Abstract
Abstract Aim Optimum shifts in species–environment relationships are intensively studied in a wide range of ecological topics, including climate change and species invasion. Numerous statistical methods are used to study optimum shifts, but, to our knowledge, none explicitly estimate it. We extended an existing model to explicitly estimate optimum shifts for multiple species having symmetrical response curves. We called this new Bayesian hierarchical model the Explicit Hierarchical Model of Optimum Shifts (EHMOS). Location All locations. Taxon All taxa. Methods In a simulation study, we compared the accuracy of EHMOS to a mean comparison method and a Bayesian generalized linear mixed model (GLMM). Specifically, we tested if the accuracy of the methods was sensitive to (1) sampling design, (2) species optimum position and (3) species ecological specialization. In addition, we compared the three methods using a real dataset of investigated optimum shifts in 24 Orthopteran species between two time periods along an elevation gradient. Results Of all the simulated scenarios, EHMOS was the most accurate method. GLMM was the most sensitive method to species optimum position, providing unreliable estimates in the presence of marginal species, that is, species with an optimum close to a sampling boundary. The mean comparison method was also sensitive to species optimum position and ecological specialization, especially in an unbalanced sampling design, with high negative bias and low interval coverage compared to EHMOS. The case study results obtained with EHMOS were consistent with what is expected considering ongoing climate change, with mostly upward shifts, which further improved confidence in the accuracy of the EHMOS method. Main Conclusions Explicit Hierarchical Model of Optimum Shifts could be used for a wide range of topics and extended to produce new insights, especially in climate change studies. Explicit estimation of optimum shifts notably allows investigation of ecological assumptions that could explain interspecific variability of these shifts.