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Modelling Ecological Systems from a Niche Theory to Lotka-Volterra Equations

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Current Trends in Dynamical Systems in Biology and Natural Sciences

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 21))

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Abstract

This paper is an attempt to analyze the notion of ecological niche as a community of different species and of ecosystem as a set of niches in order to formulate a dynamical model for an ecosystem. Our assumption is that the concept of fitness landscape allows to model the phenotype dynamics of an ensemble of species as a stochastic process. To take into account the interaction structure of different communities in the niches and the environment we introduce an ecological fitness potential to formulate a Lotka-Volterra system which describes the evolution of a mutual ecosystem in presence of finite resources. To explicitly consider the effect of fluctuations in the numerousness of the species, we associate a master equation to the average Lotka-Volterra system and we study the conditions of existence of a detailed balance equilibrium (i.e. a thermodynamic equilibrium) for the ecosystem. The explicit solution for the equilibrium probability distribution is a multinomial negative distribution and we discuss the relation between the detailed balance condition and relative species abundance distribution in the framework of Hubbell’s neutral theory. Moreover the theoretical distribution implies the existence of a correlation among the relative species distribution associated to the different communities. We use numerical simulations to illustrate the results on simple models.

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Author information

Authors and Affiliations

  1. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Paolo Freguglia

  2. Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Italy

    Eleonora Andreotti

  3. Department of Physics and Astronomy, University of Bologna, Bologna, Italy

    Armando Bazzani

  4. INFN Bologna, Bologna, Italy

    Armando Bazzani

Authors
  1. Paolo Freguglia
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  2. Eleonora Andreotti
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  3. Armando Bazzani
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Maira Aguiar

  2. Department of Mathematics, University of Évora, Évora, Portugal

    Carlos Braumann

  3. Faculty of Science, VU University Amsterdam, Amsterdam, The Netherlands

    Bob W. Kooi

  4. Department of Mathematics, University of Trento, Trento, Italy

    Andrea Pugliese

  5. Department of Mathematics “CMAF-CIO”, University of Lisbon, Lisbon, Portugal

    Nico Stollenwerk

  6. Department of Mathematics “Giuseppe Peano”, University of Turin, Torino, Italy

    Ezio Venturino

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Freguglia, P., Andreotti, E., Bazzani, A. (2020). Modelling Ecological Systems from a Niche Theory to Lotka-Volterra Equations. In: Aguiar, M., Braumann, C., Kooi, B., Pugliese, A., Stollenwerk, N., Venturino, E. (eds) Current Trends in Dynamical Systems in Biology and Natural Sciences. SEMA SIMAI Springer Series, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-41120-6_1

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