Joint Population Dynamics of Vaccinium myrtillus and V. vitis-idaea in the Protected Postfire Cladina-Vaccinium Pine Forest. Markov Model with Averaged Transition Probabilities

The joint population dynamics of the cowberry (Vaccinium vitis-idaea) and bilberry (V. myrtillus) have been studied in a protected, subxeric Cladina–Vaccinium pine forest (boreo-nemoral zone) at the middle and late stages of postfire succession. Features of the sampling design included a long observation term (25 years), a large sample size on permanent transects, a reexamination interval of 5 years, and the determination of species rooted frequency on small (20 × 20 cm) quadrats. We propose a discrete Markov chain as a model of species replacement on the quadrats. It has the following four states: both species are absent on the quadrat, only cowberry is present, only bilberry is present, and both species are simultaneously present. It was found that all possible transitions between states occurred in each time interval in the forest; this results in a complete digraph (directed graph) of transitions. The frequency of transitions from one state to another varies between the observation intervals; however, the calculation of the Mantel–Haenszel statistical test shows that the samples are homogeneous for most of the of transition variants. This makes it possible to move from the averaging of transition matrices to the averaging of the transition probabilities. We have revealed a unidirectional trend in time changes for three of the chain states: the proportion of quadrats occupied only by bilberry V. myrtillus and those with both species constantly increases, while the proportion of “empty” quadrats decreases. The fourth state (quadrats occupied only by cowberry V. vitis-idaea) has a local maximum at the middle stages of succession, followed by a later decrease in its proportion. The distribution of quadrats by state (29.1% of quadrats are occupied only by bilberry Vaccinium myrtillus, 15.2% contain only by cowberry V. vitis-idaea, 44.4% have both species, and 11.3% are species-free) is expected to be the terminal stable outcome of the species dynamics. The results confirm that the coexistence of V. myrtillus and V. vitis-idaea can be stable at the final succession stages. Several succession stages are described: the proportion of dwarf shrubs is low at the first stage; then quadrats are dominated by V. vitis-idaea at the second stage; and, finally, V. myrtillus is dominant at the third stage (although the quadrats where both species grow together prevail). The total time of postfire succession in the subxeric Cladina–Vaccinium pine forest (in the boreo-nemoral zone) is estimated to be approximately 140 years (when the state differs from the equilibrium state by less than 5%). In terms of forest typology, the modeling result indicates that the Cladina–Vaccinium pine forest is gradually transforming into a bilberry–cowberry pine forest and then into a cowberry–bilberry pine forest.