Sistem Parametrelerinin Plankton Dinamigi Üzerine Etkisi: ˘ Matematiksel Modelleme Yakla¸sımı

Fitoplankton-zooplankton modeli oksijen-plankton modelinin bir alt modeli olarak önerilmi¸s ve analiz edilmi¸stir. Matematiksel olarak, ikili diferensiyel denklem yapısı dikkate alınmı¸stır. Bu çalı¸smada, okyanuslardaki fitoplanktonlar tarafından fotosentez i¸sleminin sonucu olarak üretilen oksijen oranı, kararlı oldugu varsayılarak oksijen kon- ˘ santrasyonu sabit bir deger olarak seçilmi¸stir. Sistem parametrelerindeki de ˘ gi¸sim etkisi ˘ altındaki fitoplankton-zooplankton popülasyonunun temel özellikleri, analitik ve nümerik yöntemlerle detaylandırılmı¸stır. Özellikle, zooplanktonun büyüme hızı ve fitoplankton için tür içi rekabetin sistem davranı¸sı üzerindeki etkileri ele alınmı¸stır. Sistemin zamana baglı dei¸simini görmek için, mekâna ba ˘ glı olmayan sistem ele alınmı¸stır. Sonrasında ise ˘ mekânsal sistem, çok sayıdaki sayısal simülasyonlar yardımıyla calı¸sılmı¸stır. Mevcut model sisteminin hem zamana hem de mekâna baglı oldu ˘ gu durumda zengin dinami ˘ ge˘ sahip oldugu görülmü¸stür.

Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach

A phytoplankton-zooplankton model is proposed and analyzed as a submodel of oxygen-plankton model. Mathematically, two coupled differential equationsare considered. In this work, oxygen which is produced as a result of photosyntheticprocess by phytoplankton in ocean is assumed stable by keep oxygen concentration as aconstant value. Basic properties of the phytoplankton-zooplankton population are detailedwith analytical and numerical way under the effect of change in system parameters. Inparticular, effects of per-capita growth rate of zooplankton and intraspecific competitionfor phytoplankton on the systems’ dynamical behavior are considered. To understand thesystem temporal structure nonspatial system is detailed. Then the spatial case is focussedwith the assist of extensive numerical simulations. It is observed that the model systemhas rich patterns in both temporal and spatial case.

PDF

___

[1] Malchow, H., Petrovskii, S. V., & Venturino, E. (2007). Spatiotemporal patterns in ecology and epidemiology: theory, models, and simulation. Chapman and Hall/CRC.
[2] Bengfort, M., Feudel, U., Hilker, F. M., & Malchow, H. (2014). Plankton blooms and patchiness generated by heterogeneous physical environments. Ecological complexity, 20, 185-194.
[3] Lewis, N. D., Breckels, M. N., Archer, S. D., Morozov, A., Pitchford, J. W., Steinke, M., & Codling, E. A. (2012). Grazing-induced production of DMS can stabilize foodweb dynamics and promote the formation of phytoplankton blooms in a multitrophic plankton model. Biogeochemistry, 110(1-3), 303-313.
[4] Malchow, H., Petrovskii, S. V., & Hilker, F. M. (2003). Models of spatiotemporal pattern formation in plankton dynamics. Nova Acta Leopoldina NF, 88(332), 325-340.
[5] Petrovskii, S., Kawasaki, K., Takasu, F., & Shigesada, N. (2001). Diffusive waves, dynamical stabilization and spatiotemporal chaos in a community of three competitive species. Japan Journal of Industrial and Applied Mathematics, 18(2), 459.
[6] Brown, J. H. (1984). On the relationship between abundance and distribution of species. The american naturalist, 124(2), 255-279.
[7] Tilman, D. (1982). Resource competition and community structure (No. 17). Princeton university press.
[8] Hutchinson, G. E. (1961). The paradox of the plankton. The American Naturalist, 95(882), 137-145.
[9] Ogawa, Y. (1988). Net increase rates and dynamics of phytoplankton populations under hypereutrophic and eutrophic conditions. Japanese Journal of Limnology (Rikusuigaku Zasshi), 49(4), 261-268.
[10] Tubay, J. M., et al. (2013). The paradox of enrichment in phytoplankton by induced competitive interactions. Scientific reports, 3, 2835.
[11] Odum, H. T. (1956). Primary production in flowing waters1. Limnology and oceanography, 1(2), 102-117.
[12] Riley, G. A. (1946). Factors controlling phytoplankton population on George’s Bank. J. Mar. Res., 6, 54-73.
[13] Behrenfeld, M. J., & Falkowski, P. G. (1997). A consumer’s guide to phytoplankton primary productivity models. Limnology and Oceanography, 42(7), 1479-1491.
[14] Sekerci, Y. & Petrovskii, S. (2015a). Mathematical modelling of spatiotemporal dynamics of oxygen in a plankton system. Mathematical Modelling of Natural Phenomena, 10(2):96-114.
[15] Sekerci, Y. and Petrovskii, S. (2015b). Mathematical modelling of plankton-oxygen dynamics under the climate change. Bulletin of Mathematical Biology, 77(12):2325- 2353.
[16] Gilad, O. (2008). Competition and competition models, Encyclopedia of Ecology, 707-712.
[17] Thorp, J. H., & Rogers, D. C. (2014). Thorp and covich’s freshwater invertebrates: ecology and general biology (Vol. 1). Elsevier.
[18] Rosenzweig, M. L. (1971). Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science, 171(3969), 385-387.
[19] Roy, S., & Chattopadhyay, J. (2007). The stability of ecosystems: a brief overview of the paradox of enrichment. Journal of biosciences, 32(2), 421-428.
[20] Fussmann, G. F., Ellner, S. P., Shertzer, K. W., & Hairston Jr, N. G. (2000). Crossing the Hopf bifurcation in a live predator-prey system. Science, 290(5495), 1358-1360.
[21] Huisman, J., & Weissing, F. J. (1995). Competition for nutrients and light in a mixed water column: a theoretical analysis. The American Naturalist, 146(4), 536-564.
[22] Fasham, M. J. R., Ducklow, H. W., & McKelvie, S. M. (1990). A nitrogen-based model of plankton dynamics in the oceanic mixed layer. Journal of Marine Research, 48(3), 591-639.
[23] Fasham, M. (1978). The statistical and mathematical analysis of plankton patchiness. Oceanogr. Mar. Biol. Ann. Rev., 16, 43-79.
[24] Monin, A. S., & Yaglom, A. M. (1971). Statistical Fluid Mechanics, Vol. 1. MIT Press, Cambridge, MA, 1975, 11.
[25] Okubo, A. Diffusion and ecological problems: mathematical models. Springer-Verlag, Berlin, 1980.
[26] Monin, A. S., Lumley, J. L., & Iaglom, A. M. (1971). Statistical fluid mechanics: mechanics of turbulence. Vol. 1. MIT press.
[27] Moss, B. R. (2009). Ecology of fresh waters: man and medium, past to future. John Wiley & Sons.
[28] Petrovskii, S., Sekerci, Y., & Venturino, E. (2017). Regime shifts and ecological catastrophes in a model of planktonoxygen dynamics under the climate change. Journal of theoretical biology, 424, 91-109.