A discrete, size-structured model of phytoplankton growth in the chemostat: Introduction of inhomogeneous cell division size

Journal of Mathematical Biology

Volumn 45, Issue 4, 2002, Pages 313-336

  Arino, Julien ^a,b   Gouzé, Jean Luc ^a   Sciandra, Antoine ^c  

^a INRIA   (France)

^b UNIVERSITY OF VICTORIA   (Canada)

^c LABORATOIRE D OCÉANOGRAPHIE DE VILLEFRANCHE   (France)

Author keywords

Chemostat; Discrete model; Inhomogeneous division size; Structured population models

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOREACTOR; CELL DIVISION; CELL SIZE; COMPARATIVE STUDY; COMPUTER SIMULATION; CYTOLOGY; GROWTH, DEVELOPMENT AND AGING; PHYSIOLOGY; PHYTOPLANKTON;

ANIMALS; BIOREACTORS; CELL DIVISION; CELL SIZE; COMPUTER SIMULATION; MODELS, BIOLOGICAL; PHYTOPLANKTON;

EID: 1842855764     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s002850200160     Document Type: Article

References (17)

1. Arino, J.: Modélisation structurée de la croissance du phytoplanctoii en chemostat. PhD thesis, Université Grenoble 1, (2001)
2. Arino, O., Kimmel, M.: Asymptotic analysis of a cell cycle model based on unequal division. SIAM J. Appl. Math., 47, 128-145 (1987)
3. Berman, A. Plemmons, R.: Nonnegative matrices in the mathematical sciences, 9 of Classics in Applied Mathematics. SIAM, 1994
4. Bernard, O., Gouzé, J.-L.: Non-linear qualitative signal processing for biological systems: application to the algal growth in bioreactors. Mathematical Biosciences, 157, 357-372 (1999)
5. Bernard, O., Malara, G., Sciandra, A.: The effects of a controlled fluctuating nutrient environment on continuous cultures of phytoplankton monitored by computers. Journal of Experimental Marine Biology and Ecology, 197, 263-278 (1996)
6. Cushing, J.M.: A competition model for size-structured species. SIAM J. Appl. Math., 49(3), 838-858 (1989)
7. Cushing, J.M.: An introduction to structured population dynamics, 71 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, 1998
8. Gage, T.B., Williams, F., Horton, J.: Division synchrony and the dynamics of microbial populations: A size-specific model. Theoretical Population Biology, 26, 296-314 (1984)
9. Golubitsky, M., Keeler, E.B., Rothschild, M.: Convergence of the age structure: applications of the projective metric. Theoretical Population Biology, 7, 84-93 (1975)
10. Metz, J., Diekmann, O.: editors. The dynamics of physiologically structured populations, volume 68 of Lecture Notes in Biomathematics. Springer-Verlag, 1986
11. Pascual, M., Caswell, H.: From the cell cycle to population cycles in phytoplankton-nutrient interactions. Ecology, 78(3), 897-912 (1997)
12. Sciandra, A., Lazzara, L., Claustre, H., Babin, M.: Responses of growth rate, pigment composition and optical properties of Cryptomonas sp. to light and nitrogen stresses. Marine Ecology Progress Series, 201, 107-120 (2000)
13. Smith, H.L. A discrete, size-structured model of microbial growth and competition in the chemostat. J. Math. Biol., 34, 734-754 (1996)
14. Smith, H.L., Waltman, P.: The theory of the chemostat. Dynamics of microbial competition., volume 13 of Cambridge Studies in Mathematical Biology. Cambridge University Press, 1995
15. Smith, H.L., Zhao, X.-Q.: Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete Contin. Dyn. Syst. Ser. B, 1(2), 183-191 (2001)
16. Turkia, J., Lepistö, L.: Size variations of planktonic Aulacoseira thwaites (diatomae) in water and in sediment from Finnish lakes of varying trophic state. Journal of Plankton Research, 21(4), 757-770 (1999)
17. Williams, F.M.: Dynamics of microbial populations. In B. Patten, editor, Systems Analysis and Simulation in Ecology, 198-267. Academic Press, 1971