The Origin of Species by Means of Mathematical Modelling
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The Origin of Species by Means of Mathematical Modelling Nikolai Bessonov1 · Natalia Reinberg2 · Malay Banerjee3 · Vitaly Volpert4,5,6,7
Received: 23 October 2017 / Accepted: 25 April 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018
Abstract 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. Keywords Nonlocal reaction-diffusion equations · Travelling waves · Pulses · Darwin’s diagram Electronic supplementary material The online version of this article (https://doi.org/10.1007/ s10441-018-9328-9) contains supplementary material, which is available to authorized users. * Vitaly Volpert [email protected]‑lyon1.fr 1
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russian Federation 199178
2
Oakland University, Rochester, MI 48309, USA
3
Department of Mathematics and Statistics, IIT Kanpur, Kanpur, India
4
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
5
INRIA, Universite de Lyon, Universite Lyon 1, Institut Camille Jordan, 43 Bd. du 11 Novembre 1918, 69200 Villeurbanne Cedex, France
6
Peoples Friendship University of Russia (RUDN University), 6 Miklukho‑Maklaya St, Moscow, Russian Federation 117198
7
Poncelet Center, UMI 2615 CNRS, 11 Bolshoy Vlasyevskiy, Moscow, Russian Federation 119002
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N. Bessonov et al.
1 Evolution of Species and Darwin’s Diagram Emergence and evolution of biological species continue to attract attention from both the biological point of view and from the modelling point of view. Modern theory distinguishes three main mechanisms of speciation. Allopatric speciation implies the existence of geographic or genetic isolation where there is no gene exchange between different taxa; parapatric speciation admits partial exchange; and sympatric speciation occurs without geographic or genetic barriers (Coyne and Orr 2004; Gavrilets 2004). It is generally accepted that allopatric speciation is biologically realistic, though the mechanism which leads to the appearance of isolating barriers may sometimes be unclear [Coyne and Orr 2004 (Chapter 2)]. Sympatric speciation continues to instigate intensive discussions. In spite of the big body of experimental data, observations in nature, and theoretical models, this question remains controversial [(Coyne and Orr 2004 (Chapt
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