Using Markov chain successional models backwards.
Abstract
Markov chains are commonly used to model succession in plant and animal communities. Once fitted to data, these models are typically used to address ecological issues concerning future successional states. In some situations it may be of interest to use the present successional state to reconstruct past conditions. The properties of a time-reversed Markov chain are reviewed and used to provide an expression for the conditional probability distribution of the most recent time that the chain was in a particular successional state given its present state. The estimation of this conditional probability is discussed and a parametric bootstrap is described for constructing a confidence interval. The calculations are illustrated using a published Markov chain model of succession in a rocky subtidal community. Synthesis and applications. The term succession refers to the progressive changes over time in the state of an ecological community. Although most analyses of succession focus on characterizing the future, in some situations interest centres on reconstructing the past. For example, forensic entomologists are commonly interested in estimating time of death from the insect community present on a corpse. When succession can be modelled as a Markov chain, the results obtained here can be used for this kind of reconstruction.