Assessing impacts of small perturbations using a model-based approach

When examining the effects of a disturbance on a complex system like vegetation it is difficult to distinguish between those changes that affect the processes underlying the functioning of the system and other changes which simply shift the state of the system but have no effect on the processes. The former is obviously a more significant effect than the latter. In this paper we examine a model-based clustering procedure which can make such a distinction. Given observations on several sites on several occasions, we model the dynamics of the processes using a continuous hidden Markov model. In this model the actual Markov process is hidden, but at any observation time we can observe surrogate variables whose values will be conditional on the underlying state of the process. We further ask if there is evidence for more than one such process, i.e. whether our data are heterogeneous. By estimating the number of clusters using a Bayesian information criterion we can choose between these alternatives. An analogous assessment is made of the number of states in the underlying hidden Markov models, as well as the transition matrices between states and emission probabilities relating the underlying hidden state to the observed attributes. The methodology was applied to the question of determining if a runnelling treatment of a salt marsh for mosquito management had changed the underlying processes related to the vegetation.