Analyzing the Fine-Scale Dynamics of Two Dominant Species in a Polytrichum–Myrtillus Pine Forest. II. An Inhomogeneous Markov Chain and Averaged Indices

Data from six repeated observations in a Polytrichum-type Scots pine forest are used to construct a nonautonomous Markov model of fine-scale dynamics of the two dominant species, bilberry (Vaccinium myrtillus) and lingonberry (V. vitis-idaea), at the late stages of postfire succession. The model consists of five transition matrices dependent on the observation year, and transition to the average matrix results in a homogeneous model. The design of the field experiment featured a large sample size on permanent transects (2000 quadrats × 6 observations), a 5-year reexamination interval, and the use of species rooting frequency on 20 × 20 cm quadrats over 25 years. The discrete Markov chain used to model the observed process of species alternation on the quadrats consists of four states: an absence of both species from the quadrat, the presence of one species of the two, and the joint presence of both species. The model time step coincides with the interval between the observations. The data allow for a unique calibration of the transition matrix for each pair of sequential observations, and the formulas of finite Markov chain theory yield the vectors of steady-state square distributions for each of the five temporal transitions. Fluctuations in the species rooting frequency among the observations are shown to exert substantial effects on the values of certain elements in the transition matrices and the components of the corresponding steady-state vectors (for particular pairs of observations), but there are no major changes in the conclusions concerning the dominating components (dominating states of the quadrats), regardless of the fluctuations. The geometric mean of five transition matrices recapitulates the spatial and temporal characteristics of the process over the entire observation period. We show that the stable terminal outcome of species dynamics is expected to involve the following distribution of quadrats among the states: 37% of the quadrats with V. myrtillus alone, 11% with V. vitis-idaea alone, 38% quadrats with both species present, and 14% “empty” quadrats. It is shown for the first time that the share of quadrats with V. vitis-idaea alone decreases considerably in the course of succession, whereas the share of quadrats with both species growing together increases. The averaged characteristics of the cyclicity and stage duration of the fine-scale dynamics make it possible to estimate the total duration of the secondary postfire succession (to reach a nearly terminal state) at 46–50 years. The quadrats with V. vitis-idaea alone have the shortest average lifetime among the described states (9 years), and those with both V. myrtillus and V. vitis-idaea have the longest average lifetime (18 years), which is partly explained by the different lifetimes of the species’ shoots.