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Sistem Parametrelerinin Plankton Dinamiği Üzerine Etkisi: Matematiksel Modelleme Yaklaşımı

Yıl 2019, , 292 - 299, 25.08.2019
https://doi.org/10.19113/sdufenbed.446284

Öz

Fitoplankton-zooplankton modeli oksijen-plankton modelinin bir alt modeli olarak önerilmiş ve analiz edilmiştir. Matematiksel olarak, ikili diferensiyel denklem yapısı dikkate alınmıştır. Bu çalışmada, okyanuslardaki fitoplanktonlar tarafından fotosentez işleminin sonucu olarak üretilen oksijen oranı, kararlı olduğu varsayılarak oksijen konsantrasyonu sabit bir değer olarak seçilmiştir. Sistem parametrelerindeki değişim etkisi altındaki fitoplankton-zooplankton popülasyonunun temel özellikleri, analitik ve nümerik yöntemlerle detaylandırılmıştır. Özellikle, zooplanktonun büyüme hızı ve fitoplankton için tür içi rekabetin sistem davranışı üzerindeki etkileri ele alınmıştır. Sistemin zamana bağlı değişimini görmek için, mekâna bağlı olmayan sistem ele alınmıştır. Sonrasında ise mekânsal sistem, çok sayıdaki sayısal simülasyonlar yardımıyla calışılmıştır. Mevcut model sisteminin hem zamana hem de mekâna bağlı olduğu durumda zengin dinamiğe sahip olduğu görülmüştür.

Kaynakça

  • [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 plankton oxygen dynamics under the climate change. Journal of theoretical biology, 424, 91-109.

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

Yıl 2019, , 292 - 299, 25.08.2019
https://doi.org/10.19113/sdufenbed.446284

Öz

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

Kaynakça

  • [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 plankton oxygen dynamics under the climate change. Journal of theoretical biology, 424, 91-109.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Yadigar Şekerci Fırat 0000-0001-7545-1824

Yayımlanma Tarihi 25 Ağustos 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Şekerci Fırat, Y. (2019). Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(2), 292-299. https://doi.org/10.19113/sdufenbed.446284
AMA Şekerci Fırat Y. Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. Ağustos 2019;23(2):292-299. doi:10.19113/sdufenbed.446284
Chicago Şekerci Fırat, Yadigar. “Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23, sy. 2 (Ağustos 2019): 292-99. https://doi.org/10.19113/sdufenbed.446284.
EndNote Şekerci Fırat Y (01 Ağustos 2019) Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23 2 292–299.
IEEE Y. Şekerci Fırat, “Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 23, sy. 2, ss. 292–299, 2019, doi: 10.19113/sdufenbed.446284.
ISNAD Şekerci Fırat, Yadigar. “Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23/2 (Ağustos 2019), 292-299. https://doi.org/10.19113/sdufenbed.446284.
JAMA Şekerci Fırat Y. Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2019;23:292–299.
MLA Şekerci Fırat, Yadigar. “Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 23, sy. 2, 2019, ss. 292-9, doi:10.19113/sdufenbed.446284.
Vancouver Şekerci Fırat Y. Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2019;23(2):292-9.

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