Markov chain retrospective analysis or how to detect a position of the monitoring period in the course of postfire succession

Retrospective analysis in a Markov chain model of vegetation succession is a concept that we launched a few years ago with regard to studying the cowberry-vs.-bilberry competition dynamics in the dwarf-shrub layer of certain Scots pine forests on sandy soils. The concept was motivated by the need to know the course of succession in the past, mathematically grounded by the convergence to a unique steady state of the time-homogeneous Markov chain, and methodically provided by its being invulnerable to any shifts along the time axis. In 1980, permanent sample plots were laid down in two kinds of Scots pine forest with known dates of the last fire, and they were being repeatedly inspected for each 5 years till 2005. Two thousand quadrats sized 20 × 20 cm were checked up in each forest type for having one of the four principle statuses: both species were absent from the quadrat (∅), the bilberry was present alone (V), the cowberry was present alone (W), and the both species were present (VW). Each 5-year step detected transitions between any pair of states, and we calibrate the transition matrix by averaging the transition frequencies over the entire observation period individually for each forest type. Calibrated transition matrix gives the unique steady-state distribution of statuses among the quadrats and enables the estimation of how long the two-species succession proceeds from the very beginning till the steady state. The task is nontrivial since the general postfire succession passes certain no-berry stages after the fire, while the year when the berries appeared in quadrats for the first time is not known. An original idea of how to determine that year, hence the position of the monitoring period in the complete course of postfire succession, relies upon an optimal least-squares choice among the year-specific arrays of model distributions, and we apply here this idea to a dry Cladina–Vaccinium Scots pine forest and a wet Polytrichum–Myrtillus type. In the dry forest, the dynamics are shown to be much slower, with the dwarf-shrubs phase starting in 1975, i.e., 80 years after the fire, while it took just one 5-year step for the dwarf shrubs to appear in the wet type, i.e., 25 years prior the first field observation. Model findings are discussed with regard to the ecological knowledge of successions in pine forests.