IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v438y2015icp17-25.html
   My bibliography  Save this article

Discreteness induced extinction

Author

Listed:
  • dos Santos, Renato Vieira
  • da Silva, Linaena Méricy

Abstract

Two simple models based on ecological problems are discussed from the point of view of non-equilibrium statistical mechanics. It is shown how discrepant may be the results of the models that include spatial distribution with discrete interactions when compared with the continuous analogous models. In the continuous case we have, under certain circumstances, the population explosion. When we take into account the finiteness of the population, we get the opposite result, extinction. We will analyze how these results depend on the dimension d of the space and describe the phenomenon of the “Discreteness Inducing Extinction” (DIE). The results are interpreted in the context of the “paradox of sex”, an old problem of evolutionary biology.

Suggested Citation

  • dos Santos, Renato Vieira & da Silva, Linaena Méricy, 2015. "Discreteness induced extinction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 17-25.
    • Handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:17-25
    DOI: 10.1016/j.physa.2015.06.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115005646
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.06.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Y. Louzoun & N. M. Shnerb & S. Solomon, 2007. "Microscopic noise, adaptation and survival in hostile environments," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(2), pages 141-148, March.
    2. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    3. Lutz Becks & Aneil F. Agrawal, 2010. "Higher rates of sex evolve in spatially heterogeneous environments," Nature, Nature, vol. 468(7320), pages 89-92, November.
    4. Challet, Damien & Solomon, Sorin & Yaari, Gur, 2009. "The universal shape of economic recession and recovery after a shock," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-24.
    5. G. Yaari & A. Nowak & K. Rakocy & S. Solomon, 2008. "Microscopic study reveals the singular origins of growth," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(4), pages 505-513, April.
    6. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
    7. Messinger, Susanna M. & Ostling, Annette, 2013. "Predator attack rate evolution in space: The role of ecology mediated by complex emergent spatial structure and self-shading," Theoretical Population Biology, Elsevier, vol. 89(C), pages 55-63.
    8. Nick Colegrave, 2002. "Sex releases the speed limit on evolution," Nature, Nature, vol. 420(6916), pages 664-666, December.
    9. Slanina, Frantisek, 2013. "Essentials of Econophysics Modelling," OUP Catalogue, Oxford University Press, number 9780199299683.
    10. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    11. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    12. Lise Cats Myhre & Elisabet Forsgren & Trond Amundsen, 2013. "Effects of habitat complexity on mating behavior and mating success in a marine fish," Behavioral Ecology, International Society for Behavioral Ecology, vol. 24(2), pages 553-563.
    13. Johan Paulsson, 2004. "Summing up the noise in gene networks," Nature, Nature, vol. 427(6973), pages 415-418, January.
    14. van Wijland, F. & Oerding, K. & Hilhorst, H.J., 1998. "Wilson renormalization of a reaction–diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(1), pages 179-201.
    15. Gur Yaari & Andrzej Nowak & Kamil Rakocy & Sorin Solomon, 2008. "Microscopic Study Reveals the Singular Origins of Growth," Papers 0803.2201, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sorin Solomon & Nataša Golo, 2015. "Microeconomic structure determines macroeconomic dynamics: Aoki defeats the representative agent," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 5-30, April.
    2. G. Yaari & D. Stauffer & S. Solomon, 2008. "Intermittency and Localization," Papers 0802.3541, arXiv.org, revised Mar 2008.
    3. Nikolaos Th. Chatzarakis, 2021. "Revisiting the role and consequences of Econophysics from a Marxian perspective," Bulletin of Political Economy, Bulletin of Political Economy, vol. 15(1), pages 45-68, June.
    4. V'it Perv{z}ina & Jan M. Swart, 2016. "How much market making does a market need?," Papers 1612.00981, arXiv.org, revised Jun 2018.
    5. Upadhyay, Shashankaditya & Banerjee, Anirban & Panigrahi, Prasanta K., 2020. "Causal evolution of global crisis in financial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    6. Di Xiao & Jun Wang & Hongli Niu, 2016. "Volatility Analysis of Financial Agent-Based Market Dynamics from Stochastic Contact System," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 607-625, December.
    7. Hirdesh K. Pharasi & Kiran Sharma & Anirban Chakraborti & Thomas H. Seligman, 2018. "Complex market dynamics in the light of random matrix theory," Papers 1809.07100, arXiv.org, revised Sep 2018.
    8. Anirban Chakraborti & Hrishidev & Kiran Sharma & Hirdesh K. Pharasi, 2019. "Phase separation and scaling in correlation structures of financial markets," Papers 1910.06242, arXiv.org, revised Jul 2020.
    9. Kiran Sharma & Subhradeep Das & Anirban Chakraborti, 2017. "Global Income Inequality and Savings: A Data Science Perspective," Papers 1801.00253, arXiv.org, revised Aug 2018.
    10. A. Lykov & S. Muzychka & K. Vaninsky, 2012. "Investor's sentiment in multi-agent model of the continuous double auction," Papers 1208.3083, arXiv.org, revised Feb 2016.
    11. A. O. Glekin & A. Lykov & K. L. Vaninsky, 2014. "On Simulation of Various Effects in Consolidated Order Book," Papers 1402.4150, arXiv.org.
    12. Hong Guo & Jianwu Lin & Fanlin Huang, 2023. "Market Making with Deep Reinforcement Learning from Limit Order Books," Papers 2305.15821, arXiv.org.
    13. Zhu, Lirong & Chen, Jiawei & Di, Zengru & Chen, Liujun & Liu, Yan & Stanley, H. Eugene, 2017. "The mechanisms of labor division from the perspective of individual optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 488(C), pages 112-120.
    14. Moura, N.J. & Ribeiro, Marcelo B., 2013. "Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2088-2103.
    15. Florin Turcaș & Florin Cornel Dumiter & Marius Boiță, 2022. "Econophysics Techniques and Their Applications on the Stock Market," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    16. Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2019. "A Statistical Field Approach to Capital Accumulation," Working Papers hal-02280634, HAL.
    17. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    18. Solomon Sorin & Golo Natasa, 2013. "Minsky Financial Instability, Interscale Feedback, Percolation and Marshall–Walras Disequilibrium," Accounting, Economics, and Law: A Convivium, De Gruyter, vol. 3(3), pages 167-260, October.
    19. Zhang, Jiu & Jin, Li-Fu & Zheng, Bo & Li, Yan & Jiang, Xiong-Fei, 2022. "Simplified calculations of time correlation functions in non-stationary complex financial systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    20. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    21. T. T. Chen & B. Zheng & Y. Li & X. F. Jiang, 2017. "New approaches in agent-based modeling of complex financial systems," Papers 1703.06840, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:17-25. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.