967
Views
3
CrossRef citations to date
0
Altmetric
Research Article

Contrasting stoichiometric dynamics in terrestrial and aquatic grazer–producer systems

&
Pages S3-S34 | Received 05 Feb 2020, Accepted 06 May 2020, Published online: 27 May 2020

References

  • L. Asik and A. Peace, Dynamics of a producer-grazer model incorporating the effects of phosphorus loading on grazer's growth, Bull. Math. Biol. 81(5) (2019), pp. 1352–1368. doi: 10.1007/s11538-018-00567-9
  • N. Chitnis, J.M. Hyman, and J.M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol. 70(5) (2008), pp. 1272–1296. doi: 10.1007/s11538-008-9299-0
  • A. Dhooge, W. Govaerts, Y.A. Kuznetsov, H.G.E. Meijer, and B Sautois, New features of the software MatCont for bifurcation analysis of dynamical systems, Math. Computer Model. Dyn. Syst. 14(2) (2008), pp. 147–175. doi: 10.1080/13873950701742754
  • L. Edelstein-Keshet, Mathematical Models in Biology, Soc. Indust. and Appl. Math., Philadelphia, 2005.
  • J.J. Elser and Y. Kuang, Ecological stoichiometry, Encyclopedia Theor. Ecol. 84 (2002), pp. 718–722. Doi:10.1016/B978-008045405-4.00309-8
  • D.A. Herms and W.J. Mattson, The dilemma of plants: to grow or defend, Quarterly Rev. Biol. 67(3) (1992), pp. 283–335. doi: 10.1086/417659
  • W. Leong and J.R. Pawlik, Evidence of a resource trade-off between growth and chemical defenses among Caribbean coral reef sponges, Marine Ecol. Progress Ser. 406 (2010), pp. 71–78. doi: 10.3354/meps08541
  • X. Li, H. Wang, and Y. Kuang, Global analysis of a stoichiometric producer-grazer model with holling type functional responses, J. Math. Biol. 63(5) (2011), pp. 901–932. doi: 10.1007/s00285-010-0392-2
  • I. Loladze, Y. Kuang, and J.J. Elser, Stoichiometry in producer-grazer systems: linking energy flow with element cycling, Bull. Math. Biol. 62(6) (2000), pp. 1137–1162. doi: 10.1006/bulm.2000.0201
  • A. Peace and H. Wang, Compensatory foraging in stoichiometric producer-grazer models, Bull. Math. Biol. 81(12) (2019), pp. 4932–4950. doi: 10.1007/s11538-019-00665-2
  • A. Peace, H. Wang, and Y. Kuang, Dynamics of a producer-grazer model incorporating the effects of excess food nutrient content on grazer's growth, Bull. Math. Biol. 76(9) (2014), pp. 2175–2197. doi: 10.1007/s11538-014-0006-z
  • A. Peace, Y. Zhao, I. Loladze, J.J. Elser, and Y. Kuang, A stoichiometric producer-grazer model incorporating the effects of excess food-nutrient content on consumer dynamics, Math. Biosciences 244(2) (2013), pp. 107–115. doi: 10.1016/j.mbs.2013.04.011
  • R.A.P. Pellew, The impacts of elephant, giraffe and fire upon the Acacia tortilis woodlands of the Serengeti, African J. Ecol. 21(1) (1983), pp. 41–74. doi: 10.1111/j.1365-2028.1983.tb00311.x
  • R.A. Pellew, Food consumption and energy budgets of the giraffe. J. Appl. Ecol. 21(1) (1984), pp. 141–159. doi: 10.2307/2403043
  • J.B. Shurin, D.S. Gruner, and H. Hillebrand, All wet or dried up? Real differences between aquatic and terrestrial food webs, Proc. Royal Soc. B: Biol. Sci. 273(1582) (2005), pp. 1–9. doi: 10.1098/rspb.2005.3377
  • R.W. Sterner, J.J. Elser, Ecological Stoichiometry: the Biology of Elements From Molecules to the Biosphere, Princeton University Press, Princeton, 2002.
  • H. Wang, K. Dunning, J.J. Elser, and Y. Kuang, Daphnia species invasion, competitive exclusion, and chaotic coexistence, DCDS-B 12 (2009), pp. 481–493. doi: 10.3934/dcdsb.2009.12.481
  • H. Wang, Y. Kuang, and I. Loladze, Dynamics of a mechanistically derived stoichiometric producer-grazer model, J. Biological Dyn. 2(3) (2008), pp. 286–296. doi: 10.1080/17513750701769881
  • H. Wang, Z. Lu, and A. Raghavan, Weak dynamical threshold for the ‘strict homeostasis’ assumption in ecological stoichiometry, Ecol. Model. 384 (2018), pp. 233–240. doi: 10.1016/j.ecolmodel.2018.06.027
  • H. Wang, R.W. Sterner, and J.J. Elser, On the ‘strict homeostasis’ assumption in ecological stoichiometry, Ecological Modelling 243 (2012), pp. 81–88. doi: 10.1016/j.ecolmodel.2012.06.003
  • T. Xie, X. Yang, X. Li, and H. Wang, Complete global and bifurcation analysis of a stoichiometric predator-prey model, J. Dyn. Differ. Equ. 30(2) (2018), pp. 447–472. doi: 10.1007/s10884-016-9551-5
  • X. Yang, X. Li, H. Wang, and Y. Kuang, Stability and bifurcation in a stoichiometric producer-grazer model with knife edge, SIAM J. Applied Dyn. Sys. 15(4) (2016), pp. 2051–2077. doi: 10.1137/15M1023610