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Using G -Functions to Investigate the Evolutionary Stability of Bacterial Quorum Sensing

Author

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  • Anne Mund

    (Zentrum Mathematik, Technische Universität München Boltzmannstr. 3, 85748 Garching, Germany)

  • Christina Kuttler

    (Zentrum Mathematik, Technische Universität München Boltzmannstr. 3, 85748 Garching, Germany)

  • Judith Pérez-Velázquez

    (Zentrum Mathematik, Technische Universität München Boltzmannstr. 3, 85748 Garching, Germany)

Abstract

In ecology, G -functions can be employed to define a growth function G for a population b , which can then be universally applied to all individuals or groups b i within this population. We can further define a strategy v i for every group b i . Examples for strategies include diverse behaviour such as number of offspring, habitat choice, and time of nesting for birds. In this work, we employ G -functions to investigate the evolutionary stability of the bacterial cooperation process known as quorum sensing. We employ the G -function ansatz to model both the population dynamics and the resulting evolutionary pressure in order to find evolutionary stable states. This results in a semi-linear parabolic system of equations, where cost and benefit are taken into account separately. Depending on different biological assumptions, we analyse a variety of typical model functions. These translate into different long-term scenarios for different functional responses, ranging from single-strategy states to coexistence. As a special feature, we distinguish between the production of public goods, available for all subpopulations, and private goods, from which only the producers can benefit.

Suggested Citation

  • Anne Mund & Christina Kuttler & Judith Pérez-Velázquez, 2019. "Using G -Functions to Investigate the Evolutionary Stability of Bacterial Quorum Sensing," Mathematics, MDPI, vol. 7(11), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1112-:d:287494
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    References listed on IDEAS

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    1. Stephen P. Diggle & Ashleigh S. Griffin & Genevieve S. Campbell & Stuart A. West, 2007. "Cooperation and conflict in quorum-sensing bacterial populations," Nature, Nature, vol. 450(7168), pages 411-414, November.
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