Acta Biotheoretica

, Volume 66, Issue 4, pp 333–344 | Cite as

The Origin of Species by Means of Mathematical Modelling

  • Nikolai Bessonov
  • Natalia Reinberg
  • Malay Banerjee
  • Vitaly VolpertEmail author
Regular Article


Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in Darwin’s diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin’s definition of species, stated above, and Mayr’s definition of species (group of individuals that can reproduce) is also discussed.


Nonlocal reaction-diffusion equations Travelling waves Pulses Darwin’s diagram 



The authors are grateful to R. Penner for his help in the preparation of the manuscript. N. Bessonov was supported by Russian Foundation of Basic Research grant 16-01-00068, 2016-2018. V. Volpert was supported by the “RUDN University Program 5-100”.

Supplementary material

10441_2018_9328_MOESM1_ESM.pdf (70 kb)
Supplementary material 1 (pdf 70 KB)


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Nikolai Bessonov
    • 1
  • Natalia Reinberg
    • 2
  • Malay Banerjee
    • 3
  • Vitaly Volpert
    • 4
    • 5
    • 6
    • 7
    Email author
  1. 1.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSaint PetersburgRussian Federation
  2. 2.Oakland UniversityRochesterUSA
  3. 3.Department of Mathematics and StatisticsIIT KanpurKanpurIndia
  4. 4.Institut Camille JordanUMR 5208 CNRS, University Lyon 1VilleurbanneFrance
  5. 5.INRIA, Universite de Lyon, Universite Lyon 1Institut Camille JordanVilleurbanne CedexFrance
  6. 6.Peoples Friendship University of Russia (RUDN University)MoscowRussian Federation
  7. 7.Poncelet CenterUMI 2615 CNRSMoscowRussian Federation

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