Succession caused by beaver (Castor fiber L.) life activity: II. a refined markov model

The refined Markov model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity represents a discrete chain of the following six states: inundated forest, swamp forest, pond, herbaceous swamp, shrub swamp, and moist forest, which correspond to certain stages of succession. Those stages are defined, and a conceptual scheme of the probable transitions between them for one time step is constructed from a knowledge of beaver behavior in small river floodplains of the Bryanskii Les Nature Reserve. We calibrated the corresponding matrix of transition probabilities according to the optimization principle: minimizing differences between the model outcome and reality; the model generates a distribution of relative areas corresponding to the stages of succession, which must be compared to those gained from case studies in the Bryanskii Les Reserve during 2002–2006. The time step of the model is two years, and the first-step data in the sum of differences are given various weights, w (between 0 and 1). The value of w = 0.2 is selected due to its optimality and for some additional reasons. Using the formulas of the finite homogeneous Markov chain theory, we obtained the main results of the calibrated model, namely, a steady-state distribution of stage areas, indexes of cyclicity, and mean durations (M_j) of succession stages. The calibration results provide an objective quantitative character to the expert knowledge of the course of succession and are properly interpreted. The data from 2010, which are not involved in the calibration procedure, made it possible to assess the quality of prediction by the homogeneous model in the short term (as of 2006): the error of the model area distribution relative to the distribution observed in 2010 falls into the range of 9–17%, with the best prognosis being for the least optimal matrices (rejected values of w). This fact indicates a formally heterogeneous nature of succession processes in time. Thus, the refined version of the homogeneous Markov chain has not eliminated all of the contradictions between the model results and expert knowledge, which suggests a further model development towards a “logically inhomogeneous” version and/or refusal to postulate the Markov property in the conceptual scheme of succession.