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

Anne Mund, Christina Kuttler and Judith Pérez-Velázquez
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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

Mathematics, 2019, vol. 7, issue 11, 1-17

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.

Keywords: Evolutionary dynamics; G-function; Quorum Sensing; Public Goods; semi-linear parabolic system of equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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