Born: August 14, 1946, Irkutsk city, Russia

Citizenship: Russia

Work addresses
Permanent
Center of Forest Ecology and Productivity of Russian Academy Sciences
Novocheremushkinskaya str. 69, Moscow 117418, Russia.

E-mails: gkarev@hotmail.com ,  gkarev@math.gatech.edu

Fax (7-095) 3322917. Tel: (7-095) 3326990

• Dr. in Sci. (Mathematical Biophysics), 1994, The Institute of Biophysics of Siberian Branch of Russian Academy of Science, Krasnoyarsk.
• Thesis title: Structural Models and Dynamics of Tree Populations.
• Ph.D. (Mathematics), 1974, The Moscow Institute of Electronic Engineering.
• Thesis title: Asymptotic Behavior of Discrete Markov Processes. Supervisor acad. A. A. Lyapunov.
• M.Sc. (Mathematics, summa cum laude) 1969. The Novosibirsk State University, Department of Mathematics and Mechanics, Chair of Algebra and Mathematical Logic.
• Thesis title: The Local Algorithms of Boolean Functions Simplifying (Level “0”, Red diploma). Supervisor Acad. Ju. I. Juravlev.
• The Special Physical and Mathematical High School of The Novosibirsk State University, 1962-1964 (Level “0”, Gold Medal).

• 1999. Invited Research Professor of University Paris Sud X1, Laboratory Ecologie des populations et communautes, Campus scientifique d'Orsay, Batiment 362, 91405 Orsay cedex, France.
• 1994-recent: Professor of Mathematics in Moscow State Academy by name Maimonid; Moscow, Russia.
• 1992-recent: Head of Group of Laboratory of Mathematical Modeling of Forest Ecosystems, The Center of Forest Ecology and Productivity of Rus Ac. Sci. 69 Novocheremushkinskaya str., Moscow, Russia.
• 1985-1992 : Senior Research scientist, Scientific Council in Cybernetics of Ac. Sci. of USSR; 40 Vavilova str., Moscow, USSR.
• 1984-1985 : Senior Research scientist, the Laboratory of Mathematical Modeling in Chemistry, The Institute of Mathematics of Ac. Sci USSR; Novosibirsk, USSR.
• 1973 -1984: Research scientist, the Laboratory of Mathematical Modeling in Biology and Economics, The Institute of Mathematics of Ac. Sci USSR; Novosibirsk, USSR.
• 1974 -1976: Assistant Professor of Mathematics in Novosibirsk State University; Novosibirsk, USSR.
• 1969-1973: Junior research scientists, the Laboratory of Theoretical Cybernetics of The Institute of Hydrodynamics of Ac. Sci USSR; Novosibirsk, USSR.

During my carrier I have done various research work reflected in about 120 publications.

1. Early research was devoted to the problems of discrete analysis and theory of local algorithms; a new approach to the estimation of the realization complexity of some properties of graphs and Boolean functions was developed. The results composed the M.Sci. Thesis.

2. Some early research projects were devoted to the problems of theory and applications of random processes and random sequences of martingale types; convergence criteria, Riess decomposition, Martin boundary, some analogies of martingale inequalities were obtained. The results were applied to investigation of asymptotic behavior of random sequences.

The results composed the Ph.D. Thesis.

My major research was done on the problems of mathematical biology and ecology, mathematical modeling of populations and biological communities and developing of necessary mathematical tools.

3. Stochastic theory of populations.
The method of Liapunov function was developed on the base of martingale-liked random functions and some new limit theorems about random sequences. The results were applied to studying of asymptotic behavior of general stochastic models of populations with discrete time. The problem of population degeneration was investigated in rather general case.

4. Theory of structural individual-based models.
These works contain results describing asymptotic behavior of general autonomous age-state model with many types of individuals described by several structural variables. The exact form of limit distributions and its stability were proved; the estimates of convergence speed, method of calculating of age structure and different regulating functionals of limit distributions (so called generalized variables) were founded; methods of researching of two classes of non-linear community models - separate and Gurtin-McKamy type models were proposed.

The main results were applied to 1) structure models of metapopulations; 2) structure models of communities consisting from many populations; 3) structure models of population with complicated life circle; 4) ergodic theorems for structural models of communities.

5. Mathematical models of forest ecosystems.
The main contribution is systematic development of the theory and applications of structured models of metapopulation to the forest ecosystem modeling. Well-known forest gap-models were considered and investigated as structured metapopulation models. Asymptotic behavior of gap metapopulation models was completely analyzed. Some new models of dynamics of the main taxonomic characteristics of tree stands were constructed and verified on the base of experimental data. The methods of spatial-temporal scales enlarging were developed.

The hierarchical sequence of forest ecosystem mathematical models: single tree - gap - population - metapopulation - forest ecosystem - forest territory (landscape, region) was constructed. Methods of construction of the whole hierarchical sequence of forest models based on an arbitrary model of a single tree were developed. These results compose a mathematical theory of structured forest modeling an may be considered as theoretical base of computer gap-modeling of forest dynamics. The main results were described in monograph.

6. Ergodic theorems in biology and succession forest models.
The fundamental problem of stability and biodiversity of plant communities and other ecosystems appears to be connected closely to ergodic properties of succession association of communities. It has been proved in the frameworks of the authors structure succession model, that in a climax state of association the areas of biocenoces as their all basic characteristics (such as a forest stock, average tree high or diameter, age structure) occurs to be proportional to their proper times in succession line; the proportion constant is universal for the given model. The method of calculating of any proper time and ergodic constant was given. The “ergodic method” of estimation of forest ecosystem state and it’s deviation from a steady conditions was proposed. The analogous (but more general) results were proved for some general models of biological communities.

7. Bifurcation approach to complex ecological system modeling.
The qualitative behavior of complex system near critical modes may usually be described by a “low-dimensional” non-linear model depending on some parameters; the last model may be analyzed by bifurcation theory methods. The inverse problem of construction of “portrait-kinetic models” of complex systems, which would realize all observable qualitative types of system kinetics was considered. Both approaches were used to construction and investigation of some population models. The main results consist in consecutive analysis of wave dynamical modes of conceptual population system, described by models “reaction–taxis–diffusion” and “reaction–autotaxis–cross-diffusion” with polynomial intensities of growth and taxis. Results were applied to conceptual models of “travelling waves” and “moving density patterns” of forest insect populations and oceanic plankton community.

8. Modeling of heterogeneous populations.

The new theory of dynamics of heterogeneous population with distributed values of parameters and/or initial conditions of variables was suggested and developed. The resulting models represent systems of ordinary differential equations (under standard approaches the dynamics of heterogeneous population is described usually by partial differential equations). Essential new dynamical regimes were founded even for simplest well-known population models. This theory and corresponding individual-based models were applied to studying of the next problems: 1) the phenomenon of formation of patterns (known as gap, locus, cenon) in tree populations from initial heterogeneous subpopulation of trees; 2) the models of number dynamics of population with distributed values of a reproduction factor and/or environment parameters; 3) the conceptual model of “renewal of vanishing species”; 4) the models of global demography and the problem of “demographic explosion”.

Some separate research was also done on the “ratio-dependent prey-predator” model, the fractal approach of tree crown modeling, the stochastic modification of Emden-Fauler equation, the computer information reference system of ecological models, the computer algorithm of medical diagnostic by the Voll electropuncture method.
 
 

• Introduction to Mathematical methods of modeling (1996-now),
• State Jewish Academy by name Maimonid, Moscow.
• Linear algebra and analytical geometry (1995-1997), State Jewish Academy by name Maimonid, Moscow.
• Differential Equations (1974-1976), Novosibirsk State University.
• Foundations of Mathematics (1971-1974),
• The Special Physical and Mathematical High School of The Novosibirsk State University.

International:

1. INTAS Project “Forest Models for Sustainable Forest Management (FORMOD)”, 1999 (team leader).
2.  Travel Grant of London Mathematical Community, 1998.
3.  Project of European Forest Institute (Finland, Joensuu): The analytical survey ''Modern Approach in Forest Ecosystem Modeling'', 1997.
4.  Project of IIASA (Laxemburg, Austria) “Siberian Forests”, 1995.

Russian Fund of Fundamental Investigations:

1. Complex ecological -mathematical modeling of dynamics of forest insect number in conditions of global environment changes, grant N 99-04-00234, 1999-now.
2.  Theoretical bases of cultivation of high productive wood plantings, grant N 98-04-48502, 1998-now.
3.  Methods of analytical and numerical research of critical regimes in models of ecosystem dynamics, grant N 98-01-00483, 1998-now.
4.  Meaning of insect-pest mass outbreaks on boreal forests under global climate changes, grant  N 96-04-48340, 1996-1998.
5.  GIS Russian Forests, grant N 94-04-13775, 1994-1996.
6.  The role of mosaic structure in boreal forest dynamics, grant N 94-04-12407, 1994-1996.
7.  The State Sci. Program N18 “Problems of Global Changes of Environment and Climate”. 1994.

Monographies:

Chertov O.G., A.S. Komarov and G.P. Karev, 1999. Modern approaches in forest ecosystem modeling. Brill, Leiden-Boston-Koln. 116 pp.

Berezovskaya F.S., Karev G.P., 2000. Manual “Differential Equations and Mathematical models”, Moscow, MIREA, 140 pp.

Reviews

1. Antonovsky M.Ya., Berezovskaya F.S., Karev G.P., Shvidenko A.Z., Shugart H.H., 1991. Ecophysiological models of forest stand dynamics. WP-91-36. IIASA, Laxemburg, Austria. 97 p.

2. Berezovskaya, F.S., Karev, G.P., Shvidenko, A.Z., 1991. Modeling Stands Dynamics: Ecological-Physiological Approach. Research and Information Center on Forest Resources, Moscow. 84 p. (in Russian).

Peer reviewed papers:

1. Karev, G.P , Treskov S.A., Fridman G.Sh. 1965. On a complexity of realization of Boolean function. In: Soviet Math. Doklady ,v.165, n.4, p.745-747.

2. Karev, G.P, 1973. On convergence of functionals of a Markov chain In: Soviet Math. Doklady, v.14, n.2, p.513-516.

3. Karev G.P., Ljapunov A.A., Treskov S.A. 1975. On deterministic and stochastic approaches to evolution problems of mathematical population theory. In: Problems of Evolution. Novosibirsk, v.4, pp.5-10 (in Russian).

4. Karev G.P., Treskov S.A.,1978. On the asymptotic behavior of the population number. In: Biometrica J. v.20, n.2, p.143-150.

5. Karev G.P., Treskov S.A.,1978. Method of Luapunoff functions in stochastic population models. In: Problems of Cybernetics, v.33, p.139-178 (In Russian).

6. Karev G.P.,1985. Mathematical model of light competition in light-limiting self-thinning tree stands. In: Journal of General Biology, v.46, No 1, p.75-90. (In Russian).

7. Karev G.P.,1992. Age-dependent population dynamics with several interior variables and spatial spread. In: Ecological Modeling, v.70. P.277-288.

8. Karev G.P.,1993. Asymptotic behavior of population models with age and internal structures. In: Basykin A., Zarkhin Yu. (eds). Mathematics and modeling. Nova Science Publishers, Inc. P.329-356.

9. Karev G.P.,1994. Structural models of phytocenosis succession dynamics and the problem of global climate change In: Global and regional ecological problems. Krasnoyarsk. P.57-69.

10. Karev G.P.,1994. Structural models of natural dynamics of forest cover. Doklady Biological Sciences, v.337, pp.273-275.

11. Karev G.P.,1996. Structural models of the dynamics of biological communities. In: Doklady Mathematica, Vol 54, No.2, p.749-751.

12. Karev G.P., Skomorovsky Ju.I.,1997. Mathematical models of tree stands self-thinning. In: Lesovedenie, No.4, p.14-20.(in Russian).

13. Berezovskaya F., Karev G., Kisliuk, O., Khlebopros, R., Tselniker, Yu. 1997. Fractal approach to computer-analytical modeling of tree crown. In: TREES, V.11, No 6, pp.323-327.

14. Karev G.P., 1997. On the ergodic hypothesis in biocenology. Doklady Biological Sciences, v.353,pp.177-179.

15. Karev G.P., 1999. Gap-paradigm and the structure models of forest ecosystems. In: Syberian Ecological Journal (in Russian).

16. Berezovskaya F.S., Isaev A.S., Karev G.P. Khlebopros R.G.,1999. The role of taxis in forest insect dynamics. // Doclady Biological Sci. v.365, 1999, 148-151.

17. Berezovskaya F., Karev G., 1999 Bifurcations of traveling waves in population models with taxis. Physics-Uspekhi, v.169 , in trans. from Uspekhi fizicheskikh nayk, v.169, 9, 1999, 1011-1024.

18. Berezovskaya F.S., Karev G.P.,1999. Travelling waves in polynomial population models. Doklady Mathematics, v.60, No.2,pp.295-299.

19. Karev G.P.,1999. The ergodic properties of the stable states of forest ecosystems. In: Problems of Ecological Monitoring and Ecosystems Modeling. Hydrometeoizdat, S.-Peterburg (in Russian).

20. 34. Berezovskaya F.S., Karev G.P., Khlebopros R.G.,1999. Models of insect-phytofagan populations. Travelling waves and stability. Ibid
 

Forthcoming articles (refereed journals):

1. Karev G.P. Structured Models of Pattern Formation of Tree Populations. Natural Resource Modeling.

2. Karev G.P. The effects of non-uniformity in population models. Doklady Mathematics.

3. Berezovskaya F.S., Karev G.P. Equations with cross-diffusion as the models of populations with attractant. J. of Biophysics.

4. Berezovskaya F.S., Karev G.P. Travelling waves in polynomial population models “growth-diffusion-taxis”`type. Nonlinear analysis.

5. Berezovskaya F., Karev G., Arditi R. Parametric analysis of the ratio-dependent predator-prey models. J. Math. Biol

Conference proceedings (refereed):

1. Karev G.P.,1999. Modeling of heterogeneous populations. EQUADIF-99, Berlin, Germany.

2. Berezovskaya F.S., Karev G.P.,1999. Bifurcations of solutions “traveling waves” in population models with taxis. Ibid.

3. Karev G.P.,1998. Stability and diversity of biological communities and reserve lands. Western Multi-conference, Missia Earth -98. San Diego, USA.

4. Berezovskaya F.S., Karev G.P. 1997. New approaches to qualitative behavior modeling of complex systems. Proc. of Int. Conf. on Informatics and Control, St.-Peterburg, Russia.

5. F.Berezovskaya, N.Davidova, G.Karev, R.Khlebopros, 1996. Effects of migration in spatial dynamics of forest insects. Proceedings of the International conference: Mathematics, computer, education. Dubna, Russia (in Russian).
 

Conference abstracts (refereed):

1. Karev G.P.,1999. Population heterogeneity can be a reason of number outbreaks. TMBM-99, Amsterdam, Netherlands.

2. Berezovskaya F.S., Karev G.P.,1999. Travelling waves and “pulsing patterns” in population models with autotaxis. Ibid.

3. Karev G.P.,1998. New methods of stability estimation of forest ecosystem

states. Alcala 1st International Conference on Mathematical Ecology-1998. Alcala, Spain.

4. Berezovskaya F.S., Karev G.P. Parametric analysis of travelling waves in polynomial models "reaction-diffusion-taxis". Applications to forest insect outbreaks. Ibid.

5. Karev G.P.,1997. Structural modeling of tree cenoses. Inter. Conf. DESTOBIO-97. Sofia, Bolgaria.

6. Karev G.P.,1997. Structural models of biological communities: asymptotic behavior and ergodic theorems. International Conference on Mathematical Biology (ISEM-97), Hangzhou, China.

7. Berezovskaya F.S., Karev G.P., 1996. Bifurcations of wave solutions in some population models. Proceedings of 3rd European Conference on Mathematics Applied to Biology and Medicine -1996, Heidelberg, Germany.

8. Karev G.P., 1996. Structural models of biological community dynamics and the ergodic theorems. Mathematische Modelle in der Biologie, Mathematisches Forschungsinstitut Oberwolfach, Germany.