| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 3, 2014
Biological evolution
|
|
|---|---|---|
| Page(s) | 5 - 25 | |
| DOI | https://doi.org/10.1051/mmnp/20149302 | |
| Published online | 28 May 2014 | |
Mathematics of Darwin’s Diagram
1 Institute of Problems of Mechanical
Engineering, Russian Academy of Sciences 199178
Saint Petersburg,
Russia
2 Institut Camille Jordan, UMR 5208
CNRS, University Lyon 1, 69622
Villeurbanne,
France
⋆
Corresponding author. E-mail: volpert@math.univ-lyon1.fr
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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