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Towards a Mathematical Description of Biodiversity Evolution

Author

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  • Jorge E. Horvath

    (AstroLab Laboratory, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226 Cidade Universitária, São Paulo, SP 05579, Brazil)

Abstract

We outline in this work a mathematical description of biodiversity evolution based on a second-order differential equation (also known as the “inertial/Galilean view”). After discussing the motivations and explicit forms of the simplest “forces”, we are lead to an equation analogue to a harmonic oscillator. The known solutions for the homogeneous problem are then tentatively related to the biodiversity curves of Sepkoski and Alroy et al. , suggesting mostly an inertial behavior of the time evolution of the number of genera and a quadratic behavior in some long-term evolution after extinction events. We present the Green function for the dynamical system and apply it to the description of the recovery curve after the Permo-Triassic extinction, as recently analyzed by Burgess, Bowring and Shen. Even though the agreement is not satisfactory, we point out direct connections between observed drop times after massive extinctions and mathematical constants and discuss why the failure ensues, suggesting a more complex form of the second-order mathematical description.

Suggested Citation

  • Jorge E. Horvath, 2014. "Towards a Mathematical Description of Biodiversity Evolution," Challenges, MDPI, vol. 5(2), pages 1-10, September.
    • Handle: RePEc:gam:jchals:v:5:y:2014:i:2:p:324-333:d:40548
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    References listed on IDEAS

    as
    1. Samir Okasha, 2010. "Does diversity always grow?," Nature, Nature, vol. 466(7304), pages 318-318, July.
    2. Robert A. Rohde & Richard A. Muller, 2005. "Cycles in fossil diversity," Nature, Nature, vol. 434(7030), pages 208-210, March.
    3. James W. Kirchner & Anne Weil, 2000. "Delayed biological recovery from extinctions throughout the fossil record," Nature, Nature, vol. 404(6774), pages 177-180, March.
    Full references (including those not matched with items on IDEAS)

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