research partners    
Ph.D. students    
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Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

Structured population models for predator -prey interactions. The case of Daphnia and size selective planktivorous fish
Dariusz Wrzosek (MIM, University of Warsaw) and Zbigniew Maciej Gliwicz (Department of Hydrobiology, University of Warsaw)
The project is carried out by Jędrzej Jabłoński at University of Warsaw
The project concerns mathematical modelling in ecology of freshwater ecosystems. The biodiversity of an ecosystem heavily depends on diversity of first consumers which in the case of aquatic ecosystems are mainly various species of zooplankton feeding mostly on algae. Typical species belonging to zooplankton are that of crustaceans e.g Daphnia. In the case of fish-free habitats where main predator feeding on zooplankton is not present the diversity of phyto- and zooplankton is more frequently attributed to resource partitioning, and resource competition (Tilman 1982). This explanation fits fish-free habitats and laboratory cultures in which a competitively-superior large-bodied Daphnia monopolizes resources at carrying-capacity level (Hardin 1960). However, these scenario do not match typical freshwater habitats where Daphnia species coexist at population densities much below those at which resource competition would cause exclusion of competitively-inferior small-bodied taxa. In [1] an age-structured population model that accounts for age-dependent fecundity as well as size/age and density dependent mortality induced by size selective predator (planktivorous fish). The density of prey depends not only on that of predators being also influenced by the level of available resources. The dynamics of the latter is not taken into account in [1] being treated as an external parameter and it is one of research goals to consider three component system including interactions between resources (algae), consumers (Daphnia) and predator (planktivorous fish). In this case rather size-structured model should be constructed using concepts from [3] and [4] to describe resource-consumer interactions with that of [1] to account for predator-prey interaction. The second research goal is to build an efficient algorithm extending that of [2] and approximating model's solutions. The third important research-goal is to investigate how different feeding strategies of predator affect size/age structure of Daphnia populations. This project combines modelling in collaboration with biologists (team of Prof. Z. M. Gliwicz, Department of hydrobiology, University of Warsaw) and analytical study joint with numerical analysis and simulations in collaboration with numerical analysts team of Prof. M. Dryja and the group of Prof. Willi Jäager (IWR, University of Heidelberg).

[1] Z. M. Gliwicz and D. Wrzosek, (2008) American Nat., 172: 358-374.
[2] P. Krzyżanowski, D. Wrzosek and D. Wit, (2006) Math. Biosc., 203: 277-300.
[3] A.M. De Roos and L. Persson (2002) PNAS, 99: 12907-12912.
[4] S. Tuljapurkar and H. Caswell, (1997) Chapman & Hall, New York.