Mathematical Biosciences and Engineering (MBE)

Effects of nutrient enrichment on coevolution of a stoichiometric producer-grazer system
Pages: 841 - 875, Issue 4, August 2014

doi:10.3934/mbe.2014.11.841      Abstract        References        Full text (1785.1K)           Related Articles

Lina Hao - 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)
Xin Wang - School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, China (email)

1 P. A. Abrams and J. D. Roth, The effects of enrichment of three-species food chains with nonlinear functional response, Ecology, 75 (1994), 1118-1130.
2 A. N. Mizuno and M. Kawata, The effects of the evolution of stoichiometry-related traits on population dynamics in plankton communities, J. Theor. Biol., 259 (2009), 209-218.       
3 D. M. Anderson, P. M. Glibert and J. M. Burkholder, Harmful algal blooms and eutrophication: Nutrient sources, composition, and consequences, Estuaties, 25 (2002), 704-726.
4 A. Binzer, C. Guill, U. Brose and B. C. Rall, The dynamics of food chains under climate change and nutrient enrichment, Phil. Trans. R. Soc. B, 367 (2012), 2935-2944.
5 P. Branco, M. Stomp, M. Egas and J. Huisman, Evolution of nutrient uptake reveals a trade-off in the ecological stoichiometry of plant-herbivore interactions, Am. Nat., 176 (2010), 162-176.
6 S. Chisholm, Phytoplankton size, In Primary Productivity and Biogeochemical Cycles in the Sea, 43 (1992), 213-237.
7 M. Cortez and S. P. Ellner, Understanding rapid evolution in predator-prey interactions using the theory of fast-slow dynamical systems, Am. Nat., 176 (2010), E109-E127.
8 J. M. Davis, A. D. Rosemond, S. L. Eggert, W. F. Cross and J. B. Wallace, Long-term nutrient enrichment decouples predator and prey production, Proc. Natl. Acad. Sci. USA, 107 (2010), 121-126.
9 U. Dieckmann and R. Law, The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol., 34 (1996), 579-612.       
10 U. Dieckmann, P. Marrow and R. Law, Evolutionary cycling in predator-prey interactions: Population dynamics and the red queen, J. Theor. Biol., 176 (1995), 91-102.
11 S. Diehl, Paradoxes of enrichment: Effects of increased light versus nutrient supply on pelagic producer-grazer system, Am. Nat., 169 (2007), 173-191.
12 S. Diehl and M. Feißel, Effects of enrichment on three-level food chainswith omnivory, Am. Nat., 155 (2000), 200-218.
13 M. Doebeli and U. Dieckmann, Evolutionary branching and sympatric speciation caused by different types of ecological interactions, Am. Nat., 156 (2000), S77-S101.
14 M. R. Droop, Vitamin $b_{12}$ and marine ecology. iv. the kinetics of uptake, growth and inhibition in monochrysis lutheri, J. Mar. Biol. Assoc. UK, 48 (1968), 689-733.
15 T. H. G. Ezard, S. D. Côté and F. Pelletier, Eco-evolutionary dynamics: Disentangling phenotypic, environmental and population fluctuations, Phil. Trans. R. Soc. B, 364 (2009), 1491-1498.
16 Z. V. Finkel, M. E. Katz, J. D. Wright, O. M. E Schofield and P. G. Falkowski, Climatically driven macroevolutionary patterns in the size of marine diatoms over the cenozoic, Proc. Natl. Acad. Sci. USA, 102 (2005), 8927-8932.
17 Z. V. Finkel, J. Beardall, K. J. Flynn, A. Quigg, T. A. Rees and J. Raven, Phytoplankton in a changing world: Cell size and elemental stoichiometry, J. Plankton. Res., 32 (2010), 119-137.
18 G. F. Fussmann, S. P. Ellner and N. G. Hairston, Evolution as a critical component of plankton dynamics, Proc. R. Soc. Lond. B, 270 (2003), 1015-1022.
19 G. F. Fussmann, M. Loreau and P. A. Abrams, Eco-evolutionary dynamics of communities and ecosystems, Funct. Ecol., 21 (2007), 465-477.
20 S. A. H. Geritz and M. Gyllenberg, Seven answers from adaptive dynamics, J. EVOL. BIOL., 18 (2005), 1174-1177.
21 S. A. H. Geritz, E. Kisdi, G. Meszéna and J. A. J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evol. Ecol., 12 (1998), 35-57.
22 L. Jiang, O. M. E. Schofield and P. G. Falkowski, Adaptive evolution of phytoplankton cell size, Am. Nat., 166 (2005), 496-505.
23 M. D. John, A. D. Rosemond, S. L. Eggert, W. F. Cross and J. B. Wallace, Nutrient enrichment differentially affects body sizes of primary consumers and predators in a detritus-based stream, Limnol. Oceanogr., 55 (2010), 2305-2316.
24 L. E. Jones, L. Becks, S. P. Ellner, N. G. Hairston, T. Yoshida and G. F. Fussmann, Rapid contemporary evolution and clonal food web dynamics, Phil. Trans. R. Soc. B, 364 (2009), 1579-1591.
25 E. Kisdi, Evolutionary branching under asymmetric competition, J. Theor. Biol., 197 (1999), 149-162.
26 C. A. Klausmeier, E. Litchman and S. A. Levin, A model of flexible uptake of two essential resources, J. Theor. Biol., 246 (2007), 278-289.       
27 X. Li, H. Wang and Y. Kuang, Global analysis of a stoichiometric producer-grazer model with Holling type functional responses, J. Math. Biol., 63 (2011), 901-932.       
28 N. Loeuille and M. Loreau, Nutrient enrichment and food chains: Can evolution buffer top-down control? Theor. Popul. Biol., 65 (2004), 285-298.
29 N. Loeuille and M. Loreau, Evolutionary emergence of size-structured food webs, Proc. Natl. Acad. Sci. USA, 102 (2005), 5761-5766.
30 N. Loeuille, M. Loreau and R. Ferrière, Consequences of plant-herbivore coevolution on the dynamics and functioning of ecosystems, J. Theor. Biol., 217 (2002), 369-381.       
31 I. Loladze, Y. Kuang and J. J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow and element cycling, Bull. Math. Biol., 62 (2000), 1137-1162.
32 M. Loreau, Ecosystem development explained by competition within and between material cycles, Proc. R. Soc. Lond. B, 265 (1998), 33-38.
33 A. Mougi and Y. Iwasa, Evolution towards oscillation or stability in a predator-prey system, Proc. R. Soc. B, 277 (2010), 3163-3171.
34 A. Mougi and Y. Iwasa, Unique coevolutionary dynamics in a predator-prey system, J. Theor. Biol., 277 (2011), 83-89.       
35 E. B. Muller, R. M. Nisbet, S. A. L. M Kooijman, J. J. Elser and E. McCauley, Stoichiometric food quality and herbivore dynamics, Ecol. Lett., 4 (2001), 519-529.
36 D. Pimentel, Animal population regulation by the genetic feed-back mechanism, Am. Nat., 95 (1961), 65-79.
37 J. A. Raven, Physiological consequences of extremely small size for autotrophic organisms on the sea, Can. Bull. Fish. Aquat. Sci., 214 (1986), 1-70.
38 J. A. Raven, Why are there no picoplanktonic $o_2$ evolvers with volumes less than $10^{-19} m^3$? J. Plankton. Res., 16 (1994), 565-580.
39 M. L. Rosenzweig, Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time, Science, 171 (1971), 385-387.
40 R. W. Sterner and J. J. Elser, Ecological Stoichiometry: The Biology of Elements from Molecules to the Biosphere, NJ: Princeton University Press, Princeton, 2002.
41 D. Stiefs, G. A. K. Van Voorn, B. W. Kooi, U. Feudel and T. Gross, Food quality in producer-grazer models-: A generalized analysis, Am. Nat., 176 (2010), 367-380.
42 A. Verdy, M. Follows and G. Flierl, Optimal phytoplankton cell size in an allometric model, Mar. Ecol. Prog. Ser., 379 (2009), 1-12.
43 H. Wang, H. L. Smith, Y. Kuang and J. J. Elser, Dynamics of stoichiometric bacteria-algae interaction in epilimnion, SIAM J. Appl. Math., 68 (2007), 503-522.       
44 D. Waxman and S. Gavrilets, 20 questions on adaptive dynamics, J. Evol. Biol., 18 (2005), 1139-1154.
45 T. G. Whitham, J. K. Bailey and J. A. Schweitzer et al, A framework for community and ecosystem genetics: From genes to ecosystems, Nature Reviews Genetics, 7 (2006), 510-523.
46 S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990.       
47 T. Yoshida, L. E. Jones, S. P. Ellner, G. F. Fussmann and Jr N. G. Hairston, Rapid evolution drives ecological dynamics in a predator-prey system, Nature, 424 (2003), 303-306.
48 J. Zu, M. Mimura and J. Y. Wakano, The evolution of phenotypic traits in a predator-prey system subject to Allee effect, J. Theor. Biol., 262 (2010), 528-543.       

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