theRSPFcondition 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 theRSPFcondition 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 forRSPFcondition makesSVmethodology irrelevant in practice.