Modeling the Role of Toxic Substances in a Phytoplankton-Toxic Phytoplankton-Zooplankton System

Abstract:

In this paper, a mathematical model has been proposed, which consists of three variables: non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP) and zooplankton. In this model, an Monod- Haldane functional response is utilized to identify the grazing process of zooplankton due to the phytoplankton toxicity. The product of square of TPP density with square of NTP density is to depict the allelopathic influence on NTP. Numerical analysis indicates that the phytoplankton toxicity has a significant influence on the dynamical complexity and species biomass level through bifurcation diagrams. All these results are expected to be of significance in exploration of the dynamical complexity of ecosystems.

• Periodical: Advanced Materials Research (Volumes 726-731)
• Pages: 1600-1603
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.726-731.1600
• Online since: August 2013
• Authors: Jiang Lin Zhao, Min Zhao
• Keywords: Bifurcation Diagram, Phytoplankton, Stability, Toxin, Zooplankton

References

[1] R. Croppa and J. Norbury, Simple predator–prey interactions control dynamics in a plankton food web model, Ecol. Model. 220 (2009) 1552-1565.

DOI: 10.1016/j.ecolmodel.2009.04.003

[2] J.X. Kang, Omega-3: a link between global climate change and human health, Biotechnol. Adv. 29 (2011) 388-390.

[3] C.B. Mouw, J.A. Yoder and S.C. Doney, Impact of phytoplankton community size on a linked global ocean optical and ecosystem model, J. Marine. Syst. 89 (2012) 61-75.

DOI: 10.1016/j.jmarsys.2011.08.002

[4] T. Hallam, C. Clark and G. Jordan, Effects of toxicants on populations: a qualitative approach II: First order kinetics, J. Math. Biol. 18 (1983) 25–37.

DOI: 10.1007/bf00275908

[5] A.J. Windust, J.L.C. Wright and B McLachlan, The effects of the diarrhetic shellfish poisoning toxins, okadaic acid and dinophysistoxin-1, on the growth of microalgae, Marine Biology. 126 (1996) 19-25.

DOI: 10.1007/bf00571373

[6] F.D. Hulot and J. Huisman, Allelopathic interactions between phytoplankton species: the role of heterotrophic bacteria and mixing intensity, Limnology and Oceanography. 49 (2004) 1424-1434.

DOI: 10.4319/lo.2004.49.4_part_2.1424

[7] M. Gledhill and R.W. Van Kirk, Modeling effects of toxin exposure in fish on long-term population size, with an application to selenium toxicity in bluegill (Lepomis macrochirus), Ecol Model. 222 (2011) 3587-3597.

DOI: 10.1016/j.ecolmodel.2011.08.023

[8] J.M. Burkholder and H. G. Marshall, Toxigenic pfiesteria species-updates on biology, ecology, toxins, and impacts, Harmful Algae. 14 (2012) 196-230.

DOI: 10.1016/j.hal.2011.10.022

[9] J.P. Grovera, D.L. Roelkeb and B.W. Brooks, Modeling of plankton community dynamics characterized by algal toxicity and allelopathy: A focus on historical Prymnesium parvum blooms in a Texas reservoir, Ecol. Model. 227 (2012) 147-161.

DOI: 10.1016/j.ecolmodel.2011.12.012

[10] J. Maynard-Smith, Models in Ecology, Cambridge University Press, Cambridge, UK, 1974.

[11] J. Solé, E. García-Ladon, P. Ruardij and M. Estrada, Modelling allelopathy among marine algae, Ecol. Model. 183 (2005) 373-384.

DOI: 10.1016/j.ecolmodel.2004.08.021

[12] R. Pal, D. Basu and M. Banerjee,Modelling of phytoplankton allelopathy with Monod–Haldane type functional response-a mathematical study, Biosystems. 95 (2009) 243-253.

DOI: 10.1016/j.biosystems.2008.11.002

[13] B. Mukhopadhyay and R. Bhattacharyya, Modelling phytoplankton allelopathy in a nutrient–plankton model with spatial heterogeneity, Ecol. Model.198 (2006) 163–173.

DOI: 10.1016/j.ecolmodel.2006.04.005

[14] M.Banerjee and E. Venturino, A phytoplankton–toxic phytoplankton–zooplankton model, Ecological Complexity. 8 (2011) 239–248.

DOI: 10.1016/j.ecocom.2011.04.001

[15] J. Yang and M. Zhao, Complex behavior in a fish algae consumption model with impulsive control strategy, Discrete Dynamics in Nature and Society. (2011) ,163541.

DOI: 10.1155/2011/163541