Mathematical Biosciences and Engineering (MBE)

Effect of seasonal changing temperature on the growth of phytoplankton
Pages: 1091 - 1117, Issue 5/6, October/December 2017

doi:10.3934/mbe.2017057      Abstract        References        Full text (659.3K)           Related Articles

Ming Chen - School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, China (email)
Meng Fan - School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, China (email)
Xing Yuan - School of Urban and Environmental Sciences, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, China (email)
Huaiping Zhu - Lamps and Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada (email)

1 G. Ahlgren, Temperature functions in biology and their application to algal growth constants, Oikos, 49 (1987), 177-190.
2 O. Bernard and B. Remond, Validation of a simple model accounting for light and temperature effect on microalgal growth, Bioresource Technology, 123 (2012), 520-527.
3 R. Bouterfas, M. Belkoura and A. Dauta, Light and temperature effects on the growth rate of three freshwater [2pt] algae isolated from a eutrophic lake, Hydrobiologia, 489 (2002), 207-217.
4 C. Butterwick, S.I. Heaney and J. F. Talling, Diversity in the influence of temperature on the growth rates of freshwater algae, and its ecological relevance, Freshwater Biol, 50 (2005), 291-300.
5 M. Chen, M. Fan, R. Liu, X. Yuan and H. P. Zhu, The dynamics of temperature and light on the growth of phytoplankton, J. Theor. Biol., 385 (2015), 8-19.
6 W. Chen and A. Nauwerck, A note on composition and feeding of the crustacean zooplankton of Lake Taihu, Jiangsu Province, China, Limnologica, 26 (1996), 275-280.
7 Y. W. Chen, B. Q. Qin, K. Teubner and M. T. Dokulil, Long-term dynamics of phytoplankton assemblages: Microcystis-domination in Lake Taihu, a large shallow lake in China, J. Plankton Res., 25 (2003), 445-453.
8 L. Ding, Y. Pang and L. Li, Simulation study on algal dynamics under different hydrodynamic conditions, Acta Ecologica Sinica, 25 (2005), 1863-1868.
9 X. H. Dong, H. Bennion, R. Battarbee, X. D. Yang and E. F. Liu, Tracking eutrophication in Taihu Lake using the diatom record: potential and problems, J. Paleolimnol, 40 (2008), 413-429.
10 P. Driessche and W. James, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
11 J. J. Elser, K. Acharya, M. Kyle, J. Cotner, W. Makino, T. Markow, T. Watts, S. Hobbie, W. Fagan, J. Schade, J. Hood and R. W. Sterner, Growth rate-stoichiometry couplings in diverse biota, Ecology Letters, 6 (2003), 936-943.
12 M. Fan, Q. Wang and X. Zou, Dynamics of a non-autonomous ratio-dependent predator-prey system, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 133 (2003), 97-118.       
13 P. J. S. Franks, NPZ models of plankton dynamics: Their construction, coupling to physics, and application, J. Oceanog, 58 (2002), 379-387.
14 J. A. Freund, S. Mieruch, B. Scholze, K. Wiltshire and U. Feudel, Bloom dynamics in a seasonally forced phytoplankton zooooplankton model: trigger mechanisms and timing effects, Ecol. Complex, 3 (2006), 129-139.
15 G. F. Fussmann, S. P. Ellner, K. W. Shertzer and N. G. Hairston, Crossing the hopf bifurcation in a live predator-prey system, Science, 290 (2000), 1358-1360.
16 R. E. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.       
17 R. J. Geider, H. L. Maclntyre and T. M. Kana, A dynamic regulatory model of phytoplanktonic acclimation to light, nutrients, and temperature, Limnol. Oceanogr, 43 (1998), 679-694.
18 P. M. Glibert, Eutrophication and Harmful Algal Blooms: A Complex Global Issue, Examples from the Arabian Seas including Kuwait Bay, and an Introduction to the Global Ecology and Oceanography of Harmful Algal Blooms (GEOHAB) Programme, Int. J. Oceans and Oceanography, 2 (2007), 157-169.
19 J. C. Goldman and J. C. Edward, A kinetic approach to the effect of temperature on algal growth, Limnol. Oceanogr., 19 (1974), 756-766.
20 G. M. Grimaud, V. L. Guennec, S. D. Ayata, F. Mariret, A. Schiandra and O. Bernard, Modelling the effect of temperature on phytoplankton growth across the global ocean, IFAC-PapersOnLine, 48 (2015), 228-233.
21 J. P. Grover and T. H. Chrzanowski, Seasonal dynamics of phytoplankton in two warm temperate reservoirs: association of taxonomic composition with temperature, J. Plankt. Res, 28 (2006), 1-17.
22 C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada, 97 (1965), 5-60.
23 A. Huppert, B. Blasius, R. Olinky and L. Stone, A model for seasonal phytoplankton blooms, J. Theor. Biol., 236 (2005), 276-290.       
24 K. S. Johnson, F. P. Chavez and G. E. Friederich, Continental-shelf sediment as a primary source of iron for coastal phytoplankton, Nature, 398 (1999), 697-700.
25 R. I. Jones, The importance of temperature conditioning to the respiration of natural phytoplankton communities, British Phycological Journal, 12 (2007), 277-285.
26 S. E. Jorgensen and G. Bendoricchio, Fundamentals of Ecological Modelling, Elsevier, 2001.
27 I. Loladze, Y. Kuang and J. J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow with element cycling, Bulletin of Mathematical Biology, 62 (2000), 1137-1162.
28 J. H. Luo, Phytoplankton-zooplankton dynamics in periodic environments taking into account eutrophication, Math. Biosci., 245 (2013), 126-136.       
29 J. R. Moisan, T. A. Moisan and M. R. Abbott, Modelling the effect of temperature on the maximum growth rates of phytoplankton populations, Ecol. Model., 153 (2002), 197-215.
30 G. Phillips, R. Jackson, C. Bennett and A. Chilvers, The importance of sediment phosphorus release in the restoration of very shallow lakes (The Norfolk Broads, England) and implications for biomanipulation, Hydrobiologia, 94 (1994), 445-456.
31 L. Rosso, J. R. Lobry and J. P. Flandrois, An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model, J. Theor. Biol., 162 (1993), 447-463.
32 J. B. Shukla, A. K. Misra and P. Chandra, Modeling and analysis of the algal bloom in a lake caused by discharge of nutrients, App. Math. Comput., 196 (2008), 782-790.       
33 S. J. Thackeray, I. D. Jones and S. C. Maberly, Long-term change in the phenology of spring phytoplankton: species-specific responses to nutrient enrichement and climatic changes, J. Ecol., 96 (2008), 523-535.
34 D. Toro, M. Dominic , D. J. O'Connor and R. V. Thomann, A dynamic model of the phytoplankton population in the Sacramento San Joaquin Delta, Adv. Chem. Ser, 106 (1971), 131-180.
35 C. L. Wang, W. Y. Pan, Y. Q. Han and X. Qian, Effect of global climate change on cyanobacteria bloom in taihu lake, China Environmental Science, 30 (2010), 822-828.
36 F. B. Wang, S. B. Hsu and W. D. Wang, Dynamics of harmful algae with seasonal temperature variations in the cove-main lake, Discrete and Continuous Dynams. Systems - B, 21 (2016), 313-315.       
37 W. D. Wang and X. Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Differ. Equ., 20 (2008), 699-717.       
38 M. Winder and D. E. Schindler, Climate change uncouples trophic interactions in an aquatic ecosystem, Ecology, 85 (2004), 2100-2106.
39 M. Winder and J. E. Cloern, The annual cycles of phytoplankton biomass, Philos. T. R. Soc. B, 365 (2010), 3215-3226.
40 Q. J. Xu, B. Q. Qin, W. M. Chen, Y. W. Chen and G. Gao, Ecological simulation of algae growth in Taihu Lake, J. Lake Sci., 2 (2001), 149-157.
41 F. Zhang and X. Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516.       
42 Q. Zhao and X. Lu, Parameter estimation in a three-dimensional marine ecosystem model using the adjoint technique, J. Marine Syst., 74 (2008), 443-452.
43 X. Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2003.       

Go to top