Markov chain model of phytoplankton dynamics
International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) no. 4, pp. 763-771.

Voir la notice de l'article provenant de la source Library of Science

A discrete-time stochastic spatial model of plankton dynamics is given. We focus on aggregative behaviour of plankton cells. Our aim is to show the convergence of a microscopic, stochastic model to a macroscopic one, given by an evolution equation. Some numerical simulations are also presented.
Keywords: phytoplankton dynamics, coagulation, fragmentation, Markov chains
Mots-clés : dynamika fitoplanktonu, koagulacja, fragmentacja, łańcuch Markowa
@article{IJAMCS_2010_20_4_a12,
     author = {Wieczorek, R.},
     title = {Markov chain model of phytoplankton dynamics},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {763--771},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_4_a12/}
}
TY  - JOUR
AU  - Wieczorek, R.
TI  - Markov chain model of phytoplankton dynamics
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2010
SP  - 763
EP  - 771
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_4_a12/
LA  - en
ID  - IJAMCS_2010_20_4_a12
ER  - 
%0 Journal Article
%A Wieczorek, R.
%T Markov chain model of phytoplankton dynamics
%J International Journal of Applied Mathematics and Computer Science
%D 2010
%P 763-771
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_4_a12/
%G en
%F IJAMCS_2010_20_4_a12
Wieczorek, R. Markov chain model of phytoplankton dynamics. International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) no. 4, pp. 763-771. http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_4_a12/

[1] Adler, R. (1997). Superprocesses and plankton dynamics, Monte Carlo Simulation in Oceanography: Proceedings of the 'Aha Huliko'a Hawaiian Winter Workshop, Manoa, HI, pp. 121-128.

[2] Aldous, D. (1999). Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli 5(1): 3-48.

[3] Arino, O. and Rudnicki, R. (2004). Phytoplankton dynamics, Comptes Rendus Biologies 327(11): 961-969.

[4] Clark, P. and Evans, F. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations, Ecology 35(4): 445-453.

[5] El Saadi, N. and Bah, A. (2007). An individual-based model for studying the aggregation behavior in phytoplankton, Ecological Modelling 204(1-2): 193-212.

[6] Ethier, S.N. and Kurtz, T.G. (1986). Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley Sons, Inc., New York, NY.

[7] Franks, P.J.S. (2002). NPZ models of plankton dynamics: Their construction, coupling to physics, and application, Journal of Oceanography 58(2): 379-387.

[8] Henderson, P.A. (2003). Practical Methods in Ecology, Wiley-Blackwell, Malden, MA.

[9] Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley Sons Ltd, Chichester.

[10] Jackson, G. (1990). A model of the formation of marine algal flocs by physical coagulation processes, Deep-Sea Research 37(8): 1197-1211.

[11] Laurenc¸ot, P. and Mischler, S. (2002). The continuous coagulation-fragmentation equations with diffusion, Archive for Rational Mechanics and Analysis 162(1): 45-99.

[12] Levin, S.A. and Segel, L.A. (1976). Hypothesis for origin of planktonic patchiness, Nature 259.

[13] Passow, U. and Alldredge, A. (1995). Aggregation of a diatom bloom in a mesocosm: The role of transparent exopolymer particles (TEP), Deep-Sea Research II 42(1): 99-109.

[14] Rudnicki, R. and Wieczorek, R. (2006a). Fragmentation coagulation models of phytoplankton, Bulletin of the Polish Academy of Sciences: Mathematics 54(2): 175-191.

[15] Rudnicki, R. and Wieczorek, R. (2006b). Phytoplankton dynamics: from the behaviour of cells to a transport equation, Mathematical Modelling of Natural Phenomena 1(1): 83-100.

[16] Rudnicki, R. and Wieczorek, R. (2008). Mathematical models of phytoplankton dynamics, Dynamic Biochemistry, Process Biotechnology and Molecular Biology 2 (1): 55-63.

[17] Wieczorek, R. (2007). Fragmentation, coagulation and diffusion processes as limits of individual-based aggregation models, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences, Warsaw, (in Polish).

[18] Young, W., Roberts, A. and Stuhne, G. (2001). Reproductive pair correlations and the clustering of organisms, Nature 412(6844): 328-331.