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Mathematics of Darwin’s Diagram

Published online by Cambridge University Press:  28 May 2014

N. Bessonov ,
N. Reinberg  and
V. Volpert
N. Bessonov
Affiliation:
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences 199178 Saint Petersburg, Russia
N. Reinberg
Affiliation:
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences 199178 Saint Petersburg, Russia
V. Volpert*
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
*
⋆ Corresponding author. E-mail: volpert@math.univ-lyon1.fr
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Abstract

Darwin illustrated his theory about emergence and evolution of biological species with a diagram. It shows how species exist, evolve, appear and disappear. The goal of this work is to give a mathematical interpretation of this diagram and to show how it can be reproduced in mathematical models. It appears that conventional models in population dynamics are not sufficient, and we introduce a number of new models which take into account local, nonlocal and global consumption of resources, and models with space and time dependent coefficients.

Keywords

speciationevolutionnonlocal reaction-diffusion equations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 3: Biological evolution , 2014 , pp. 5 - 25
Copyright
© EDP Sciences, 2014

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