Bilberry vs. cowberry in a Scots pine boreal forest: Exclusion or coexistence in a post-fire succession?

Although the famous competition exclusion principle was thoroughly elaborated in the framework of multispecies population models, its illustrations with field data were facing certain obstacles. The data we deal with were collected by 6 consecutive examinations of bilberry (Vaccinium myrtillus) and cowberry (V. vitis-idaea) presence/absence in 20 x 20 cm quadrats located along permanent transects in a Scots pine boreal forest. These data feature a great sample size (2000 quadrats x 6 examinations) and a 5-year interval for each pair of examination/re-examination, and the data have enabled us to construct a Markov chain model for the fine-scale dynamics of these dominant species at the later stages of post-fire succession. The discrete-time nonautonomous model consists of the five time-dependent, one-step transition matrices that describe changes occurring in the quadrat status for the 5 years in the following 4 terms: species-free quadrat; bilberry alone, cowberry alone, both species. Calibrated on the data, each one-step transition matrix transforms the current distribution of quadrats among their statuses exactly to the next one observed and yields a steady-state distribution as its (time-specific) positive eigenvector. Step-by-step variations in the elements of transition matrices do affect the components of the corresponding eigenvectors, but do not change the dominance relationships among them. Calculated as the 5-th power matrix root from the product of those five transition matrices (in the chronological order within their product), the geometric average, treated again as a transition matrix, provides for the spatial and temporal characteristics of the observed dynamics summarizing the whole observation period. We reveal the expected terminal stable outcome of species dynamics to be a distribution where 37% of quadrats are occupied by the bilberry alone, 11% by cowberry alone, 38% by the both species, and 14% be species-free. It is shown for the first time that the share of cowberry-alone quadrats decreases notably in the course of succession, whereas the share of species coexistence quadrats increase. The averaged characteristics of cyclicity and status duration in the fine-scale dynamics enable us to estimate the total time of the secondary post-fire succession as 46-50 years (till reaching a distribution close to the terminal one). Of the four statuses considered, the cowberry-alone quadrats have the least mean duration time (9 years), while the bilberry-and-cowberry quadrats have the longest time (18 years), which are explainable by different life spans of the shoots in proper species.