臺灣博碩士論文加值系統

本文探討均質水域中浮游植物競爭系統，考慮何種機制能促進物種的多樣性。
第一個模型在浮游生物動態行為中考慮光抑制的效應，其結果展現多重的穩定平衡解，物種在此模型中不會達到共存。第二個模型中兩物種同時競爭陽光及單一養分，其競爭結果有下列的可能性，只有單一物種存活，兩物種共存，或者是雙穩定現象。第三個模型對於物種競爭陽光時，考慮物種在吸收不同的光波有相對的喜好程度，兩物種競爭結果與第二個模型類似。第四個模型考慮在周期變化的環境中兩物種對單一養分的競爭，其結果可能達到兩物種共存，甚至可能逆轉競爭結果，然而卻不可能達到雙穩定的現象

We consider several phytoplankton competition models in a well-mixed water column to explore which mechanisms promote bio-diversity. The dynamics of phytoplankton communities under photo-inhibition shows that alternative stable states exist, and coexistence does not occur. The dynamics of two
microbial species competing for nutrient and light exhibits competitive exclusion, coexistence, and bi-stability. The competition of phytoplankton species for light with wavelength can also promote bio-diversity. The competition of two microorganisms for nutrient with seasonal succession in chemostat can exhibit coexistence, reversing competition outcomes, but not bi-stability.

Contents

Acknowledgements

Abstract

1. Preliminary

2. Dynamics of phytoplankton communities under photo-inhibition
2.1 Introduction . . . . . . . . . . . . . . .. . . . . . 11
2.2 The model and main results . . . . . . . . . . . . . 12
2.3 Feasibility of theoretical predictions . .. . . . . . 24
2.4 Discussion . . . . . . . . . . . . . . . .. . . . . . 28

3 Dynamics of two microbial species competing for nutrient
and light
3.1 Introduction . . . . . . . . . . . . . . .. . . . . . 33
3.2 Single species growth model . . . . . . . . . . . . . 36
3.3 Two species model . . . . . . . . . . . . . . . . . . 41
3.4 The proofs . . . . . . . . . . . . . . . .. . . . . . 50
3.5 Graphical method . . . . . . . . . . . . . .. . . . . 57
3.6 Discussion . . . . . . . . . . . . . . . .. . . . . . 63

4 Competition of phytoplankton species for light with wave-
length
4.1 Introduction . . . . . . . . . . . . . . .. . . . . . 65
4.2 Competition model with constant wavelength. . . . . . 67
4.3 Same specific absorption spectrum. . . . . . . .. . . 71
4.4 Identical species with different specific absorption spectrum
4.4.1 The case n = 1 . . . . . . . . . . . . . . . . .. . 75
4.4.2 The case n = 2 . . . . . . . . . . . . . . . . .. . 77
4.5 Discussion . . . . . . . . . . . . . . . .. . . . . . 84

5 Competition of two microorganisms for nutrient with sea-
sonal succession in chemostat
5.1 Introduction . . . . . . . . . . . . . . . . . . . . 87
5.2 Single species . . . . . . . . . . . . . .. . . . . . 90
5.3 Competition model . . . . . . . . . . . . . . . . . . 91
5.4 The global behavior of competition model. . . . . . . 96
5.5 Discussion . . . . . . . . . . . . . . . .. . . . . . 99

Bibliography

[1] Andrews, J. F., 1968. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnology and Bio-engineering 10, 707-723.

[2] Butler, G. J., Wolkowicz, G. S. K., 1985. A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM Journal on Applied Mathematics 45, 138-151.

[3] M. Droop, Some thoughts on nutrient limitation in algae, J. Phycol., 9 (1973), 264–272.

[4] Eilers, P.H.C., Peeters, J.C.H., 1988, A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton. Ecological Modelling 42, 199-215.

[5] Gerla, D.J., Mooij, W.M., Huisman, J., 2011. Photoinhibition and the assembly of light-limited phytoplankton communities. Oikos 120, 359-368.

[6] J. P. Grover, Constant- and variable-yield models of population growth: Responses to environmental variability and implications for competition, J. Theoret. Biol., 158 (1992), 409–428

[7] Han, B. P., 2002. A mechanistic model of algal photoinhibition induced by photodamage to photosystem-II. Journal of Theoretical Biology 214, 519-527.

[8] Henley, W. J., 1993. Measurement and interpretation of photosynthetic light-response curves in algae in the context of photoinhibition and diel changes. Journal of Phycology 29, 729-739.
[9] S. B. Hsu and X. Q. Zhao, Lotka-Volterra Competition model with season succession, J. Math. Biology (2012), 64, p.109-130.

[10] S.-B. Hsu, K.-S. Cheng and S. P. Hubbell, Exploitative competition of microorganism for two complementary nutrients in continuous cultures , SIAM J. Appl. Math., 41(3)(1981) , 422–444.

[11] S.-B. Hsu and T.-H. Hsu, Competitive exclusion of microbial species for a single-nutrient with internal storage, SIAM J. Appl. Math., 68(6)(2008), 1600–1617.

[12] S.-B. Hsu, S. P. Hubbell, and P. Waltman, A mathematical theory for Single–Nutrient competition in continuous culture of Micro–Organisms, SIAM J. Appl. Math., 32(2)(1977) , 366–382.

[13] 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.

[14] Huisman, J., 1997. The struggle for light. PhD thesis, Rijksuniversiteit Groningen.

[15] Huisman, J., Weissing, F. J., 1994. Light-limited growth and competition for light in well-mixed aquatic environments: an elementary model. Ecology 75, 507-520.

[16] Huisman, J., Weissing, F. J., 1995. Competition for nutrients and light in a mixed water column: a theoretical analysis. American Naturalist 146, 536-564.

[17] J. Jiang, X. Liang and X. Zhao, Saddle-point behavior for monotone semifolws and reaction-diffusion models , J. Diff. Equations, 203 (2004), 313–330.

[18] Klausmeier, C. A., Litchman, E., 2001. Algal Games: The Vertical distribution of phytoplankton in poorly mixed water columns. Limnology and Oceanography 46, 1998-2007.

[19] C. A. Klausmeier, Floquet theory: A useful tool for understanding nonequilibrium dynamics, Theoretical Ecology, 1(2008): 153–163.

[20] C. A. Klausmeier, Successional state dynamics : A novel approach to modeling nonequilibrium foodweb dynamics, Journal of Theoretical Biology, 262(2010), 584–595.

[21] B. Li and H. L. Smith, Global dynamics of microbial competition fortwo resources with internal storage, J. Math. Biol., 55 (2007) 481–515.

[22] E. Litchman and C. A. Klausmeier, Competition of phytoplankton under fluctuating light, American Naturalist, 157(2001), 170–187.

[23] Litchman, E., Neale, P. J., 2005. UV effects on photosynthesis, growth and acclimation of an estuarine diatom and cryptomonad. Marine Ecology Progress Series 300, 53-62.

[24] Litchman, E., Neale, P. J., Banaszak, A. T., 2002. Increased sensitivity to ultraviolet radiation in nitrogen-limited dinoflagellates: Photoprotection and repair. Limnology and Oceanography 47, 86-94.

[25] Mellard, J. P., Yoshiyama, K., Litchman, E., Klausmeier, C. A., 2011. The vertical distribution of phytoplankton in stratified water columns. Journal of Theoretical Biology 269, 16-30.

[26] Muller, E.B., 2010. Synthesizing units as modeling tool for photosynthesizing organisms with photoinhibition and nutrient limitation. Ecological Modelling 222, 637-644.

[27] Oliver, R.L., Whittington, J., Lorenz, Z., Webster, I.T., 2003. The influence of vertical mixing on the photoinhibition of variable chlorophyll a fluorescence and its inclusion in a model of phytoplankton photosynthesis.
Journal of Plankton Research 25, 1107-1129.

[28] J. Passarge, S. Hol, M. Escher, and J. Huisman, Competition for nutrients and light: stable coexistence, alternative stable states, or competitive exclusion?, Ecological Monographs, 76(1) (2006) 57–72.

[29] Ryabov, A. B., Rudolf, L., Blasius, B., 2010. Vertical distribution and composition of phytoplankton under the influence of an upper mixed layer. Journal of Theoretical Biology 263, 120-133.

[30] Schwaderer, A.S., Yoshiyama, K., de Tezanos Pinto, P., Swenson, N. G., Klausmeier, C. A., Litchman, E., 2011. Eco-evolutionary differences in light utilization traits and distributions of freshwater phytoplankton. Limnology and Oceanography 56: 589-598.

[31] H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systmes, American Mathematical Society, 1995.

[32] H. L. Smith and H. R. Thieme, Stable coexistence and bi-stablility for competitive systems on ordered Banach spaces, J. Diff. Equations, 176(2001), 195-222.


[33] H. L. Smith and P. Waltman, The Theory of the Chemostat, Cambridge University Press, 1995.

[34] Stomp, M., Huisman, J., Voros, L., Pick, F. R., Laamanen, M., Haverkamp, T., Stal, L. J., 2007. Colourful coexistence of red and green picocyanobacteria in lakes and seas. Ecology Letters 10, 290-298.

[35] Tyystjärvi, E., 2008. Photoinhibition of photosystem II and photodamage of the oxygen evolving manganese cluster. Coordination Chemistry Reviews 252, 361-376.

[36] Weissing, F. J., Huisman, J., 1994. Growth and competition in a light gradient. Journal of Theoretical Biology 168, 323-336.

[37] Yoshiyama, K., Mellard, J. P., Litchman, E., Klausmeier, C. A., 2009. Phytoplankton competition for nutrients and light in a stratified water column. American Naturalist 174, 190-203.

[38] Yoshiyama, K., Nakajima, H., 2002. Catastrophic transition in vertical distributions of phytoplankton: alternative equilibria in a water column. Journal of Theoretical Biology 216, 397-408.

[39] Zonneveld, C., 1998. Photoinhibition as affected by photoacclimation in phytoplankton: a model approach. Journal of Theoretical Biology 193, 115-123.

[40] X.-Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.