Markov models for community dynamics allowing for observation error

Markov models are dynamic models that characterize transitions among discrete ecological states with transition probability matrices. Such models are widely used to infer community dynamics of sessile organisms because transition probabilities (the elements of transition probability matrices) can be estimated with time series data from "grid sampling," where species occupancy states are assessed at multiple fixed points in a quadrat or transect. These estimates, however, are known to be biased when resampling error exists. In this study, we used the perspective of multistate dynamic occupancy models to develop a new Markov model that is structured hierarchically such that transitions among occupancy states and observation processes are considered explicitly at each fixed point. We show that, by adopting a hierarchical Bayesian approach, our model provides estimates for transition probabilities that are robust to sampling error. We also show that error rate may be estimated without additional data obtained from rapid repeated sampling. Considerations for the analysis for the application to real data set and potential extensions of the proposed model are discussed.