Accounting for misidentification and heterogeneity in occupancy studies using hidden Markov models

•Occupancy models including false positives are formulated as hidden Markov models.•Such models can be extended to account for heterogeneity in detection.•Models not accounting for heterogeneity in detection produce biased results.•Heterogeneity in detection can be due to a heterogeneous sampling effort. Occupancy models allow assessing species occurrence while accounting for imperfect detection. As with any statistical models, occupancy models rely on several assumptions amongst which (i) there should be no unmodelled heterogeneity in the detection probability and (ii) the species should not be detected when absent from a site, in other words there should be no false positives (e.g., due to misidentification). In the real world, these two assumptions are often violated. To date, models accounting simultaneously for both detection heterogeneity and false positives are yet to be developed. Here, we first show how occupancy models with false positives can be formulated as hidden Markov models (HMM). Second, benefiting from the HMM framework flexibility, we extend models with false positives to account for heterogeneity with finite mixtures. First, using simulations, we demonstrate that, as the level of heterogeneity increases, occupancy models accounting for both heterogeneity and misidentification perform better in terms of bias and precision than models accounting for misidentification only. Next, we illustrate the implementation of our new model to a real case study with grey wolves (Canis lupus) in France. We demonstrate that heterogeneity in wolf detection (false negatives) is mainly due to a heterogeneous sampling effort across space. In addition to providing a novel modeling formulation, this work illustrates the flexibility of HMM framework to formulate complex ecological models and relax important assumptions that are not always likely to hold. In particular, we show how to decompose the model structure in several simple components, in a way that provides much clearer ecological interpretation.