ijaers social
google plus

International Journal of Advanced
Engineering, Management and Science

ijaems google ijaems academia ijaems pbn nauka gov JournalToc Scilit logo neliti neliti microsoft academic search Tyndale Library WorldCat indiana Library WorldCat aalborg university Library J-Gate academickeys ijaems rootindexing ijaems reddit ijaems research bib ijaems slideshare ijaers digg ijaems tumblr ijaems plurk ijaems I2OR ijaems ASI ijaems bibsonomy

Modelling the Increasing Differential Effects of the First Inter-Competition Coefficient on the Biodiversity Value; Competition between two Phytoplankton Species
( Vol-4,Issue-10,October 2018 )


P. Y. Igwe, J. U. Atsu, E.N. Ekaka-a, A.O. Nwaoburu


Differential effect, inter-competition coefficient, phytoplankton specie, biodiversity richness, continuous differential equation.


One of the intrinsic factors that affects the growth of two phytoplankton species is called the inter-competition coefficient. When this parameter value is decreased, the first phytoplankton specie benefit from biodiversity gain whereas the second phytoplankton specie is vulnerable to biodiversity loss. In contrast, when the same parameter value is increased from the value of 0.0525 to 0.099 the first phytoplankton specie dominantly suffers from a biodiversity loss whereas the second phytoplankton specie benefits from a biodiversity gain. The novel results that we have obtained have not been seen elsewhere but compliments our current contribution to knowledge in this challenging interdisciplinary research; these full results are presented and discussed quantitatively.

ijaers doi crossrefDOI:


Cite This Article:
Show All (MLA | APA | Chicago | Harvard | IEEE | Bibtex)
Paper Statistics:
  • Total View : 81
  • Downloads : 7
  • Page No: 737-740

[1] Anderson D.M. (1989). Toxic algae blooms and red tides: a global perspective, in: T. Okaichi, D.M. Anderson, T. Nemoto (Eds.), Red Tides: Biology, Environ. Sci. Toxicol., Elsevier, New York, pp. 11–21.
[2] Atsu, J. U. & Ekaka-a, E. N.(2017). Modelling intervention with respect to biodiversity loss: A case study of forest resource biomass undergoing changing length of growing season. International Journal of Engineering, Management and Science. 3(9).
[3] Bandyopadhyaya M., Saha T., Pal R. (2008). Deterministic and Stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment, Elsevier, 2:958–970.
[4] Bandyopadhyaya M. (2006). Dynamical analysis of a allelopathic phytoplankton model, J. Biol. Sys. 14: 205–218.
[5] Chattopadhyay J., Sarkar R.R., Mondal S. (2002). Toxin-producing phytoplankton may act as a biological control for planktonic blooms-field study and mathematical modeling, J. Theor. Biol. 215: 333–344.
[6] Chattopadhyay J. (1996). Effects of toxic substances on a two-species competitive system, Ecol. Model. 84: 287–289.
[7] Common, M., Perrings, C. (1992). Towards an ecological economics of sustainability. Ecol. Economics 6, 7–34.
[8] Duinker J., Wefer G (1994). Das CO2 und die rolle des ozeans, Naturwissenschahten, 81:237–242.
[9] Ekaka-a E.N (2009). Computational and mathematical modelling of plant species interactions in a harsh climate. Ph.D Thesis, Department of Mathematics, The University of Liverpool and The University of Chester, United Kingdom, 2009.
[10] Hallegraeff G.M. (1993). A review of harmful algae blooms and the apparent global increase, Phycologia 32:79–99.
[11] Hernándes-Bermejo, B., Fairén, V., (1995). Lotka-Volterra representation of general nonlinear systems.Math. Biosci. 140: 1–32.
[12] Loreau, M., (2000). Biodiversity and ecosystem functioning: recent theoretical advances. Oicos 91(1), 3–17.
[13] May R.M. (2001). Stability and Complexity in Model Ecosystems, Princeton University Press, New Jercy.
[14] Maynard-Smith J. (1974), Models in Ecology, Cambridge University Press, Cambridge.
[15] Nisbet R.M., Gurney W.S.C. (1982). Modelling Fluctuating Populations, Wiley Interscience, New York.
[16] Perrings, C., (1995). Ecological resilience in the sustainability of economic development. Economie Appliquée 48(2), 121–142.
[17] Pykh Yu, A. (2002). Lyapunov functions as a measure of biodiversity:theoretical background, Ecological Indicators 2: 123–133.
[18] Rice E. (1984). Allelopathy, Academic Press, New York.
[19] Saha, T. & Bandyopadhyay, M. (2009). Dynamical analysis of toxin producing phytoplankton interactions. Nonlinear Analysis, Real World Applications 10: 314-332.
[20] Sarkar R.R., Chattopadhyay J. (2003). The role of environmental stochasticity in a toxic phytoplankton-non-toxic phytoplankton-zooplankton system, Environmetrics, 14: 775–792.
[21] Smayda T. (1990). Novel and nuisance phytoplankton blooms in the sea: Evidance for a global epidemic, In: E. Graneli, B. Sundstrom, L. Edler, D.M. Anderson (Eds.), Toxic Marine Phytoplankton, Elsevier, New York , pp. 29–40.
[22] Solé J., García-Ladona E., Ruardij P., Estrada M. (2005). Modelling allelopathy among marine algae, Ecol. Model. 183:373–384.
[23] Tapaswi P.K., Mukhopadhyay A. (1999). Effects of environmental fluctuation on plankton allelopathy, J. Math. Biol. 39: 39–58