March  2016, 21(2): 523-536. doi: 10.3934/dcdsb.2016.21.523

Competition of two phytoplankton species for light with wavelength

1. 

Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan

Received  December 2014 Revised  May 2015 Published  November 2015

We study the competition of two phytoplankton species for a single resource-light with wavelength in a well mixed water column. The model was proposed by Stomp et al. in 2007, in this model each species prefers different interval of light spectrum. Their experimental results show that colorful phytoplankton species coexist.
    We classify the global behavior of the model by stability of equilibrium and the theory of monotone dynamical systems. The conclusion is that one of the following holds: one species competitively excludes the other, two species coexist, bistability of two species. We also analyze the special case when species have linear growth function, and the outcome is either competitive exclusion or two species coexistence; the results are consistent with the Stomp's experiments in 2004.
Citation: Chiu-Ju Lin. Competition of two phytoplankton species for light with wavelength. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 523-536. doi: 10.3934/dcdsb.2016.21.523
References:
[1]

G. Hardin et al., The competitive exclusion principle, science, 131 (1960), 1292-1297. Google Scholar

[2]

S. B. Hsu, H. L. Smith and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), 4083-4094, doi: 10.1090/S0002-9947-96-01724-2.  Google Scholar

[3]

S.-B. Hsu, Ordinary Differential Equations with Applications, vol. 21 of Series on Applied Mathematics, $2^{nd}$ edition, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013, doi: 10.1142/8744.  Google Scholar

[4]

S. B. Hsu and T. H. Hsu, Competitive exclusion of microbial species for a single nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), 1600-1617. doi: 10.1137/070700784.  Google Scholar

[5]

J. Huisman and F. J. Weissing, Light-limited growth and competition for light in well-mixed aquatic environments: An elementary model, Ecology, 75 (1994), 507-520. doi: 10.2307/1939554.  Google Scholar

[6]

G. E. Hutchinson, The paradox of the plankton, American Naturalist, 95 (1961), 137-145. doi: 10.1086/282171.  Google Scholar

[7]

J. Jiang, X. Liang and X. Q. Zhao, Saddle-point behavior for monotone semiflows and reaction-diffusion models, J. Differential Equations, 203 (2004), 313-330. doi: 10.1016/j.jde.2004.05.002.  Google Scholar

[8]

S. Sathyendranath and T. Platt, Computation of aquatic primary production: Extended formalism to include effect of angular and spectral distribution of light, Limnology and Oceanography, 34 (1989), 188-198. doi: 10.4319/lo.1989.34.1.0188.  Google Scholar

[9]

H. L. Smith, Monotone Dynamical Systems, An introduction to the theory of competitive and cooperative systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995.  Google Scholar

[10]

H. L. Smith and P. Waltman, The Theory of the Chemostat, Dynamics of microbial competition, 13. Cambridge University Press, Cambridge, 1995. doi: 10.1017/CBO9780511530043.  Google Scholar

[11]

M. Stomp, J. Huisman, F. de Jongh, A. J. Veraart, D. Gerla, M. Rijkeboer, B. W. Ibelings, U. I. Wollenzien and L. J. Stal, Adaptive divergence in pigment composition promotes phytoplankton biodiversity, Nature, 432 (2004), 104-107. doi: 10.1038/nature03044.  Google Scholar

[12]

M. Stomp, J. Huisman, L. Vörös, F. R. Pick, M. Laamanen, T. Haverkamp and L. J. Stal, Colourful coexistence of red and green picocyanobacteria in lakes and seas, Ecology Letters, 10 (2007), 290-298. doi: 10.1111/j.1461-0248.2007.01026.x.  Google Scholar

show all references

References:
[1]

G. Hardin et al., The competitive exclusion principle, science, 131 (1960), 1292-1297. Google Scholar

[2]

S. B. Hsu, H. L. Smith and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), 4083-4094, doi: 10.1090/S0002-9947-96-01724-2.  Google Scholar

[3]

S.-B. Hsu, Ordinary Differential Equations with Applications, vol. 21 of Series on Applied Mathematics, $2^{nd}$ edition, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013, doi: 10.1142/8744.  Google Scholar

[4]

S. B. Hsu and T. H. Hsu, Competitive exclusion of microbial species for a single nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), 1600-1617. doi: 10.1137/070700784.  Google Scholar

[5]

J. Huisman and F. J. Weissing, Light-limited growth and competition for light in well-mixed aquatic environments: An elementary model, Ecology, 75 (1994), 507-520. doi: 10.2307/1939554.  Google Scholar

[6]

G. E. Hutchinson, The paradox of the plankton, American Naturalist, 95 (1961), 137-145. doi: 10.1086/282171.  Google Scholar

[7]

J. Jiang, X. Liang and X. Q. Zhao, Saddle-point behavior for monotone semiflows and reaction-diffusion models, J. Differential Equations, 203 (2004), 313-330. doi: 10.1016/j.jde.2004.05.002.  Google Scholar

[8]

S. Sathyendranath and T. Platt, Computation of aquatic primary production: Extended formalism to include effect of angular and spectral distribution of light, Limnology and Oceanography, 34 (1989), 188-198. doi: 10.4319/lo.1989.34.1.0188.  Google Scholar

[9]

H. L. Smith, Monotone Dynamical Systems, An introduction to the theory of competitive and cooperative systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995.  Google Scholar

[10]

H. L. Smith and P. Waltman, The Theory of the Chemostat, Dynamics of microbial competition, 13. Cambridge University Press, Cambridge, 1995. doi: 10.1017/CBO9780511530043.  Google Scholar

[11]

M. Stomp, J. Huisman, F. de Jongh, A. J. Veraart, D. Gerla, M. Rijkeboer, B. W. Ibelings, U. I. Wollenzien and L. J. Stal, Adaptive divergence in pigment composition promotes phytoplankton biodiversity, Nature, 432 (2004), 104-107. doi: 10.1038/nature03044.  Google Scholar

[12]

M. Stomp, J. Huisman, L. Vörös, F. R. Pick, M. Laamanen, T. Haverkamp and L. J. Stal, Colourful coexistence of red and green picocyanobacteria in lakes and seas, Ecology Letters, 10 (2007), 290-298. doi: 10.1111/j.1461-0248.2007.01026.x.  Google Scholar

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