Succession caused by beaver (Castor fiber L.) activity: I. What is learnt from the calibration of a simple Markov model

Abstract

A homogeneous Markov chain of three aggregated states "pond--swamp--wood" is proposed as a model of cyclic zoogenic successions caused by beaver (Castor fiber L.) life activity in a forest biogeocoenosis. To calibrate the chain transition matrix, the data have appeared sufficient that were gained from field studies undertaken in "Bryanskii Les" Reserve in the years of 2002-2008. Major outcomes of the calibrated model ensue from the formulae of finite homogeneous Markov chain theory: the stationary probability distribution of states, thematrix (T) of mean first passage times, and the mean durations (M(j)) of succession stages. The former illustrates the distribution of relative areas under succession stages if the current trends and transition rates of succession are conserved in the long-term--it has appeared close to the observed distribution. Matrix T provides for quantitative characteristics of the cyclic process, specifying the ranges the experts proposed for the duration of stages in the conceptual scheme of succession. The calculated values of M(j) detect potential discrepancies between empirical data, the expert knowledge that summarizes the data, and the postulates accepted in the mathematical model. The calculated M2 value falls outside the expert range, which gives a reason to doubt the validity of expert estimation proposed, the aggregation mode chosen for chain states, or/and the accuracy-of data available, i.e., to draw certain "lessons" from partially successful calibration. Refusal to postulate the time homogeneity or the Markov property of the chain is also discussed among possible ways to improve the model.