The semi-Markov process: a useful tool in the analysis of vegetation dynamics for management

Abstract A general mathematical model of vegetation dynamics is presented which is based on the semi-Markov process (an extension of the Markov process). When biological models of succession and natural disturbance are used in conjunction with it to define the community states, the semi-Markov process overcomes the well-known problems of the Markov process as a model of vegetation change. The semi-Markov model may also be used to analyse plant-by-plant replacement processes. Analysis of the semi-Markov model produces equations giving quantities of interest to land managers: (1) the probability that a vegetation stand will be in a particular state at a given time, (2) mean times to local extinction of vulnerable species and (3) optimal use of a prescribed disturbance, given an assessment of the value of each community state. The analyses are illustrated with an example from forests of western Montana. In order to construct the example, the vital attributes scheme of Noble and Slatyer (1980) has been both corrected in order to make it dynamically sufficient and extended to accommodate multiple disturbance types.