[Analyzing the fine-scale dynamics of two dominant species in a Polytrichum—Myrtillus pine forest. I. A homogeneous Markov chain and cyclicity indices].

Using long-term direct observations in a Polytrichum-Myrtillus pine forest, we have constructed and verified a homogeneous Markov chain model for two dominant species (Vaccinium myrtillus and V. vitis-idaed) at the late stages of succession. The sampling design features a large sample size (2000 quadrats) on permanent transects, several re-examinations with the interval of 5 years, and the use of species rooted frequency.

[Local population of Eritrichium caucasicum as an object of mathematical modelling. I. Life cycle graph and a nonautonomous matrix model].

For the plant species, which is considered a short-lived perennial, we have composed a scale of ontogenetic stages and the life cycle graph (LCG) according to annual observations on permanent sample plots in an Alpine lichen heath during the 2009-2014 period. The LCG that reflects seed reproduction has been reduced to the one that avoids the stage of soil seed bank, yet preserves the arcs of annual recruitment. The corresponding matrix model of stage-structured population dynamics has four stages: juvenile plants (including seedlings), virginal, generative, and 'terminally generative' (the plants die after seed production).

[From uncertainty to an exact number: Developing a method to estimate the fitness of a clonal species with poly variant ontogeny].

The task to estimate the fitness of a clonal plant with polyvariant ontogeny reduces to compiling a life cycle graph, constructing and calibrating the corresponding matrix model of the discrete-structured population, and calculating the dominant eigenvalue (λ1) of the model matrix. We demonstrate a solution to this task with a sample of Calamagrostis epigeios , a perennial long-rhizome grass propagating vegetatively, and data on the age-stage structure of its local population. A traditional technique of successive censuses fixing the age-stage status of all individuals on a permanent sample plot (SP) provides for calculating frequencies of ontogenetic transitions directly from the data, but leaves uncertain the status-specific reproduction rates as the recruit parents are unknown (“reproductive uncertainty”).

[Polyvariant ontogeny in woodreeds: Novel models and new discoveries].

Polyvariant ontogeny (PVO) is expressed visually in the life cycle graphs (LCGs) for Calamagrostis woodreeds as a variety of pathways for individual plants to develop through many of their states distinguishable by the ontogenetic stage and chronological age (in years). PVO is recognized as the basic mechanism of adaptation in local plant populations to their environments, while they find a quantitative measure of the adaptation via developing a matrix model of double-structured population, calibrating the matrix of vital rates from empirical data, and calculating its dominant eigenvalue λ1. This approach encounters an obstacle typical for rhizome grasses: while the rates of aging and ontogenetic transitions can be deterinined from field data mainly by the morphology of aboveground parts of the plant, the rates of vegetative propagation can be reliably determined only from digging up the belowground rhizome system, i.

Selection on stability across ecological scales.

Much of the focus in evolutionary biology has been on the adaptive differentiation among organisms. It is equally important to understand the processes that result in similarities of structure among systems. Here, we discuss examples of similarities occurring at different ecological scales, from predator-prey relations (attack rates and handling times) through communities (food-web structures) to ecosystem properties.

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

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.

[Two paradigms of mathematical population biology. Attempting to synthesise].

Whatever popular the slogan of nonlinear ecological interactions has been in theory, practical ecology professes the projection matrix paradigm, which is essentially linear, i.e., the linear matrix model paradigm for discrete-structured population dynamics.

[Svirezhev's substitution principle and matrix models for dynamics of populations with complex structures].

Matrix models of discrete-structured population dynamics became a traditional tool in plant and animal demography, aided with developments in the proper mathematics and wide spread of software products, which greatly facilitate creating models in the man-machine dialogue mode, but leave behind the scenes the issue of whether the methods applied are adequate to the problem posed. A principal discrepancy of this kind does appear in a problem to calibrate the projection matrix on observation data of the "identified individuals with uncertain parents" type: simplifying recipes from an ecological software package contradict the idea of polyvariant ontogeny as an adaptation mechanism. The problem becomes solvable if we substitute an extremal adaptation principle for the uncertainty in data as follows: the unknown reproduction rates are assumed to distribute among the reproductive groups in such a way that maximizes the potential growth rate of the model population under the current conditions.

[On the competition among discrete-structured populations: a matrix model for population dynamics of woodreed and birch growing together].

Presented is a synthesis of field, theoretical and modelling studies on joint dynamics of two species--common birch (Betula pendula Roth) and wood small reed (Calamagrostis epigeios (L.) Roth)--overgrowing a spruce forest clear-cut. A nonlinear matrix model for population dynamics of two species, which both possess non-trivial population structures and compete for a resource in common was developed as an expansion of the linear models for single-species, age-stage-structured population dynamics.

The monoculture vs. rotation strategies in forestry: formalization and prediction by means of Markov-chain modelling.

The monoculture strategy of forest management, where the same tree species (e.g., Picea abies) is cultivated in a number of successive planting-growing-felling cycles, is generally considered to be economically efficient, yet not sustainable as it reduces biodiversity in the forest.

[Successions in the forest-steppe under climate changes: a modelling approach].

The paper represents an attempt to apply the general principles of modelling vegetation dynamics under climate changes to a study of the long-term vegetation dynamics in the forest-steppe zone of the European territory of Russia, with a purpose to forecast under special climatic scenarios. An original technique is used to construct a Markov chain as a model of vegetation succession. The technique emanated from gebotanic knowledge generalized as a scheme of successional transitions with estimates of the average duration for certain stages of succession.

[The structure and dynamics of woodreed Calamagrostis canescens population: a modelling approach].

A scale of ontogenetic states has been developed for woodreed Calamagrostis canescens, a perennial species dominating the grass layer of fell forest areas. The population structure is considered as a set of age-stage groups of individuals differing both in the ontogenetic stage and the chronological age measured in years. to describe the dynamics through years a special kind of matrix formalism has been proposed which is reducible neither to the classic Leslie matrix for an age-structured population, nor to the well-known Lefkovitch matrix for a stage-structured one, and which does not suffer from excessiveness of the "two-dimensional" representation for the structure implying the projection matrix of a block pattern.

The model for human population dynamics as a part of the global biosphere model: some aspects of modeling in a dialogue regime.

"A matrix model for an age structured population with 4 groups is presented...