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

摘要

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.