×

Population dynamics of rotifers in chemostats. (English) Zbl 0939.92035

A model for the dynamics of rotifer populations in chemostats is considered. The author concluded that the derivation of the state-structured delay differential equations model based on structured partial differential equation models for each stage gives the correct expression for the population growth rate.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
35Q80 Applications of PDE in areas other than physics (MSC2000)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Walz, N., Plankton Regulation Dynamics, (Ecological Studies (1993), Springer-Verlag: Springer-Verlag New York)
[2] Boraas, M. E., Population dynamics of food-limited rotifers in two-stage chemostat culture, Limnol. Oceanogr., 28, 546-563 (1983)
[3] Kooijman, S. A.L. M.; Kooi, B. W.; Boer, M. P., Rotifers do it with delay: The behaviour of reproducers vs dividers in chemostats, Nonlin. World, 3, 107-128 (1996) · Zbl 0894.92033
[4] Kooijman, S. A.L. M., Dynamic Energy Budgets in Biological Systems; Theory and Applications in Ecotoxicology (1993), Cambridge University Press
[5] Murphy, L. F., A nonlinear growth mechanism in size structured population dynamics, J. Theor. Biol., 104, 493-506 (1983)
[6] Gurney, W. S.C.; Nisbet, R. M.; Blythe, S. P., The systematic formulation of models of stage-structured populations, (Metz, J. A.J.; Diekmann, O., The dynamics of physiologically structured populations. The dynamics of physiologically structured populations, Lecture Notes in Biomathematics, volume 68 (1986), Springer-Verlag), 474-494 · Zbl 0542.92019
[7] Nisbet, R. M.; Gurney, W. S.C., The systematic formulation of population models for insects with dynamically varying instar duration, Theoretical Population Biology, 23, 114-135 (1983) · Zbl 0514.92021
[8] Caswell, H., On instantaneous and finite birth rates, Limnol. Oceanogr., 17, 787-791 (1972)
[9] Paloheimo, J. E., Calculation of instantaneous birth rate, Limnol. Oceanogr., 19, 692-694 (1974)
[10] Walz, N., Rotifer populations in plankton communities: Energetics and life history strategies, Experientia, 51, 437-453 (1995)
[11] Kooi, B. W.; Kooijman, S. A.L. M., Existence and stability of microbial prey-predator systems, J. theor. Biol., 170, 75-85 (1994)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.