A.M.Obukhov Institute of Atmospheric Physics
Russian Academy of Sciences

Project dates        2005-2007

Summary

A synthesis of field, theoretical and modelling studies has enabled representing the early stages of secondary successions on clear-cut areas as a result of competition between the dominant species, such as woodreeds, raspberry, spruce, birch, aspen). The population structure dynamics in the dominant species which appear after drastic changes in the vegetation of spruce forests due to clear cuts have been studied on permanent sample plots laid down at various times in forest of several kinds within the buffer zone of the Central Forest State Reserve (Tverskaya oblast). The vegetation in each plot represented a typical kind dominated by a single species: the woodred (Calamagrostis epigeios (L.) Roth or Calamagrostis canescens (Web.)), or raspberry (Rubus idaeus), - or with the domination change by the common birch (Betula pendula Roth.) or the European aspen (Populus tremula L.). Life cycles of each plant have neen monitored, during a number of years, in terms of the proper ontogenetic scales, ages and origine (vegetative/seed). New databases have been created and the existing ones updated for each species, which combine multi-year observations on the marked plants. A conceptual scheme has been proposed for how to account for competition effects in the dynamics of species under study, and a nonlinear matrix model for dynamics of two species which both posses non-trivial population structures and compete for a resource in common has been developed as an expansion of the linear models for single-species, age-stage-structured population dynamics. When calibrated on the data for joint dynamics of the common birch and small woodreed, the nonlinear model illustrates the observed change in domination and predicts steady development towards the birch forest with suppressed woodreed population. As an object of more general mathematical study, the model also possesses a potential to forecast other versions of the secondary succession.

The proper software has been developed in a MatLab environment.

Publications

Logofet D.O., Ulanova N. G., Klochkova I. N. and Demidova A. N.
Structure and dynamics of a clonal plant population: Classical model results in a non-classic formulation.   Ecological Modelling, 2006, v.196, p. 95-106

Logofet D.O., Belova I.N.
Nonnegative matrices as a tool to model population dynamics: classical models and contemporary expansions. Journal of Mathematical Sciences. 2008, (in press).

Ulanova N.G., Zavalishin N.N. and Logofet D.O.
Competition between and within aspen (Populus tremula) and raspberry (Rubus idaeus) after clear-cutting: matrix models of structured populations dynamics. Forest Science and Technology. 2007, Vol. 3, №1.

Zhukovskaya O.V., Ulanova N.G.
Influence of brushing frequency on birch population structure after felling. Ecoscience. 2006, v.13, 2, pp. 219-225.

Klochkova I.N.
Nonnegative matrices as a tool for modelling structured population dynamics: motivated expansions and new findings. Abstracts of the 13th ILAS. 2006, Vrije Universiteit, Amsterdam. P. 71-72

Klochkova I.N. and Demidova A.N.
Competition dynamics between two double-structured populations. European Conference on Mathematical and Theoretical Biology ECMTB05, Book of Abstracts 2. 2005, Center for Information Service and High Performance Computing, Dresden University of Technology, Dresden, Germany. P. 120.

Logofet D.O.
Double structures within an ordinary formalism: matrix models of plant population dynamics. European Conference on Mathematical and Theoretical Biology ECMTB05, Book of Abstracts 2. 2005, Center for Information Service and High Performance Computing, Dresden University of Technology, Dresden, Germany. P. 117.

Logofet D.O.
Certainly stable matrices with uncertain entries: ‘berries’ to come from ‘flowers’. Abstracts of the 13th ILAS. 2006, Vrije Universiteit, Amsterdam. P. 72-73.

Logofet D.O.
Overcoming principal uncertainties in calibration of matrix population models. II International Conference on Matrix Methods and Operator Equations, Moscow, July 23–27. 2007, Institute of Numerical Mathematics, Russian Acad. Sci., Moscow. P. 51–52.

Ulanova N.G., Logofet D.O.
Early successional changes in forest ecosystems after a gap-forming disturbance. Proceeedings IUFRO Conference on Forest Landscape Restoration, Seoul, Republic of Korea, May 14-17. 2007, Seoul: Korea Forest Reseach Institute. P. 154-155.

Project participants

Laboratory of Mathematical Ecology (IAP RAS):

Dept. of Geobotany, Biological Faculty, Lomonosov Moscow State University