Search Advanced

Mathematical Biosciences and Engineering

2004, Volume 1, Issue 2: 215-222. doi: 10.3934/mbe.2004.1.215
Previous Article Next Article

Stoichiometric Plant-Herbivore Models and Their Interpretation

  • 1.
    Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804
  • 2.
    Aquatic Microbiology, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam
  • 3.
    Department of Biology, Arizona State University, Tempe, AZ 85287-1501
  • Received: 01 May 2004 Accepted: 29 June 2018 Published: 01 July 2004

  • MSC : 92D25 and 34C60.

  • The purpose of this note is to mechanistically formulate a mathematically tractable model that specifically deals with the dynamics of plant-herbivore interaction in a closed phosphorous (P) limiting environment. The key to our approach is the employment of the plant cell P quota and the Droop equation for its growth. Our model takes the simple form of a system of two autonomous ordinary differential equations. It can be shown that our model includes the LKE model (Loladze, Kuang and Elser (2000)) as a special case. Our study reveals that the details of ecological stoichiometry models really matter for quantitative predictions of plant-herbivore dynamics, especially at intermediate ranges of the carrying capacity.

    Citation: Yang Kuang, Jef Huisman, James J. Elser. Stoichiometric Plant-Herbivore Models and Their Interpretation[J]. Mathematical Biosciences and Engineering, 2004, 1(2): 215-222. doi: 10.3934/mbe.2004.1.215

    Related Papers:

    [1] Guangyu Sui, Meng Fan, Irakli Loladze, Yang Kuang . The dynamics of a stoichiometric plant-herbivore model and its discrete analog. Mathematical Biosciences and Engineering, 2007, 4(1): 29-46. doi: 10.3934/mbe.2007.4.29
    [2] Md Nazmul Hassan, Angela Peace . Mechanistically derived Toxicant-mediated predator-prey model under Stoichiometric constraints. Mathematical Biosciences and Engineering, 2020, 17(1): 349-365. doi: 10.3934/mbe.2020019
    [3] Ming Chen, Menglin Gong, Jimin Zhang, Lale Asik . Comparison of dynamic behavior between continuous- and discrete-time models of intraguild predation. Mathematical Biosciences and Engineering, 2023, 20(7): 12750-12771. doi: 10.3934/mbe.2023569
    [4] Ilse Domínguez-Alemán, Itzel Domínguez-Alemán, Juan Carlos Hernández-Gómez, Francisco J. Ariza-Hernández . A predator-prey fractional model with disease in the prey species. Mathematical Biosciences and Engineering, 2024, 21(3): 3713-3741. doi: 10.3934/mbe.2024164
    [5] Md Nazmul Hassan, Kelsey Thompson, Gregory Mayer, Angela Peace . Effect of Excess Food Nutrient on Producer-Grazer Model under Stoichiometric and Toxicological Constraints. Mathematical Biosciences and Engineering, 2019, 16(1): 150-167. doi: 10.3934/mbe.2019008
    [6] P. Auger, N. H. Du, N. T. Hieu . Evolution of Lotka-Volterra predator-prey systems under telegraph noise. Mathematical Biosciences and Engineering, 2009, 6(4): 683-700. doi: 10.3934/mbe.2009.6.683
    [7] Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Amelia G. Nobile . A non-autonomous stochastic predator-prey model. Mathematical Biosciences and Engineering, 2014, 11(2): 167-188. doi: 10.3934/mbe.2014.11.167
    [8] Paulo Amorim, Bruno Telch, Luis M. Villada . A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing. Mathematical Biosciences and Engineering, 2019, 16(5): 5114-5145. doi: 10.3934/mbe.2019257
    [9] Ya Li, Z. Feng . Dynamics of a plant-herbivore model with toxin-induced functional response. Mathematical Biosciences and Engineering, 2010, 7(1): 149-169. doi: 10.3934/mbe.2010.7.149
    [10] Xinru Zhou, Xinmiao Rong, Meng Fan, Josué-Antonio Nescolarde-Selvaa . Stoichiometric modeling of aboveground-belowground interaction of herbaceous plant. Mathematical Biosciences and Engineering, 2019, 16(1): 25-55. doi: 10.3934/mbe.2019002
  • The purpose of this note is to mechanistically formulate a mathematically tractable model that specifically deals with the dynamics of plant-herbivore interaction in a closed phosphorous (P) limiting environment. The key to our approach is the employment of the plant cell P quota and the Droop equation for its growth. Our model takes the simple form of a system of two autonomous ordinary differential equations. It can be shown that our model includes the LKE model (Loladze, Kuang and Elser (2000)) as a special case. Our study reveals that the details of ecological stoichiometry models really matter for quantitative predictions of plant-herbivore dynamics, especially at intermediate ranges of the carrying capacity.


  • This article has been cited by:

    1. Harlan Stech, Bruce Peckham, John Pastor, Quasi-equilibrium reduction in a general class of stoichiometric producer–consumer models, 2012, 6, 1751-3758, 992, 10.1080/17513758.2012.713124
    2. Hao Wang, Hal L. Smith, Yang Kuang, James J. Elser, Dynamics of Stoichiometric Bacteria-Algae Interactions in the Epilimnion, 2007, 68, 0036-1399, 503, 10.1137/060665919
    3. Angela Peace, Effects of light, nutrients, and food chain length on trophic efficiencies in simple stoichiometric aquatic food chain models, 2015, 312, 03043800, 125, 10.1016/j.ecolmodel.2015.05.019
    4. Shengnan Zhao, Sanling Yuan, Hao Wang, Threshold behavior in a stochastic algal growth model with stoichiometric constraints and seasonal variation, 2020, 268, 00220396, 5113, 10.1016/j.jde.2019.11.004
    5. CONGBO XIE, MENG FAN, WEI ZHAO, DYNAMICS OF A DISCRETE STOICHIOMETRIC TWO PREDATORS ONE PREY MODEL, 2010, 18, 0218-3390, 649, 10.1142/S0218339010003457
    6. Lale Asik, Jackson Kulik, Kevin R. Long, Angela Peace, Seasonal Variation of Nutrient Loading in a Stoichiometric Producer–Consumer System, 2019, 81, 0092-8240, 2768, 10.1007/s11538-019-00629-6
    7. Sanling Yuan, Dongmei Wu, Guijie Lan, Hao Wang, Noise-Induced Transitions in a Nonsmooth Producer–Grazer Model with Stoichiometric Constraints, 2020, 82, 0092-8240, 10.1007/s11538-020-00733-y
    8. Andrew P. Allen, James F. Gillooly, Towards an integration of ecological stoichiometry and the metabolic theory of ecology to better understand nutrient cycling, 2009, 12, 1461023X, 369, 10.1111/j.1461-0248.2009.01302.x
    9. Hao Wang, Yang Kuang, Irakli Loladze, Dynamics of a mechanistically derived stoichiometric producer-grazer model, 2008, 2, 1751-3758, 286, 10.1080/17513750701769881
    10. Mehdi Cherif, Michel Loreau, Towards a more biologically realistic use of Droop's equations to model growth under multiple nutrient limitation, 2010, 119, 00301299, 897, 10.1111/j.1600-0706.2010.18397.x
    11. Xiong Li, Hao Wang, Yang Kuang, Global analysis of a stoichiometric producer–grazer model with Holling type functional responses, 2011, 63, 0303-6812, 901, 10.1007/s00285-010-0392-2
    12. Harlan Stech, Bruce Peckham, John Pastor, Enrichment in a general class of stoichiometric producer–consumer population growth models, 2012, 81, 00405809, 210, 10.1016/j.tpb.2012.01.003
    13. James J. Elser, Irakli Loladze, Angela L. Peace, Yang Kuang, Lotka re-loaded: Modeling trophic interactions under stoichiometric constraints, 2012, 245, 03043800, 3, 10.1016/j.ecolmodel.2012.02.006
    14. E. M. Elsayed, Qamar Din, Period-doubling and Neimark–Sacker bifurcations of plant–herbivore models, 2019, 2019, 1687-1847, 10.1186/s13662-019-2200-7
    15. Qamar Din, M. Sajjad Shabbir, M. Asif Khan, Khalil Ahmad, Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response, 2019, 13, 1751-3758, 481, 10.1080/17513758.2019.1638976
    16. Aaron Packer, Yantao Li, Tom Andersen, Qiang Hu, Yang Kuang, Milton Sommerfeld, Growth and neutral lipid synthesis in green microalgae: A mathematical model, 2011, 102, 09608524, 111, 10.1016/j.biortech.2010.06.029
    17. Hao Liu, Aaron Packer, Yang Kuang, Stoichiometric producer-grazer models with varying nitrogen pools and ammonia toxicity, 2014, 7, 1937-1179, 1305, 10.3934/dcdss.2014.7.1305
    18. A stoichiometrically derived algal growth model and its global analysis, 2010, 7, 1551-0018, 825, 10.3934/mbe.2010.7.825
    19. Ming Chen, Meng Fan, Yang Kuang, Global dynamics in a stoichiometric food chain model with two limiting nutrients, 2017, 289, 00255564, 9, 10.1016/j.mbs.2017.04.004
    20. Meng Fan, Irakli Loladze, Yang Kuang ∥, James J. Elser #, Dynamics of a stoichiometric discrete producer-grazer model, 2005, 11, 1023-6198, 347, 10.1080/10236190412331335427
    21. Jana Isanta‐Navarro, Clay Prater, Logan M. Peoples, Irakli Loladze, Tin Phan, Punidan D. Jeyasingh, Matthew J. Church, Yang Kuang, James J. Elser, Revisiting the growth rate hypothesis: Towards a holistic stoichiometric understanding of growth, 2022, 25, 1461-023X, 2324, 10.1111/ele.14096
    22. Juping Ji, Russell Milne, Hao Wang, Stoichiometry and environmental change drive dynamical complexity and unpredictable switches in an intraguild predation model, 2023, 86, 0303-6812, 10.1007/s00285-023-01866-z
    23. Ming Chen, Hao Wang, Menglin Gong, Discrete-time versus continuous-time toxic predation models, 2022, 28, 1023-6198, 244, 10.1080/10236198.2022.2038586
    24. Yequan Liang, Xiuxiang Liu, Xiao Yu, Threshold dynamics of a periodic stoichiometric model, 2023, 0, 1531-3492, 0, 10.3934/dcdsb.2023065
    25. Muhammad Sajjad Shabbir, Qamar Din, Manuel De la Sen, J. F. Gómez-Aguilar, Exploring dynamics of plant–herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response, 2024, 88, 0303-6812, 10.1007/s00285-023-02020-5
    26. Ling Xue, Sitong Chen, Xinmiao Rong, Dynamics of competition model between two plants based on stoichiometry, 2023, 20, 1551-0018, 18888, 10.3934/mbe.2023836
    27. Pingping Cong, Meng Fan, Xingfu Zou, Population dynamics of a stoichiometric aquatic tri-trophic level model with fear effect, 2024, 368, 00255564, 109130, 10.1016/j.mbs.2023.109130
    28. Muhammad Qurban, Abdul Khaliq, Kottakkaran Scooppy Nisar, Nehad Ali Shah, Dynamics and Control of a Plant-Herbivore Model Incorporating Allee's Effect, 2024, 24058440, e30754, 10.1016/j.heliyon.2024.e30754
  • Reader Comments
  • © 2004 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(3399) PDF downloads(571) Cited by(28)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog