Math. Model. Nat. Phenom.
Volume 9, Number 3, 2014Biological evolution
|Page(s)||5 - 25|
|Published online||28 May 2014|
Mathematics of Darwin’s Diagram
1 Institute of Problems of Mechanical
Engineering, Russian Academy of Sciences 199178
2 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 92D15 / 35K57
Key words: speciation / evolution / nonlocal reaction-diffusion equations
© EDP Sciences, 2014
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