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Thoughts on the Geometry of Meso-evolution: Collecting Mathematical Elements for a Postmodern Synthesis

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The Mathematics of Darwin’s Legacy

Part of the book series: Mathematics and Biosciences in Interaction ((MBI))

Abstract

Adaptive dynamics (AD) is a recently developed framework geared towards making the transition from micro-evolution to long-term evolution based on a time scale separation approximation. This assumption allows defining the fitness of a mutant as the rate constant of initial exponential growth of the mutant population in the environment created by the resident community dynamics. This definition makes that all resident types have fitness zero. If in addition it is assumed that mutational steps are small, evolution can be visualized as an uphill walk in a fitness landscape that keeps changing as a result of the evolution it engenders. The chapter summarises the main tools for analysing special eco-evolutionary models based on these simplifications. In addition it describes a number of general predictions that directly derive from the AD perspective a such, without making any further assumptions.

Mathematics Subject Classification (2000). 92D15.

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Authors and Affiliations

  1. Institute of Biology and Mathematical Institute, Leiden, Netherlands

    J. A. J. Hans Metz

  2. Evolution and Ecology Program, IIASA, Laxenburg, Austria

    J. A. J. Hans Metz

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Correspondence to J. A. J. Hans Metz .

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  1. , Departamento de Matemática, Universidade Nova de Lisboa, Quinta da Torre, Caparica, 2829-516, Portugal

    Fabio A. C. C. Chalub

  2. CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto 2, Lisboa, 1649-003, Portugal

    José Francisco Rodrigues

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Metz, J.A.J.H. (2011). Thoughts on the Geometry of Meso-evolution: Collecting Mathematical Elements for a Postmodern Synthesis. In: Chalub, F., Rodrigues, J. (eds) The Mathematics of Darwin’s Legacy. Mathematics and Biosciences in Interaction. Springer, Basel. https://doi.org/10.1007/978-3-0348-0122-5_11

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